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| <h1>decompositions</h1> |
| </div> |
| |
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| <span class="name">decompositions</span> |
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| |
| <div id="comment" class="fullcommenttop"><div class="comment cmt"><p>This package holds all decomposition and factorization-like methods, all that we were able to make |
| distributed engine-independent so far, anyway. |
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| <h3>Type Members</h3> |
| <ol><li name="org.apache.mahout.math.decompositions.FactorizationResult" visbl="pub" data-isabs="false" fullComment="no" group="Ungrouped"> |
| <a id="FactorizationResult[K]=org.apache.mahout.math.decompositions.ALS.Result[K]"></a> |
| <a id="FactorizationResult[K]:FactorizationResult[K]"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">type</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">FactorizationResult</span><span class="tparams">[<span name="K">K</span>]</span><span class="result"> = <span class="extype" name="org.apache.mahout.math.decompositions.ALS.Result">Result</span>[<span class="extype" name="org.apache.mahout.math.decompositions.FactorizationResult.K">K</span>]</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">Result for distributed ALS-type two-component factorization algorithms</p> |
| </li><li name="org.apache.mahout.math.decompositions.FactorizationResultInCore" visbl="pub" data-isabs="false" fullComment="no" group="Ungrouped"> |
| <a id="FactorizationResultInCore=org.apache.mahout.math.decompositions.ALS.InCoreResult"></a> |
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| <span class="modifier_kind"> |
| <span class="modifier"></span> |
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| <span class="symbol"> |
| <span class="name">FactorizationResultInCore</span><span class="result"> = <span class="extype" name="org.apache.mahout.math.decompositions.ALS.InCoreResult">InCoreResult</span></span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">Result for distributed ALS-type two-component factorization algorithms, in-core matrices</p> |
| </li></ol> |
| </div> |
| |
| |
| |
| <div id="values" class="values members"> |
| <h3>Value Members</h3> |
| <ol><li name="org.apache.mahout.math.decompositions.DQR" visbl="pub" data-isabs="false" fullComment="no" group="Ungrouped"> |
| <a id="DQR"></a> |
| <a id="DQR:DQR"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">object</span> |
| </span> |
| <span class="symbol"> |
| <a href="DQR$.html"><span class="name">DQR</span></a> |
| </span> |
| </h4> |
| |
| </li><li name="org.apache.mahout.math.decompositions.DSPCA" visbl="pub" data-isabs="false" fullComment="no" group="Ungrouped"> |
| <a id="DSPCA"></a> |
| <a id="DSPCA:DSPCA"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">object</span> |
| </span> |
| <span class="symbol"> |
| <a href="DSPCA$.html"><span class="name">DSPCA</span></a> |
| </span> |
| </h4> |
| |
| </li><li name="org.apache.mahout.math.decompositions.DSSVD" visbl="pub" data-isabs="false" fullComment="no" group="Ungrouped"> |
| <a id="DSSVD"></a> |
| <a id="DSSVD:DSSVD"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">object</span> |
| </span> |
| <span class="symbol"> |
| <a href="DSSVD$.html"><span class="name">DSSVD</span></a> |
| </span> |
| </h4> |
| |
| </li><li name="org.apache.mahout.math.decompositions.package#dals" visbl="pub" data-isabs="false" fullComment="yes" group="Ungrouped"> |
| <a id="dals[K](drmA:org.apache.mahout.math.drm.DrmLike[K],k:Int,lambda:Double,maxIterations:Int,convergenceThreshold:Double)(implicitevidence$4:scala.reflect.ClassTag[K]):org.apache.mahout.math.decompositions.package.FactorizationResult[K]"></a> |
| <a id="dals[K](DrmLike[K],Int,Double,Int,Double)(ClassTag[K]):FactorizationResult[K]"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">def</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">dals</span><span class="tparams">[<span name="K">K</span>]</span><span class="params">(<span name="drmA">drmA: <a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dals.K">K</span>]</span>, <span name="k">k: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">50</span></span>, <span name="lambda">lambda: <span class="extype" name="scala.Double">Double</span> = <span class="symbol">0.0</span></span>, <span name="maxIterations">maxIterations: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">10</span></span>, <span name="convergenceThreshold">convergenceThreshold: <span class="extype" name="scala.Double">Double</span> = <span class="symbol">0.10</span></span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: <span class="extype" name="scala.reflect.ClassTag">ClassTag</span>[<span class="extype" name="org.apache.mahout.math.decompositions.dals.K">K</span>]</span>)</span><span class="result">: <a href="#FactorizationResult[K]=org.apache.mahout.math.decompositions.ALS.Result[K]" class="extmbr" name="org.apache.mahout.math.decompositions.FactorizationResult">FactorizationResult</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dals.K">K</span>]</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">Run ALS.</p><div class="fullcomment"><div class="comment cmt"><p>Run ALS. |
| <P></p><p>Example:</p><p><pre> |
| val (u,v,errors) = als(input, k).toTuple |
| </pre></p><p>ALS runs until (rmse[i-1]-rmse[i])/rmse[i-1] < convergenceThreshold, or i==maxIterations, |
| whichever earlier. |
| <P> |
| </p></div><dl class="paramcmts block"><dt class="tparam">K</dt><dd class="cmt"><p>row key type of the input (100 is probably more than enough)</p></dd><dt class="param">drmA</dt><dd class="cmt"><p>The input matrix</p></dd><dt class="param">k</dt><dd class="cmt"><p>required rank of decomposition (number of cols in U and V results)</p></dd><dt class="param">lambda</dt><dd class="cmt"><p>regularization rate</p></dd><dt class="param">maxIterations</dt><dd class="cmt"><p>maximum iterations to run regardless of convergence</p></dd><dt class="param">convergenceThreshold</dt><dd class="cmt"><p>stop sooner if (rmse[i-1] - rmse[i])/rmse[i - 1] is less than this |
| value. If <=0 then we won't compute RMSE and use convergence test.</p></dd><dt>returns</dt><dd class="cmt"><p>{ @link org.apache.mahout.math.drm.decompositions.ALS.Result} |
| </p></dd></dl></div> |
| </li><li name="org.apache.mahout.math.decompositions.package#dqrThin" visbl="pub" data-isabs="false" fullComment="yes" group="Ungrouped"> |
| <a id="dqrThin[K](drmA:org.apache.mahout.math.drm.DrmLike[K],checkRankDeficiency:Boolean)(implicitevidence$1:scala.reflect.ClassTag[K]):(org.apache.mahout.math.drm.DrmLike[K],org.apache.mahout.math.Matrix)"></a> |
| <a id="dqrThin[K](DrmLike[K],Boolean)(ClassTag[K]):(DrmLike[K],Matrix)"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">def</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">dqrThin</span><span class="tparams">[<span name="K">K</span>]</span><span class="params">(<span name="drmA">drmA: <a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dqrThin.K">K</span>]</span>, <span name="checkRankDeficiency">checkRankDeficiency: <span class="extype" name="scala.Boolean">Boolean</span> = <span class="symbol">true</span></span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: <span class="extype" name="scala.reflect.ClassTag">ClassTag</span>[<span class="extype" name="org.apache.mahout.math.decompositions.dqrThin.K">K</span>]</span>)</span><span class="result">: (<a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dqrThin.K">K</span>], <span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span>)</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">Distributed _thin_ QR.</p><div class="fullcomment"><div class="comment cmt"><p>Distributed _thin_ QR. A'A must fit in a memory, i.e. if A is m x n, then n should be pretty |
| controlled (<5000 or so). <P></p><p>It is recommended to checkpoint A since it does two passes over it. <P></p><p>It also guarantees that Q is partitioned exactly the same way (and in same key-order) as A, so |
| their RDD should be able to zip successfully. |
| </p></div></div> |
| </li><li name="org.apache.mahout.math.decompositions.package#dspca" visbl="pub" data-isabs="false" fullComment="yes" group="Ungrouped"> |
| <a id="dspca[K](drmA:org.apache.mahout.math.drm.DrmLike[K],k:Int,p:Int,q:Int)(implicitevidence$3:scala.reflect.ClassTag[K]):(org.apache.mahout.math.drm.DrmLike[K],org.apache.mahout.math.drm.DrmLike[Int],org.apache.mahout.math.Vector)"></a> |
| <a id="dspca[K](DrmLike[K],Int,Int,Int)(ClassTag[K]):(DrmLike[K],DrmLike[Int],Vector)"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">def</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">dspca</span><span class="tparams">[<span name="K">K</span>]</span><span class="params">(<span name="drmA">drmA: <a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dspca.K">K</span>]</span>, <span name="k">k: <span class="extype" name="scala.Int">Int</span></span>, <span name="p">p: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">15</span></span>, <span name="q">q: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">0</span></span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: <span class="extype" name="scala.reflect.ClassTag">ClassTag</span>[<span class="extype" name="org.apache.mahout.math.decompositions.dspca.K">K</span>]</span>)</span><span class="result">: (<a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dspca.K">K</span>], <a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="scala.Int">Int</span>], <span class="extype" name="org.apache.mahout.math.Vector">Vector</span>)</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">Distributed Stochastic PCA decomposition algorithm.</p><div class="fullcomment"><div class="comment cmt"><p>Distributed Stochastic PCA decomposition algorithm. A logical reflow of the "SSVD-PCA options.pdf" |
| document of the MAHOUT-817. |
| </p></div><dl class="paramcmts block"><dt class="param">drmA</dt><dd class="cmt"><p>input matrix A</p></dd><dt class="param">k</dt><dd class="cmt"><p>request SSVD rank</p></dd><dt class="param">p</dt><dd class="cmt"><p>oversampling parameter</p></dd><dt class="param">q</dt><dd class="cmt"><p>number of power iterations (hint: use either 0 or 1)</p></dd><dt>returns</dt><dd class="cmt"><p>(U,V,s). Note that U, V are non-checkpointed matrices (i.e. one needs to actually use them |
| e.g. save them to hdfs in order to trigger their computation. |
| </p></dd></dl></div> |
| </li><li name="org.apache.mahout.math.decompositions.package#dssvd" visbl="pub" data-isabs="false" fullComment="yes" group="Ungrouped"> |
| <a id="dssvd[K](drmA:org.apache.mahout.math.drm.DrmLike[K],k:Int,p:Int,q:Int)(implicitevidence$2:scala.reflect.ClassTag[K]):(org.apache.mahout.math.drm.DrmLike[K],org.apache.mahout.math.drm.DrmLike[Int],org.apache.mahout.math.Vector)"></a> |
| <a id="dssvd[K](DrmLike[K],Int,Int,Int)(ClassTag[K]):(DrmLike[K],DrmLike[Int],Vector)"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">def</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">dssvd</span><span class="tparams">[<span name="K">K</span>]</span><span class="params">(<span name="drmA">drmA: <a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dssvd.K">K</span>]</span>, <span name="k">k: <span class="extype" name="scala.Int">Int</span></span>, <span name="p">p: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">15</span></span>, <span name="q">q: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">0</span></span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: <span class="extype" name="scala.reflect.ClassTag">ClassTag</span>[<span class="extype" name="org.apache.mahout.math.decompositions.dssvd.K">K</span>]</span>)</span><span class="result">: (<a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="org.apache.mahout.math.decompositions.dssvd.K">K</span>], <a href="../drm/DrmLike.html" class="extype" name="org.apache.mahout.math.drm.DrmLike">DrmLike</a>[<span class="extype" name="scala.Int">Int</span>], <span class="extype" name="org.apache.mahout.math.Vector">Vector</span>)</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">Distributed Stochastic Singular Value decomposition algorithm.</p><div class="fullcomment"><div class="comment cmt"><p>Distributed Stochastic Singular Value decomposition algorithm. |
| </p></div><dl class="paramcmts block"><dt class="param">drmA</dt><dd class="cmt"><p>input matrix A</p></dd><dt class="param">k</dt><dd class="cmt"><p>request SSVD rank</p></dd><dt class="param">p</dt><dd class="cmt"><p>oversampling parameter</p></dd><dt class="param">q</dt><dd class="cmt"><p>number of power iterations</p></dd><dt>returns</dt><dd class="cmt"><p>(U,V,s). Note that U, V are non-checkpointed matrices (i.e. one needs to actually use them |
| e.g. save them to hdfs in order to trigger their computation. |
| </p></dd></dl></div> |
| </li><li name="org.apache.mahout.math.decompositions.package#spca" visbl="pub" data-isabs="false" fullComment="yes" group="Ungrouped"> |
| <a id="spca(a:org.apache.mahout.math.Matrix,k:Int,p:Int,q:Int):(org.apache.mahout.math.Matrix,org.apache.mahout.math.Matrix,org.apache.mahout.math.Vector)"></a> |
| <a id="spca(Matrix,Int,Int,Int):(Matrix,Matrix,Vector)"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">def</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">spca</span><span class="params">(<span name="a">a: <span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span></span>, <span name="k">k: <span class="extype" name="scala.Int">Int</span></span>, <span name="p">p: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">15</span></span>, <span name="q">q: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">0</span></span>)</span><span class="result">: (<span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span>, <span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span>, <span class="extype" name="org.apache.mahout.math.Vector">Vector</span>)</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">PCA based on SSVD that runs without forming an always-dense A-(colMeans(A)) input for SVD.</p><div class="fullcomment"><div class="comment cmt"><p>PCA based on SSVD that runs without forming an always-dense A-(colMeans(A)) input for SVD. This |
| follows the solution outlined in MAHOUT-817. For in-core version it, for most part, is supposed |
| to save some memory for sparse inputs by removing direct mean subtraction.<P></p><p>Hint: Usually one wants to use AV which is approsimately USigma, i.e.<code>u %*%: diagv(s)</code>. |
| If retaining distances and orignal scaled variances not that important, the normalized PCA space |
| is just U.</p><p>Important: data points are considered to be rows. |
| </p></div><dl class="paramcmts block"><dt class="param">a</dt><dd class="cmt"><p>input matrix A</p></dd><dt class="param">k</dt><dd class="cmt"><p>request SSVD rank</p></dd><dt class="param">p</dt><dd class="cmt"><p>oversampling parameter</p></dd><dt class="param">q</dt><dd class="cmt"><p>number of power iterations</p></dd><dt>returns</dt><dd class="cmt"><p>(U,V,s) |
| </p></dd></dl></div> |
| </li><li name="org.apache.mahout.math.decompositions.package#ssvd" visbl="pub" data-isabs="false" fullComment="yes" group="Ungrouped"> |
| <a id="ssvd(a:org.apache.mahout.math.Matrix,k:Int,p:Int,q:Int):(org.apache.mahout.math.Matrix,org.apache.mahout.math.Matrix,org.apache.mahout.math.Vector)"></a> |
| <a id="ssvd(Matrix,Int,Int,Int):(Matrix,Matrix,Vector)"></a> |
| <h4 class="signature"> |
| <span class="modifier_kind"> |
| <span class="modifier"></span> |
| <span class="kind">def</span> |
| </span> |
| <span class="symbol"> |
| <span class="name">ssvd</span><span class="params">(<span name="a">a: <span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span></span>, <span name="k">k: <span class="extype" name="scala.Int">Int</span></span>, <span name="p">p: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">15</span></span>, <span name="q">q: <span class="extype" name="scala.Int">Int</span> = <span class="symbol">0</span></span>)</span><span class="result">: (<span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span>, <span class="extype" name="org.apache.mahout.math.Matrix">Matrix</span>, <span class="extype" name="org.apache.mahout.math.Vector">Vector</span>)</span> |
| </span> |
| </h4> |
| <p class="shortcomment cmt">In-core SSVD algorithm.</p><div class="fullcomment"><div class="comment cmt"><p>In-core SSVD algorithm. |
| </p></div><dl class="paramcmts block"><dt class="param">a</dt><dd class="cmt"><p>input matrix A</p></dd><dt class="param">k</dt><dd class="cmt"><p>request SSVD rank</p></dd><dt class="param">p</dt><dd class="cmt"><p>oversampling parameter</p></dd><dt class="param">q</dt><dd class="cmt"><p>number of power iterations</p></dd><dt>returns</dt><dd class="cmt"><p>(U,V,s) |
| </p></dd></dl></div> |
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