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| |
| <h1 class="title"><a href="mllib-guide.html">MLlib</a> - Data Types</h1> |
| |
| |
| <ul id="markdown-toc"> |
| <li><a href="#local-vector" id="markdown-toc-local-vector">Local vector</a></li> |
| <li><a href="#labeled-point" id="markdown-toc-labeled-point">Labeled point</a></li> |
| <li><a href="#local-matrix" id="markdown-toc-local-matrix">Local matrix</a></li> |
| <li><a href="#distributed-matrix" id="markdown-toc-distributed-matrix">Distributed matrix</a> <ul> |
| <li><a href="#rowmatrix" id="markdown-toc-rowmatrix">RowMatrix</a></li> |
| <li><a href="#indexedrowmatrix" id="markdown-toc-indexedrowmatrix">IndexedRowMatrix</a></li> |
| <li><a href="#coordinatematrix" id="markdown-toc-coordinatematrix">CoordinateMatrix</a></li> |
| <li><a href="#blockmatrix" id="markdown-toc-blockmatrix">BlockMatrix</a></li> |
| </ul> |
| </li> |
| </ul> |
| |
| <p>MLlib supports local vectors and matrices stored on a single machine, |
| as well as distributed matrices backed by one or more RDDs. |
| Local vectors and local matrices are simple data models |
| that serve as public interfaces. The underlying linear algebra operations are provided by |
| <a href="http://www.scalanlp.org/">Breeze</a> and <a href="http://jblas.org/">jblas</a>. |
| A training example used in supervised learning is called a “labeled point” in MLlib.</p> |
| |
| <h2 id="local-vector">Local vector</h2> |
| |
| <p>A local vector has integer-typed and 0-based indices and double-typed values, stored on a single |
| machine. MLlib supports two types of local vectors: dense and sparse. A dense vector is backed by |
| a double array representing its entry values, while a sparse vector is backed by two parallel |
| arrays: indices and values. For example, a vector <code>(1.0, 0.0, 3.0)</code> can be represented in dense |
| format as <code>[1.0, 0.0, 3.0]</code> or in sparse format as <code>(3, [0, 2], [1.0, 3.0])</code>, where <code>3</code> is the size |
| of the vector.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p>The base class of local vectors is |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vector"><code>Vector</code></a>, and we provide two |
| implementations: <a href="api/scala/index.html#org.apache.spark.mllib.linalg.DenseVector"><code>DenseVector</code></a> and |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.SparseVector"><code>SparseVector</code></a>. We recommend |
| using the factory methods implemented in |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.Vectors$"><code>Vectors</code></a> to create local vectors.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="o">{</span><span class="nc">Vector</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">}</span> |
| |
| <span class="c1">// Create a dense vector (1.0, 0.0, 3.0).</span> |
| <span class="k">val</span> <span class="n">dv</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)</span> |
| <span class="c1">// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.</span> |
| <span class="k">val</span> <span class="n">sv1</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">))</span> |
| <span class="c1">// Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries.</span> |
| <span class="k">val</span> <span class="n">sv2</span><span class="k">:</span> <span class="kt">Vector</span> <span class="o">=</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="nc">Seq</span><span class="o">((</span><span class="mi">0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">),</span> <span class="o">(</span><span class="mi">2</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)))</span></code></pre></div> |
| |
| <p><strong><em>Note:</em></strong> |
| Scala imports <code>scala.collection.immutable.Vector</code> by default, so you have to import |
| <code>org.apache.spark.mllib.linalg.Vector</code> explicitly to use MLlib’s <code>Vector</code>.</p> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>The base class of local vectors is |
| <a href="api/java/org/apache/spark/mllib/linalg/Vector.html"><code>Vector</code></a>, and we provide two |
| implementations: <a href="api/java/org/apache/spark/mllib/linalg/DenseVector.html"><code>DenseVector</code></a> and |
| <a href="api/java/org/apache/spark/mllib/linalg/SparseVector.html"><code>SparseVector</code></a>. We recommend |
| using the factory methods implemented in |
| <a href="api/java/org/apache/spark/mllib/linalg/Vectors.html"><code>Vectors</code></a> to create local vectors.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span> |
| |
| <span class="c1">// Create a dense vector (1.0, 0.0, 3.0).</span> |
| <span class="n">Vector</span> <span class="n">dv</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">);</span> |
| <span class="c1">// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.</span> |
| <span class="n">Vector</span> <span class="n">sv</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">},</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">});</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| <p>MLlib recognizes the following types as dense vectors:</p> |
| |
| <ul> |
| <li>NumPy’s <a href="http://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html"><code>array</code></a></li> |
| <li>Python’s list, e.g., <code>[1, 2, 3]</code></li> |
| </ul> |
| |
| <p>and the following as sparse vectors:</p> |
| |
| <ul> |
| <li>MLlib’s <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.SparseVector"><code>SparseVector</code></a>.</li> |
| <li>SciPy’s |
| <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csc_matrix.html#scipy.sparse.csc_matrix"><code>csc_matrix</code></a> |
| with a single column</li> |
| </ul> |
| |
| <p>We recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented |
| in <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.Vectors"><code>Vectors</code></a> to create sparse vectors.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> |
| <span class="kn">import</span> <span class="nn">scipy.sparse</span> <span class="kn">as</span> <span class="nn">sps</span> |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span> |
| |
| <span class="c"># Use a NumPy array as a dense vector.</span> |
| <span class="n">dv1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span> |
| <span class="c"># Use a Python list as a dense vector.</span> |
| <span class="n">dv2</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]</span> |
| <span class="c"># Create a SparseVector.</span> |
| <span class="n">sv1</span> <span class="o">=</span> <span class="n">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span> |
| <span class="c"># Use a single-column SciPy csc_matrix as a sparse vector.</span> |
| <span class="n">sv2</span> <span class="o">=</span> <span class="n">sps</span><span class="o">.</span><span class="n">csc_matrix</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])),</span> <span class="n">shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span></code></pre></div> |
| |
| </div> |
| </div> |
| |
| <h2 id="labeled-point">Labeled point</h2> |
| |
| <p>A labeled point is a local vector, either dense or sparse, associated with a label/response. |
| In MLlib, labeled points are used in supervised learning algorithms. |
| We use a double to store a label, so we can use labeled points in both regression and classification. |
| For binary classification, a label should be either <code>0</code> (negative) or <code>1</code> (positive). |
| For multiclass classification, labels should be class indices starting from zero: <code>0, 1, 2, ...</code>.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="scala"> |
| |
| <p>A labeled point is represented by the case class |
| <a href="api/scala/index.html#org.apache.spark.mllib.regression.LabeledPoint"><code>LabeledPoint</code></a>.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span> |
| |
| <span class="c1">// Create a labeled point with a positive label and a dense feature vector.</span> |
| <span class="k">val</span> <span class="n">pos</span> <span class="k">=</span> <span class="nc">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">))</span> |
| |
| <span class="c1">// Create a labeled point with a negative label and a sparse feature vector.</span> |
| <span class="k">val</span> <span class="n">neg</span> <span class="k">=</span> <span class="nc">LabeledPoint</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">)))</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>A labeled point is represented by |
| <a href="api/java/org/apache/spark/mllib/regression/LabeledPoint.html"><code>LabeledPoint</code></a>.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span> |
| |
| <span class="c1">// Create a labeled point with a positive label and a dense feature vector.</span> |
| <span class="n">LabeledPoint</span> <span class="n">pos</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">));</span> |
| |
| <span class="c1">// Create a labeled point with a negative label and a sparse feature vector.</span> |
| <span class="n">LabeledPoint</span> <span class="n">neg</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">},</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">}));</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| |
| <p>A labeled point is represented by |
| <a href="api/python/pyspark.mllib.html#pyspark.mllib.regression.LabeledPoint"><code>LabeledPoint</code></a>.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">SparseVector</span> |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span> |
| |
| <span class="c"># Create a labeled point with a positive label and a dense feature vector.</span> |
| <span class="n">pos</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span> |
| |
| <span class="c"># Create a labeled point with a negative label and a sparse feature vector.</span> |
| <span class="n">neg</span> <span class="o">=</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">SparseVector</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]))</span></code></pre></div> |
| |
| </div> |
| </div> |
| |
| <p><strong><em>Sparse data</em></strong></p> |
| |
| <p>It is very common in practice to have sparse training data. MLlib supports reading training |
| examples stored in <code>LIBSVM</code> format, which is the default format used by |
| <a href="http://www.csie.ntu.edu.tw/~cjlin/libsvm/"><code>LIBSVM</code></a> and |
| <a href="http://www.csie.ntu.edu.tw/~cjlin/liblinear/"><code>LIBLINEAR</code></a>. It is a text format in which each line |
| represents a labeled sparse feature vector using the following format:</p> |
| |
| <pre><code>label index1:value1 index2:value2 ... |
| </code></pre> |
| |
| <p>where the indices are one-based and in ascending order. |
| After loading, the feature indices are converted to zero-based.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p><a href="api/scala/index.html#org.apache.spark.mllib.util.MLUtils$"><code>MLUtils.loadLibSVMFile</code></a> reads training |
| examples stored in LIBSVM format.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.rdd.RDD</span> |
| |
| <span class="k">val</span> <span class="n">examples</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">LabeledPoint</span><span class="o">]</span> <span class="k">=</span> <span class="nc">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">"data/mllib/sample_libsvm_data.txt"</span><span class="o">)</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| <p><a href="api/java/org/apache/spark/mllib/util/MLUtils.html"><code>MLUtils.loadLibSVMFile</code></a> reads training |
| examples stored in LIBSVM format.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">examples</span> <span class="o">=</span> |
| <span class="n">MLUtils</span><span class="o">.</span><span class="na">loadLibSVMFile</span><span class="o">(</span><span class="n">jsc</span><span class="o">.</span><span class="na">sc</span><span class="o">(),</span> <span class="s">"data/mllib/sample_libsvm_data.txt"</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">();</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| <p><a href="api/python/pyspark.mllib.html#pyspark.mllib.util.MLUtils"><code>MLUtils.loadLibSVMFile</code></a> reads training |
| examples stored in LIBSVM format.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.util</span> <span class="kn">import</span> <span class="n">MLUtils</span> |
| |
| <span class="n">examples</span> <span class="o">=</span> <span class="n">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="p">(</span><span class="n">sc</span><span class="p">,</span> <span class="s">"data/mllib/sample_libsvm_data.txt"</span><span class="p">)</span></code></pre></div> |
| |
| </div> |
| </div> |
| |
| <h2 id="local-matrix">Local matrix</h2> |
| |
| <p>A local matrix has integer-typed row and column indices and double-typed values, stored on a single |
| machine. MLlib supports dense matrices, whose entry values are stored in a single double array in |
| column-major order, and sparse matrices, whose non-zero entry values are stored in the Compressed Sparse |
| Column (CSC) format in column-major order. For example, the following dense matrix <code>\[ \begin{pmatrix} |
| 1.0 & 2.0 \\ |
| 3.0 & 4.0 \\ |
| 5.0 & 6.0 |
| \end{pmatrix} |
| \]</code> |
| is stored in a one-dimensional array <code>[1.0, 3.0, 5.0, 2.0, 4.0, 6.0]</code> with the matrix size <code>(3, 2)</code>.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p>The base class of local matrices is |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.Matrix"><code>Matrix</code></a>, and we provide two |
| implementations: <a href="api/scala/index.html#org.apache.spark.mllib.linalg.DenseMatrix"><code>DenseMatrix</code></a>, |
| and <a href="api/scala/index.html#org.apache.spark.mllib.linalg.SparseMatrix"><code>SparseMatrix</code></a>. |
| We recommend using the factory methods implemented |
| in <a href="api/scala/index.html#org.apache.spark.mllib.linalg.Matrices$"><code>Matrices</code></a> to create local |
| matrices. Remember, local matrices in MLlib are stored in column-major order.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="o">{</span><span class="nc">Matrix</span><span class="o">,</span> <span class="nc">Matrices</span><span class="o">}</span> |
| |
| <span class="c1">// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))</span> |
| <span class="k">val</span> <span class="n">dm</span><span class="k">:</span> <span class="kt">Matrix</span> <span class="o">=</span> <span class="nc">Matrices</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">))</span> |
| |
| <span class="c1">// Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))</span> |
| <span class="k">val</span> <span class="n">sm</span><span class="k">:</span> <span class="kt">Matrix</span> <span class="o">=</span> <span class="nc">Matrices</span><span class="o">.</span><span class="n">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">3</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">1</span><span class="o">),</span> <span class="nc">Array</span><span class="o">(</span><span class="mi">9</span><span class="o">,</span> <span class="mi">6</span><span class="o">,</span> <span class="mi">8</span><span class="o">))</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>The base class of local matrices is |
| <a href="api/java/org/apache/spark/mllib/linalg/Matrix.html"><code>Matrix</code></a>, and we provide two |
| implementations: <a href="api/java/org/apache/spark/mllib/linalg/DenseMatrix.html"><code>DenseMatrix</code></a>, |
| and <a href="api/java/org/apache/spark/mllib/linalg/SparseMatrix.html"><code>SparseMatrix</code></a>. |
| We recommend using the factory methods implemented |
| in <a href="api/java/org/apache/spark/mllib/linalg/Matrices.html"><code>Matrices</code></a> to create local |
| matrices. Remember, local matrices in MLlib are stored in column-major order.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Matrices</span><span class="o">;</span> |
| |
| <span class="c1">// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))</span> |
| <span class="n">Matrix</span> <span class="n">dm</span> <span class="o">=</span> <span class="n">Matrices</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">3.0</span><span class="o">,</span> <span class="mf">5.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="mf">4.0</span><span class="o">,</span> <span class="mf">6.0</span><span class="o">});</span> |
| |
| <span class="c1">// Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))</span> |
| <span class="n">Matrix</span> <span class="n">sm</span> <span class="o">=</span> <span class="n">Matrices</span><span class="o">.</span><span class="na">sparse</span><span class="o">(</span><span class="mi">3</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">0</span><span class="o">,</span> <span class="mi">1</span><span class="o">,</span> <span class="mi">3</span><span class="o">},</span> <span class="k">new</span> <span class="kt">int</span><span class="o">[]</span> <span class="o">{</span><span class="mi">0</span><span class="o">,</span> <span class="mi">2</span><span class="o">,</span> <span class="mi">1</span><span class="o">},</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[]</span> <span class="o">{</span><span class="mi">9</span><span class="o">,</span> <span class="mi">6</span><span class="o">,</span> <span class="mi">8</span><span class="o">});</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| |
| <p>The base class of local matrices is |
| <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.Matrix"><code>Matrix</code></a>, and we provide two |
| implementations: <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.DenseMatrix"><code>DenseMatrix</code></a>, |
| and <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.SparseMatrix"><code>SparseMatrix</code></a>. |
| We recommend using the factory methods implemented |
| in <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.Matrices"><code>Matrices</code></a> to create local |
| matrices. Remember, local matrices in MLlib are stored in column-major order.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.</span><span class="p">{</span><span class="n">Matrix</span><span class="p">,</span> <span class="n">Matrices</span><span class="p">}</span> |
| |
| <span class="o">//</span> <span class="n">Create</span> <span class="n">a</span> <span class="n">dense</span> <span class="n">matrix</span> <span class="p">((</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">),</span> <span class="p">(</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">),</span> <span class="p">(</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">))</span> |
| <span class="n">dm2</span> <span class="o">=</span> <span class="n">Matrices</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">])</span> |
| |
| <span class="o">//</span> <span class="n">Create</span> <span class="n">a</span> <span class="n">sparse</span> <span class="n">matrix</span> <span class="p">((</span><span class="mf">9.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">),</span> <span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">6.0</span><span class="p">))</span> |
| <span class="n">sm</span> <span class="o">=</span> <span class="n">Matrices</span><span class="o">.</span><span class="n">sparse</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">])</span></code></pre></div> |
| |
| </div> |
| |
| </div> |
| |
| <h2 id="distributed-matrix">Distributed matrix</h2> |
| |
| <p>A distributed matrix has long-typed row and column indices and double-typed values, stored |
| distributively in one or more RDDs. It is very important to choose the right format to store large |
| and distributed matrices. Converting a distributed matrix to a different format may require a |
| global shuffle, which is quite expensive. Three types of distributed matrices have been implemented |
| so far.</p> |
| |
| <p>The basic type is called <code>RowMatrix</code>. A <code>RowMatrix</code> is a row-oriented distributed |
| matrix without meaningful row indices, e.g., a collection of feature vectors. |
| It is backed by an RDD of its rows, where each row is a local vector. |
| We assume that the number of columns is not huge for a <code>RowMatrix</code> so that a single |
| local vector can be reasonably communicated to the driver and can also be stored / |
| operated on using a single node. |
| An <code>IndexedRowMatrix</code> is similar to a <code>RowMatrix</code> but with row indices, |
| which can be used for identifying rows and executing joins. |
| A <code>CoordinateMatrix</code> is a distributed matrix stored in <a href="https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_.28COO.29">coordinate list (COO)</a> format, |
| backed by an RDD of its entries.</p> |
| |
| <p><strong><em>Note</em></strong></p> |
| |
| <p>The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size. |
| In general the use of non-deterministic RDDs can lead to errors.</p> |
| |
| <h3 id="rowmatrix">RowMatrix</h3> |
| |
| <p>A <code>RowMatrix</code> is a row-oriented distributed matrix without meaningful row indices, backed by an RDD |
| of its rows, where each row is a local vector. |
| Since each row is represented by a local vector, the number of columns is |
| limited by the integer range but it should be much smaller in practice.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p>A <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.RowMatrix"><code>RowMatrix</code></a> can be |
| created from an <code>RDD[Vector]</code> instance. Then we can compute its column summary statistics and decompositions. |
| <a href="https://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</a> is of the form A = QR where Q is an orthogonal matrix and R is an upper triangular matrix. |
| For <a href="https://en.wikipedia.org/wiki/Singular_value_decomposition">singular value decomposition (SVD)</a> and <a href="https://en.wikipedia.org/wiki/Principal_component_analysis">principal component analysis (PCA)</a>, please refer to <a href="mllib-dimensionality-reduction.html">Dimensionality reduction</a>.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.RowMatrix</span> |
| |
| <span class="k">val</span> <span class="n">rows</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">Vector</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of local vectors</span> |
| <span class="c1">// Create a RowMatrix from an RDD[Vector].</span> |
| <span class="k">val</span> <span class="n">mat</span><span class="k">:</span> <span class="kt">RowMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">RowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">)</span> |
| |
| <span class="c1">// Get its size.</span> |
| <span class="k">val</span> <span class="n">m</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="o">()</span> |
| <span class="k">val</span> <span class="n">n</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="o">()</span> |
| |
| <span class="c1">// QR decomposition </span> |
| <span class="k">val</span> <span class="n">qrResult</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">tallSkinnyQR</span><span class="o">(</span><span class="kc">true</span><span class="o">)</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>A <a href="api/java/org/apache/spark/mllib/linalg/distributed/RowMatrix.html"><code>RowMatrix</code></a> can be |
| created from a <code>JavaRDD<Vector></code> instance. Then we can compute its column summary statistics.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.RowMatrix</span><span class="o">;</span> |
| |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Vector</span><span class="o">></span> <span class="n">rows</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of local vectors</span> |
| <span class="c1">// Create a RowMatrix from an JavaRDD<Vector>.</span> |
| <span class="n">RowMatrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">RowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> |
| |
| <span class="c1">// Get its size.</span> |
| <span class="kt">long</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numRows</span><span class="o">();</span> |
| <span class="kt">long</span> <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numCols</span><span class="o">();</span> |
| |
| <span class="c1">// QR decomposition </span> |
| <span class="n">QRDecomposition</span><span class="o"><</span><span class="n">RowMatrix</span><span class="o">,</span> <span class="n">Matrix</span><span class="o">></span> <span class="n">result</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">tallSkinnyQR</span><span class="o">(</span><span class="kc">true</span><span class="o">);</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| |
| <p>A <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.distributed.RowMatrix"><code>RowMatrix</code></a> can be |
| created from an <code>RDD</code> of vectors.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg.distributed</span> <span class="kn">import</span> <span class="n">RowMatrix</span> |
| |
| <span class="c"># Create an RDD of vectors.</span> |
| <span class="n">rows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]])</span> |
| |
| <span class="c"># Create a RowMatrix from an RDD of vectors.</span> |
| <span class="n">mat</span> <span class="o">=</span> <span class="n">RowMatrix</span><span class="p">(</span><span class="n">rows</span><span class="p">)</span> |
| |
| <span class="c"># Get its size.</span> |
| <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="p">()</span> <span class="c"># 4</span> |
| <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="p">()</span> <span class="c"># 3</span> |
| |
| <span class="c"># Get the rows as an RDD of vectors again.</span> |
| <span class="n">rowsRDD</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">rows</span></code></pre></div> |
| |
| </div> |
| |
| </div> |
| |
| <h3 id="indexedrowmatrix">IndexedRowMatrix</h3> |
| |
| <p>An <code>IndexedRowMatrix</code> is similar to a <code>RowMatrix</code> but with meaningful row indices. It is backed by |
| an RDD of indexed rows, so that each row is represented by its index (long-typed) and a local |
| vector.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p>An |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix"><code>IndexedRowMatrix</code></a> |
| can be created from an <code>RDD[IndexedRow]</code> instance, where |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.IndexedRow"><code>IndexedRow</code></a> is a |
| wrapper over <code>(Long, Vector)</code>. An <code>IndexedRowMatrix</code> can be converted to a <code>RowMatrix</code> by dropping |
| its row indices.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.</span><span class="o">{</span><span class="nc">IndexedRow</span><span class="o">,</span> <span class="nc">IndexedRowMatrix</span><span class="o">,</span> <span class="nc">RowMatrix</span><span class="o">}</span> |
| |
| <span class="k">val</span> <span class="n">rows</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">IndexedRow</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of indexed rows</span> |
| <span class="c1">// Create an IndexedRowMatrix from an RDD[IndexedRow].</span> |
| <span class="k">val</span> <span class="n">mat</span><span class="k">:</span> <span class="kt">IndexedRowMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">IndexedRowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">)</span> |
| |
| <span class="c1">// Get its size.</span> |
| <span class="k">val</span> <span class="n">m</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="o">()</span> |
| <span class="k">val</span> <span class="n">n</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="o">()</span> |
| |
| <span class="c1">// Drop its row indices.</span> |
| <span class="k">val</span> <span class="n">rowMat</span><span class="k">:</span> <span class="kt">RowMatrix</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toRowMatrix</span><span class="o">()</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>An |
| <a href="api/java/org/apache/spark/mllib/linalg/distributed/IndexedRowMatrix.html"><code>IndexedRowMatrix</code></a> |
| can be created from an <code>JavaRDD<IndexedRow></code> instance, where |
| <a href="api/java/org/apache/spark/mllib/linalg/distributed/IndexedRow.html"><code>IndexedRow</code></a> is a |
| wrapper over <code>(long, Vector)</code>. An <code>IndexedRowMatrix</code> can be converted to a <code>RowMatrix</code> by dropping |
| its row indices.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRow</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.RowMatrix</span><span class="o">;</span> |
| |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">IndexedRow</span><span class="o">></span> <span class="n">rows</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of indexed rows</span> |
| <span class="c1">// Create an IndexedRowMatrix from a JavaRDD<IndexedRow>.</span> |
| <span class="n">IndexedRowMatrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IndexedRowMatrix</span><span class="o">(</span><span class="n">rows</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> |
| |
| <span class="c1">// Get its size.</span> |
| <span class="kt">long</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numRows</span><span class="o">();</span> |
| <span class="kt">long</span> <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numCols</span><span class="o">();</span> |
| |
| <span class="c1">// Drop its row indices.</span> |
| <span class="n">RowMatrix</span> <span class="n">rowMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">toRowMatrix</span><span class="o">();</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| |
| <p>An <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.distributed.IndexedRowMatrix"><code>IndexedRowMatrix</code></a> |
| can be created from an <code>RDD</code> of <code>IndexedRow</code>s, where |
| <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.distributed.IndexedRow"><code>IndexedRow</code></a> is a |
| wrapper over <code>(long, vector)</code>. An <code>IndexedRowMatrix</code> can be converted to a <code>RowMatrix</code> by dropping |
| its row indices.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg.distributed</span> <span class="kn">import</span> <span class="n">IndexedRow</span><span class="p">,</span> <span class="n">IndexedRowMatrix</span> |
| |
| <span class="c"># Create an RDD of indexed rows.</span> |
| <span class="c"># - This can be done explicitly with the IndexedRow class:</span> |
| <span class="n">indexedRows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([</span><span class="n">IndexedRow</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span> |
| <span class="n">IndexedRow</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]),</span> |
| <span class="n">IndexedRow</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]),</span> |
| <span class="n">IndexedRow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">])])</span> |
| <span class="c"># - or by using (long, vector) tuples:</span> |
| <span class="n">indexedRows</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([(</span><span class="mi">0</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]),</span> |
| <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">]),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">])])</span> |
| |
| <span class="c"># Create an IndexedRowMatrix from an RDD of IndexedRows.</span> |
| <span class="n">mat</span> <span class="o">=</span> <span class="n">IndexedRowMatrix</span><span class="p">(</span><span class="n">indexedRows</span><span class="p">)</span> |
| |
| <span class="c"># Get its size.</span> |
| <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="p">()</span> <span class="c"># 4</span> |
| <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="p">()</span> <span class="c"># 3</span> |
| |
| <span class="c"># Get the rows as an RDD of IndexedRows.</span> |
| <span class="n">rowsRDD</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">rows</span> |
| |
| <span class="c"># Convert to a RowMatrix by dropping the row indices.</span> |
| <span class="n">rowMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toRowMatrix</span><span class="p">()</span> |
| |
| <span class="c"># Convert to a CoordinateMatrix.</span> |
| <span class="n">coordinateMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toCoordinateMatrix</span><span class="p">()</span> |
| |
| <span class="c"># Convert to a BlockMatrix.</span> |
| <span class="n">blockMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toBlockMatrix</span><span class="p">()</span></code></pre></div> |
| |
| </div> |
| |
| </div> |
| |
| <h3 id="coordinatematrix">CoordinateMatrix</h3> |
| |
| <p>A <code>CoordinateMatrix</code> is a distributed matrix backed by an RDD of its entries. Each entry is a tuple |
| of <code>(i: Long, j: Long, value: Double)</code>, where <code>i</code> is the row index, <code>j</code> is the column index, and |
| <code>value</code> is the entry value. A <code>CoordinateMatrix</code> should be used only when both |
| dimensions of the matrix are huge and the matrix is very sparse.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p>A |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.CoordinateMatrix"><code>CoordinateMatrix</code></a> |
| can be created from an <code>RDD[MatrixEntry]</code> instance, where |
| <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.MatrixEntry"><code>MatrixEntry</code></a> is a |
| wrapper over <code>(Long, Long, Double)</code>. A <code>CoordinateMatrix</code> can be converted to an <code>IndexedRowMatrix</code> |
| with sparse rows by calling <code>toIndexedRowMatrix</code>. Other computations for |
| <code>CoordinateMatrix</code> are not currently supported.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.</span><span class="o">{</span><span class="nc">CoordinateMatrix</span><span class="o">,</span> <span class="nc">MatrixEntry</span><span class="o">}</span> |
| |
| <span class="k">val</span> <span class="n">entries</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">MatrixEntry</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of matrix entries</span> |
| <span class="c1">// Create a CoordinateMatrix from an RDD[MatrixEntry].</span> |
| <span class="k">val</span> <span class="n">mat</span><span class="k">:</span> <span class="kt">CoordinateMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">)</span> |
| |
| <span class="c1">// Get its size.</span> |
| <span class="k">val</span> <span class="n">m</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="o">()</span> |
| <span class="k">val</span> <span class="n">n</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="o">()</span> |
| |
| <span class="c1">// Convert it to an IndexRowMatrix whose rows are sparse vectors.</span> |
| <span class="k">val</span> <span class="n">indexedRowMatrix</span> <span class="k">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toIndexedRowMatrix</span><span class="o">()</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>A |
| <a href="api/java/org/apache/spark/mllib/linalg/distributed/CoordinateMatrix.html"><code>CoordinateMatrix</code></a> |
| can be created from a <code>JavaRDD<MatrixEntry></code> instance, where |
| <a href="api/java/org/apache/spark/mllib/linalg/distributed/MatrixEntry.html"><code>MatrixEntry</code></a> is a |
| wrapper over <code>(long, long, double)</code>. A <code>CoordinateMatrix</code> can be converted to an <code>IndexedRowMatrix</code> |
| with sparse rows by calling <code>toIndexedRowMatrix</code>. Other computations for |
| <code>CoordinateMatrix</code> are not currently supported.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.CoordinateMatrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.MatrixEntry</span><span class="o">;</span> |
| |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">MatrixEntry</span><span class="o">></span> <span class="n">entries</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of matrix entries</span> |
| <span class="c1">// Create a CoordinateMatrix from a JavaRDD<MatrixEntry>.</span> |
| <span class="n">CoordinateMatrix</span> <span class="n">mat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> |
| |
| <span class="c1">// Get its size.</span> |
| <span class="kt">long</span> <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numRows</span><span class="o">();</span> |
| <span class="kt">long</span> <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">numCols</span><span class="o">();</span> |
| |
| <span class="c1">// Convert it to an IndexRowMatrix whose rows are sparse vectors.</span> |
| <span class="n">IndexedRowMatrix</span> <span class="n">indexedRowMatrix</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="na">toIndexedRowMatrix</span><span class="o">();</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| |
| <p>A <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.distributed.CoordinateMatrix"><code>CoordinateMatrix</code></a> |
| can be created from an <code>RDD</code> of <code>MatrixEntry</code> entries, where |
| <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.distributed.MatrixEntry"><code>MatrixEntry</code></a> is a |
| wrapper over <code>(long, long, float)</code>. A <code>CoordinateMatrix</code> can be converted to a <code>RowMatrix</code> by |
| calling <code>toRowMatrix</code>, or to an <code>IndexedRowMatrix</code> with sparse rows by calling <code>toIndexedRowMatrix</code>.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg.distributed</span> <span class="kn">import</span> <span class="n">CoordinateMatrix</span><span class="p">,</span> <span class="n">MatrixEntry</span> |
| |
| <span class="c"># Create an RDD of coordinate entries.</span> |
| <span class="c"># - This can be done explicitly with the MatrixEntry class:</span> |
| <span class="n">entries</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([</span><span class="n">MatrixEntry</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">),</span> <span class="n">MatrixEntry</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">2.1</span><span class="p">),</span> <span class="n">MatrixEntry</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">3.7</span><span class="p">)])</span> |
| <span class="c"># - or using (long, long, float) tuples:</span> |
| <span class="n">entries</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">2.1</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">3.7</span><span class="p">)])</span> |
| |
| <span class="c"># Create an CoordinateMatrix from an RDD of MatrixEntries.</span> |
| <span class="n">mat</span> <span class="o">=</span> <span class="n">CoordinateMatrix</span><span class="p">(</span><span class="n">entries</span><span class="p">)</span> |
| |
| <span class="c"># Get its size.</span> |
| <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="p">()</span> <span class="c"># 3</span> |
| <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="p">()</span> <span class="c"># 2</span> |
| |
| <span class="c"># Get the entries as an RDD of MatrixEntries.</span> |
| <span class="n">entriesRDD</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">entries</span> |
| |
| <span class="c"># Convert to a RowMatrix.</span> |
| <span class="n">rowMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toRowMatrix</span><span class="p">()</span> |
| |
| <span class="c"># Convert to an IndexedRowMatrix.</span> |
| <span class="n">indexedRowMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toIndexedRowMatrix</span><span class="p">()</span> |
| |
| <span class="c"># Convert to a BlockMatrix.</span> |
| <span class="n">blockMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toBlockMatrix</span><span class="p">()</span></code></pre></div> |
| |
| </div> |
| |
| </div> |
| |
| <h3 id="blockmatrix">BlockMatrix</h3> |
| |
| <p>A <code>BlockMatrix</code> is a distributed matrix backed by an RDD of <code>MatrixBlock</code>s, where a <code>MatrixBlock</code> is |
| a tuple of <code>((Int, Int), Matrix)</code>, where the <code>(Int, Int)</code> is the index of the block, and <code>Matrix</code> is |
| the sub-matrix at the given index with size <code>rowsPerBlock</code> x <code>colsPerBlock</code>. |
| <code>BlockMatrix</code> supports methods such as <code>add</code> and <code>multiply</code> with another <code>BlockMatrix</code>. |
| <code>BlockMatrix</code> also has a helper function <code>validate</code> which can be used to check whether the |
| <code>BlockMatrix</code> is set up properly.</p> |
| |
| <div class="codetabs"> |
| <div data-lang="scala"> |
| |
| <p>A <a href="api/scala/index.html#org.apache.spark.mllib.linalg.distributed.BlockMatrix"><code>BlockMatrix</code></a> can be |
| most easily created from an <code>IndexedRowMatrix</code> or <code>CoordinateMatrix</code> by calling <code>toBlockMatrix</code>. |
| <code>toBlockMatrix</code> creates blocks of size 1024 x 1024 by default. |
| Users may change the block size by supplying the values through <code>toBlockMatrix(rowsPerBlock, colsPerBlock)</code>.</p> |
| |
| <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.</span><span class="o">{</span><span class="nc">BlockMatrix</span><span class="o">,</span> <span class="nc">CoordinateMatrix</span><span class="o">,</span> <span class="nc">MatrixEntry</span><span class="o">}</span> |
| |
| <span class="k">val</span> <span class="n">entries</span><span class="k">:</span> <span class="kt">RDD</span><span class="o">[</span><span class="kt">MatrixEntry</span><span class="o">]</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// an RDD of (i, j, v) matrix entries</span> |
| <span class="c1">// Create a CoordinateMatrix from an RDD[MatrixEntry].</span> |
| <span class="k">val</span> <span class="n">coordMat</span><span class="k">:</span> <span class="kt">CoordinateMatrix</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">)</span> |
| <span class="c1">// Transform the CoordinateMatrix to a BlockMatrix</span> |
| <span class="k">val</span> <span class="n">matA</span><span class="k">:</span> <span class="kt">BlockMatrix</span> <span class="o">=</span> <span class="n">coordMat</span><span class="o">.</span><span class="n">toBlockMatrix</span><span class="o">().</span><span class="n">cache</span><span class="o">()</span> |
| |
| <span class="c1">// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.</span> |
| <span class="c1">// Nothing happens if it is valid.</span> |
| <span class="n">matA</span><span class="o">.</span><span class="n">validate</span><span class="o">()</span> |
| |
| <span class="c1">// Calculate A^T A.</span> |
| <span class="k">val</span> <span class="n">ata</span> <span class="k">=</span> <span class="n">matA</span><span class="o">.</span><span class="n">transpose</span><span class="o">.</span><span class="n">multiply</span><span class="o">(</span><span class="n">matA</span><span class="o">)</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>A <a href="api/java/org/apache/spark/mllib/linalg/distributed/BlockMatrix.html"><code>BlockMatrix</code></a> can be |
| most easily created from an <code>IndexedRowMatrix</code> or <code>CoordinateMatrix</code> by calling <code>toBlockMatrix</code>. |
| <code>toBlockMatrix</code> creates blocks of size 1024 x 1024 by default. |
| Users may change the block size by supplying the values through <code>toBlockMatrix(rowsPerBlock, colsPerBlock)</code>.</p> |
| |
| <div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.BlockMatrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.CoordinateMatrix</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix</span><span class="o">;</span> |
| |
| <span class="n">JavaRDD</span><span class="o"><</span><span class="n">MatrixEntry</span><span class="o">></span> <span class="n">entries</span> <span class="o">=</span> <span class="o">...</span> <span class="c1">// a JavaRDD of (i, j, v) Matrix Entries</span> |
| <span class="c1">// Create a CoordinateMatrix from a JavaRDD<MatrixEntry>.</span> |
| <span class="n">CoordinateMatrix</span> <span class="n">coordMat</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">CoordinateMatrix</span><span class="o">(</span><span class="n">entries</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> |
| <span class="c1">// Transform the CoordinateMatrix to a BlockMatrix</span> |
| <span class="n">BlockMatrix</span> <span class="n">matA</span> <span class="o">=</span> <span class="n">coordMat</span><span class="o">.</span><span class="na">toBlockMatrix</span><span class="o">().</span><span class="na">cache</span><span class="o">();</span> |
| |
| <span class="c1">// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.</span> |
| <span class="c1">// Nothing happens if it is valid.</span> |
| <span class="n">matA</span><span class="o">.</span><span class="na">validate</span><span class="o">();</span> |
| |
| <span class="c1">// Calculate A^T A.</span> |
| <span class="n">BlockMatrix</span> <span class="n">ata</span> <span class="o">=</span> <span class="n">matA</span><span class="o">.</span><span class="na">transpose</span><span class="o">().</span><span class="na">multiply</span><span class="o">(</span><span class="n">matA</span><span class="o">);</span></code></pre></div> |
| |
| </div> |
| |
| <div data-lang="python"> |
| |
| <p>A <a href="api/python/pyspark.mllib.html#pyspark.mllib.linalg.distributed.BlockMatrix"><code>BlockMatrix</code></a> |
| can be created from an <code>RDD</code> of sub-matrix blocks, where a sub-matrix block is a |
| <code>((blockRowIndex, blockColIndex), sub-matrix)</code> tuple.</p> |
| |
| <div class="highlight"><pre><code class="language-python" data-lang="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.linalg</span> <span class="kn">import</span> <span class="n">Matrices</span> |
| <span class="kn">from</span> <span class="nn">pyspark.mllib.linalg.distributed</span> <span class="kn">import</span> <span class="n">BlockMatrix</span> |
| |
| <span class="c"># Create an RDD of sub-matrix blocks.</span> |
| <span class="n">blocks</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">parallelize</span><span class="p">([((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Matrices</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">])),</span> |
| <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Matrices</span><span class="o">.</span><span class="n">dense</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">]))])</span> |
| |
| <span class="c"># Create a BlockMatrix from an RDD of sub-matrix blocks.</span> |
| <span class="n">mat</span> <span class="o">=</span> <span class="n">BlockMatrix</span><span class="p">(</span><span class="n">blocks</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> |
| |
| <span class="c"># Get its size.</span> |
| <span class="n">m</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numRows</span><span class="p">()</span> <span class="c"># 6</span> |
| <span class="n">n</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">numCols</span><span class="p">()</span> <span class="c"># 2</span> |
| |
| <span class="c"># Get the blocks as an RDD of sub-matrix blocks.</span> |
| <span class="n">blocksRDD</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">blocks</span> |
| |
| <span class="c"># Convert to a LocalMatrix.</span> |
| <span class="n">localMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toLocalMatrix</span><span class="p">()</span> |
| |
| <span class="c"># Convert to an IndexedRowMatrix.</span> |
| <span class="n">indexedRowMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toIndexedRowMatrix</span><span class="p">()</span> |
| |
| <span class="c"># Convert to a CoordinateMatrix.</span> |
| <span class="n">coordinateMat</span> <span class="o">=</span> <span class="n">mat</span><span class="o">.</span><span class="n">toCoordinateMatrix</span><span class="p">()</span></code></pre></div> |
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