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| <div class="collapse" id="collapse_background"> |
| <li><a href="/docs/Background/TheChallenge.html">•The Challenge</a></li> |
| <li><a href="/docs/Background/SketchOrigins.html">•Sketch Origins</a></li> |
| <li><a href="/docs/Background/SketchElements.html">•Sketch Elements</a></li> |
| <li><a href="/docs/Background/Presentations.html">•Presentations</a></li> |
| <li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/DataSketches_deck.pdf">•Overview Slide Deck</a></li> |
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| <li><a href="/docs/Architecture/MajorSketchFamilies.html">•The Major Sketch Families</a></li> |
| <li><a href="/docs/Architecture/LargeScale.html">•Large Scale Computing</a></li> |
| <li><a href="/docs/Architecture/KeyFeatures.html">•Key Features</a></li> |
| <li><a href="/docs/Architecture/SketchFeaturesMatrix.html">•Sketch Features Matrix</a></li> |
| <li><a href="/docs/Architecture/Components.html">•Components</a></li> |
| <li><a href="/docs/Architecture/SketchesByComponent.html">•Sketches by Component</a></li> |
| <li><a href="/docs/Architecture/SketchCriteria.html">•Sketch Criteria</a></li> |
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| <p id="memory-component"> |
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| <li><a href="/docs/Memory/MemoryComponent.html">•Memory Component</a></li> |
| <li><a href="/docs/Memory/MemoryPerformance.html">•Memory Component Performance</a></li> |
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| <li><a href="/docs/Architecture/OrderSensitivity.html">•Notes on Order Sensitivity</a></li> |
| <li><a href="/docs/Architecture/Concurrency.html">•Notes on Concurrency</a></li> |
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| <li><a href="/docs/DistinctCountFeaturesMatrix.html">•Features Matrix</a></li> |
| <li><a href="/docs/DistinctCountMeritComparisons.html">•Figures-of-Merit Comparison</a></li> |
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| <p id="cpc-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_cpc_sketches">CPC Sketches</a> |
| </p> |
| <div class="collapse" id="collapse_cpc_sketches"> |
| <li><a href="/docs/CPC/CPC.html">•CPC Sketch</a></li> |
| <li><a href="/docs/CPC/CpcPerformance.html">•CPC Sketch Performance</a></li> |
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| <a data-toggle="collapse" class="menu collapsed" href="#collapse_cpc_examples">CPC Examples</a> |
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| <li><a href="/docs/CPC/CpcJavaExample.html">•CPC Sketch Java Example</a></li> |
| <li><a href="/docs/CPC/CpcCppExample.html">•CPC Sketch C++ Example</a></li> |
| <li><a href="/docs/CPC/CpcPigExample.html">•CPC Sketch Pig UDFs</a></li> |
| <li><a href="/docs/CPC/CpcHiveExample.html">•CPC Sketch Hive UDFs</a></li> |
| </div> |
| </div> |
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| <p id="hyperloglog-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_hyperloglog_sketches">HyperLogLog Sketches</a> |
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| <li><a href="/docs/HLL/HLL.html">•HLL Sketch</a></li> |
| <li><a href="/docs/HLL/HllMap.html">•HLL Map Sketch</a></li> |
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| <p id="hll-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_hll_examples">HLL Examples</a> |
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| <li><a href="/docs/HLL/HllJavaExample.html">•HLL Sketch Java Example</a></li> |
| <li><a href="/docs/HLL/HllCppExample.html">•HLL Sketch C++ Example</a></li> |
| <li><a href="/docs/HLL/HllPigUDFs.html">•HLL Sketch Pig UDFs</a></li> |
| <li><a href="/docs/HLL/HllHiveUDFs.html">•HLL Sketch Hive UDFs</a></li> |
| </div> |
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| <p id="hll-studies"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_hll_studies">HLL Studies</a> |
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| <div class="collapse" id="collapse_hll_studies"> |
| <li><a href="/docs/HLL/HllPerformance.html">•HLL Sketch Performance</a></li> |
| <li><a href="/docs/HLL/Hll_vs_CS_Hllpp.html">•HLL vs Clearspring HLL++</a></li> |
| <li><a href="/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html">•HLL Sketch vs Druid HyperLogLogCollector</a></li> |
| </div> |
| </div> |
| |
| <p id="theta-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_sketches">Theta Sketches</a> |
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| <div class="collapse" id="collapse_theta_sketches"> |
| <li><a href="/docs/Theta/ThetaSketchFramework.html">•Theta Sketch Framework</a></li> |
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| <p id="theta-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_examples">Theta Examples</a> |
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| <div class="collapse" id="collapse_theta_examples"> |
| <li><a href="/docs/Theta/ConcurrentThetaSketch.html">•Concurrent Theta Sketch</a></li> |
| <li><a href="/docs/Theta/ThetaJavaExample.html">•Theta Sketch Java Example</a></li> |
| <li><a href="/docs/Theta/ThetaSparkExample.html">•Theta Sketch Spark Example</a></li> |
| <li><a href="/docs/Theta/ThetaPigUDFs.html">•Theta Sketch Pig UDFs</a></li> |
| <li><a href="/docs/Theta/ThetaHiveUDFs.html">•Theta Sketch Hive UDFs</a></li> |
| </div> |
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| <p id="kmv-tutorial"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_kmv_tutorial">KMV Tutorial</a> |
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| <div class="collapse" id="collapse_kmv_tutorial"> |
| <li><a href="/docs/Theta/InverseEstimate.html">•The Inverse Estimate</a></li> |
| <li><a href="/docs/Theta/KMVempty.html">•Empty Sketch</a></li> |
| <li><a href="/docs/Theta/KMVfirstEst.html">•First Estimator</a></li> |
| <li><a href="/docs/Theta/KMVbetterEst.html">•Better Estimator</a></li> |
| <li><a href="/docs/Theta/KMVrejection.html">•Rejection Rules</a></li> |
| <li><a href="/docs/Theta/KMVupdateVkth.html">•Update V(kth) Rule</a></li> |
| </div> |
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| <p id="set-operations-and-p-sampling"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_set_operations_and_p-sampling">Set Operations and P-sampling</a> |
| </p> |
| <div class="collapse" id="collapse_set_operations_and_p-sampling"> |
| <li><a href="/docs/Theta/ThetaSketchSetOps.html">•Set Operations</a></li> |
| <li><a href="/docs/Theta/ThetaSetOpsCornerCases.html">•Model & Test Set Operations</a></li> |
| <li><a href="/docs/Theta/ThetaPSampling.html">•<i>p</i>-Sampling</a></li> |
| </div> |
| |
| <p id="accuracy"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_accuracy">Accuracy</a> |
| </p> |
| <div class="collapse" id="collapse_accuracy"> |
| <li><a href="/docs/Theta/ThetaAccuracy.html">•Basic Accuracy</a></li> |
| <li><a href="/docs/Theta/ThetaAccuracyPlots.html">•Accuracy Plots</a></li> |
| <li><a href="/docs/Theta/ThetaErrorTable.html">•Relative Error Table</a></li> |
| <li><a href="/docs/Theta/ThetaSketchSetOpsAccuracy.html">•SetOp Accuracy</a></li> |
| <li><a href="/docs/Theta/AccuracyOfDifferentKUnions.html">•Unions With Different k</a></li> |
| </div> |
| |
| <p id="size"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_size">Size</a> |
| </p> |
| <div class="collapse" id="collapse_size"> |
| <li><a href="/docs/Theta/ThetaSize.html">•Theta Sketch Size</a></li> |
| </div> |
| |
| <p id="speed"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_speed">Speed</a> |
| </p> |
| <div class="collapse" id="collapse_speed"> |
| <li><a href="/docs/Theta/ThetaUpdateSpeed.html">•Update Speed</a></li> |
| <li><a href="/docs/Theta/ThetaMergeSpeed.html">•Merge Speed</a></li> |
| </div> |
| |
| <p id="theta-sketch-theory"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_sketch_theory">Theta Sketch Theory</a> |
| </p> |
| <div class="collapse" id="collapse_theta_sketch_theory"> |
| <li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/ThetaSketchFramework.pdf">•Theta Sketch Framework (PDF)</a></li> |
| <li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/ThetaSketchEquations.pdf">•Theta Sketch Equations (PDF)</a></li> |
| <li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/DataSketches.pdf">•DataSketches (PDF)</a></li> |
| <li><a href="/docs/Theta/ThetaConfidenceIntervals.html">•Confidence Intervals Notes</a></li> |
| <li><a href="/docs/Theta/ThetaMergingAlgorithm.html">•Merging Algorithm Notes</a></li> |
| <li><a href="/docs/Theta/ThetaReferences.html">•Theta References</a></li> |
| </div> |
| </div> |
| |
| <p id="tuple-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_tuple_sketches">Tuple Sketches</a> |
| </p> |
| <div class="collapse" id="collapse_tuple_sketches"> |
| <li><a href="/docs/Tuple/TupleOverview.html">•Tuple Overview</a></li> |
| |
| <p id="tuple-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_tuple_examples">Tuple Examples</a> |
| </p> |
| <div class="collapse" id="collapse_tuple_examples"> |
| <li><a href="/docs/Tuple/TupleJavaExample.html">•Tuple Java Example</a></li> |
| <li><a href="/docs/Tuple/TupleEngagementExample.html">•Tuple Engagement Example</a></li> |
| <li><a href="/docs/Tuple/TuplePigUDFs.html">•Tuple Pig UDFs</a></li> |
| <li><a href="/docs/Tuple/TupleHiveUDFs.html">•Tuple Hive UDFs</a></li> |
| </div> |
| </div> |
| </div> |
| |
| <p id="most-frequent"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_most_frequent">Most Frequent</a> |
| </p> |
| <div class="collapse" id="collapse_most_frequent"> |
| <li><a href="/docs/Frequency/FrequencySketchesOverview.html">•Frequency Sketches Overview</a></li> |
| |
| <p id="frequent-item-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_frequent_item_sketches">Frequent Item Sketches</a> |
| </p> |
| <div class="collapse" id="collapse_frequent_item_sketches"> |
| <li><a href="/docs/Frequency/FrequentItemsOverview.html">•Frequent Items Overview</a></li> |
| <li><a href="/docs/Frequency/FrequentItemsErrorTable.html">•Frequent Items Error Table</a></li> |
| <li><a href="/docs/Frequency/FrequentItemsReferences.html">•Frequent Items References</a></li> |
| <li><a href="/docs/Frequency/FrequentItemsPerformance.html">•Frequent Items Performance</a></li> |
| |
| <p id="most-frequent-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_most_frequent_examples">Most Frequent Examples</a> |
| </p> |
| <div class="collapse" id="collapse_most_frequent_examples"> |
| <li><a href="/docs/Frequency/FrequentItemsJavaExample.html">•Frequent Items Java Example</a></li> |
| <li><a href="/docs/Frequency/FrequentItemsCppExample.html">•Frequent Items C++ Example</a></li> |
| <li><a href="/docs/Frequency/FrequentItemsPigUDFs.html">•Frequent Items Pig UDFs</a></li> |
| <li><a href="/docs/Frequency/FrequentItemsHiveUDFs.html">•Frequent Items Hive UDFs</a></li> |
| </div> |
| </div> |
| |
| <p id="frequent-distinct-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_frequent_distinct_sketches">Frequent Distinct Sketches</a> |
| </p> |
| <div class="collapse" id="collapse_frequent_distinct_sketches"> |
| <li><a href="/docs/Frequency/FrequentDistinctTuplesSketch.html">•Frequent Distinct Tuples Sketch</a></li> |
| </div> |
| </div> |
| |
| <p id="quantiles-and-histograms"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a> |
| </p> |
| <div class="collapse" id="collapse_quantiles_and_histograms"> |
| <li><a href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and Ranks Tutorial</a></li> |
| <li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles Overview</a></li> |
| <li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li> |
| <li><a href="/docs/KLL/KLLAccuracyAndSize.html">•KLL Sketch Accuracy and Size</a></li> |
| <li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li> |
| <li><a href="/docs/Quantiles/OrigQuantilesSketch.html">•Original QuantilesSketch</a></li> |
| |
| <p id="quantiles-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_examples">Quantiles Examples</a> |
| </p> |
| <div class="collapse" id="collapse_quantiles_examples"> |
| <li><a href="/docs/Quantiles/QuantilesJavaExample.html">•Quantiles Sketch Java Example</a></li> |
| <li><a href="/docs/KLL/KLLCppExample.html">•KLL Quantiles Sketch C++ Example</a></li> |
| <li><a href="/docs/Quantiles/QuantilesPigUDFs.html">•Quantiles Sketch Pig UDFs</a></li> |
| <li><a href="/docs/Quantiles/QuantilesHiveUDFs.html">•Quantiles Sketch Hive UDFs</a></li> |
| </div> |
| |
| <p id="quantiles-studies"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_studies">Quantiles Studies</a> |
| </p> |
| <div class="collapse" id="collapse_quantiles_studies"> |
| <li><a href="/docs/QuantilesStudies/DruidApproxHistogramStudy.html">•Druid Approximate Histogram</a></li> |
| <li><a href="/docs/QuantilesStudies/MomentsSketchStudy.html">•Moments Sketch Study</a></li> |
| <li><a href="/docs/QuantilesStudies/QuantilesStreamAStudy.html">•Quantiles StreamA Study</a></li> |
| <li><a href="/docs/QuantilesStudies/ExactQuantiles.html">•Exact Quantiles for Studies</a></li> |
| </div> |
| |
| <p id="quantiles-sketch-theory"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_sketch_theory">Quantiles Sketch Theory</a> |
| </p> |
| <div class="collapse" id="collapse_quantiles_sketch_theory"> |
| <li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/Quantiles_KLL.pdf">•Optimal Quantile Approximation in Streams</a></li> |
| <li><a href="/docs/Quantiles/QuantilesReferences.html">•Quantiles References</a></li> |
| </div> |
| </div> |
| |
| <p id="sampling"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_sampling">Sampling</a> |
| </p> |
| <div class="collapse" id="collapse_sampling"> |
| <li><a href="/docs/Sampling/ReservoirSampling.html">•Reservoir Sampling</a></li> |
| <li><a href="/docs/Sampling/ReservoirSamplingPerformance.html">•Reservoir Sampling Performance</a></li> |
| <li><a href="/docs/Sampling/VarOptSampling.html">•VarOpt Sampling</a></li> |
| |
| <p id="sampling-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_sampling_examples">Sampling Examples</a> |
| </p> |
| <div class="collapse" id="collapse_sampling_examples"> |
| <li><a href="/docs/Sampling/ReservoirSamplingJava.html">•Reservoir Sampling Java Example</a></li> |
| <li><a href="/docs/Sampling/ReservoirSamplingPigUDFs.html">•Reservoir Sampling Pig UDFs</a></li> |
| <li><a href="/docs/Sampling/VarOptSamplingJava.html">•VarOpt Sampling Java Example</a></li> |
| <li><a href="/docs/Sampling/VarOptPigUDFs.html">•VarOpt Sampling Pig UDFs</a></li> |
| </div> |
| </div> |
| </div> |
| |
| <p id="system-integrations"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_system_integrations">System Integrations</a> |
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| <h1 id="kll-sketch-vs-t-digest">KLL sketch vs t-digest</h1> |
| |
| <p>The goal of this article is to do an objective comparison of the KLL quantiles sketch implemented in this library and the <a href="https://github.com/tdunning/t-digest">t-digest</a>.</p> |
| |
| <h2 id="versions">Versions</h2> |
| |
| <ul> |
| <li>KLL sketch form <a href="https://github.com/DataSketches/sketches-core/releases/tag/sketches-core-0.11.1">sketches-core-0.11.1</a></li> |
| <li><a href="https://github.com/tdunning/t-digest/commit/01ea144ca865361be6786fd502bb554c75105e3c">t-digest code as of Sep 14, 2017</a> (there is no published jar)</li> |
| </ul> |
| |
| <h2 id="definition-of-rank">Definition of rank</h2> |
| |
| <p>Consider the stream of <i>n</i> values presented to the sketch. The rank of a value would be its index in the sorted version of the input stream. If we divide the rank by <i>n</i>, it becomes the normalized rank, which is between 0 and 1. Suppose a particular value <i>x</i> is repeated several times. There is a range of ranks in the hypothetical sorted stream that might be assigned to <i>x</i>:</p> |
| |
| <ul> |
| <li><i>min rule</i>: mass of the distribution of values less than <i>x</i></li> |
| <li><i>max rule</i>: mass of the distribution of values less than or equal to <i>x</i></li> |
| <li><i>mid rule</i>: halfway between the <i>min rule</i> and the <i>max rule</i></li> |
| </ul> |
| |
| <p>KLL sketch uses the <i>min rule</i>. If one value is added to the sketch (even repeatedly), its rank is 0.</p> |
| |
| <p>It is not clear what rule t-digest uses. There is a discrepancy between the definition of rank in Javadoc and the implementation. The definition reads (above cdf(x) method in TDigest.java): “returns the fraction of all points added which are <= x”. This would be the <i>max rule</i>. However, there is a helping method in tests that implements the <i>mid rule</i>. Moreover, experiments with streams of the same repeated value show that the <i>min rule</i> might explain the results better (see the plot below), but not exactly. For completeness the comparison was done using all tree rules for t-digest.</p> |
| |
| <p>This plot is to validate the basic assumptions about the sketches. The same repeated value was used as the input. The expected rank error is 0%.</p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-error-same-value.png" alt="same value rank error plot" /></p> |
| |
| <h2 id="size">Size</h2> |
| |
| <p>The starting point in this comparison is a choice of parameters for KLL sketch and t-digest in such a way that they have approximately the same size. It is quite difficult to measure the size of a Java object in memory, therefore the serialized size was used as the best available measure of size, which is also important for many practical applications in large systems. There are two ways to serialize t-digest: asBytes() and asSmallBytes(). It was found that t-digest with compression=100 (recommended in the documentation) approximately matches the size of KLL with the default parameter K=200 if the asBytes() method is used, and compression=200 approximately matches KLL if serialized using asSmallBytes() method. For completeness the comparison was done at both levels of compression.</p> |
| |
| <p>The input for the following size measurements was generated using uniform random values from 0 to 1 (Random.nextFloat() for KLL sketch and Random.nextDouble() for t-digest)</p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-size.png" alt="KLL200 vs TD100 serialized size plot" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td200-size.png" alt="KLL200 vs TD200 serialized size plot" /></p> |
| |
| <h2 id="accuracy">Accuracy</h2> |
| |
| <h3 id="specification-of-error-of-kll-sketch">Specification of error of KLL sketch</h3> |
| |
| <p>The error ε of the KLL sketch is specified as a fraction of the normalized rank of the hypothetical sorted stream of values presented to the sketch.</p> |
| |
| <p>Suppose the sketch is queried using getRank() method to obtain the estimated rank <i>r<sub>est</sub></i> of a value presented to the sketch. If the true rank of this value is <i>r<sub>true</sub></i>, the estimated rank must be within the specified rank error ε of the true rank with 99% probability: |
| | <i>r<sub>est</sub></i> - <i>r<sub>true</sub></i> | < ε</p> |
| |
| <p>KLL sketch has methods to obtain normalized rank error for both single-sided (rank) and double-sided (PMF) queries. The provided rank error is the best fit to 99th percentile of empirically measured maximum error in thousands of trials.</p> |
| |
| <p>Note that KLL sketch does not make any assumptions about the distribution of values. In principle the values do not even have to be numeric. The only requirement is the “less than” relation in the value space. The implementation under test is specialized for values of type float, but the algorithm does not take into account any “distance” in the value space. Therefore there are no error guarantees in terms of values, only the bounds are provided: lower and upper bound values such that the true quantile should be found somewhere between them with 99% probability.</p> |
| |
| <h3 id="specification-of-error-of-t-digest">Specification of error of t-digest</h3> |
| |
| <p>The error of the t-digest is specified, similarly to KLL sketch, as a fraction of the normalized rank.</p> |
| |
| <p>The t-digest algorithm is taking into account the distance between values, but does not provide any accuracy guarantees in the value space.</p> |
| |
| <p>The implementation of t-digest (as of this writing) doesn’t have any methods to obtain rank error or error bounds.</p> |
| |
| <h3 id="accuracy-plots">Accuracy plots</h3> |
| |
| <h4 id="input">Input</h4> |
| |
| <ul> |
| <li>Uniform distribution between 0 and 1 (Random.nextFloat() for KLL sketch and Random.nextDouble() for t-digest)</li> |
| <li>Gaussian distribution with mean 0 and standard deviation 1 (Random.nextGaussian())</li> |
| <li>Growing blocks of repeated values (starts with 1 and 0.001 probability of incrementing, after every increment the probability is decreased by the factor of 0.98)</li> |
| </ul> |
| |
| <h4 id="vertical-scale">Vertical scale</h4> |
| |
| <p>Since t-digest shows rank error up to 100%, Y axis was plotted using logarithmic scale to be able to see details in the sub 1% region. Zero values were substituted with 10<sup>-2</sup>.</p> |
| |
| <h4 id="t-digest-compression100">t-digest compression=100</h4> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-error-uniform.png" alt="KLL200 vs TD100 rank error uniform input" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-error-gaussian.png" alt="KLL200 vs TD100 rank error gaussian input" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-error-blocky.png" alt="KLL200 vs TD100 rank error blocky input" /></p> |
| |
| <h4 id="t-digest-compression200">t-digest compression=200</h4> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td200-error-uniform.png" alt="KLL200 vs TD200 rank error uniform input" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td200-error-gaussian.png" alt="KLL200 vs TD200 rank error gaussian input" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td200-error-blocky.png" alt="KLL200 vs TD200 rank error blocky input" /></p> |
| |
| <h2 id="speed">Speed</h2> |
| |
| <p>The input for the following speed measurements was generated using uniform random values from 0 to 1 (Random.nextFloat() for KLL sketch and Random.nextDouble() for t-digest)</p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-td200-update-time.png" alt="KLL200 vs TD100 and TD200 update time" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-serialize-time.png" alt="KLL200 vs TD100 serialize time" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td200-serialize-time.png" alt="KLL200 vs TD200 serialize time" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td100-deserialize-time.png" alt="KLL200 vs TD100 deserialize time" /></p> |
| |
| <p><img class="doc-img-full" src="/docs/img/kll/kll200-vs-td200-deserialize-time.png" alt="KLL200 vs TD200 deserialize time" /></p> |
| |
| <h2 id="source-code">Source code</h2> |
| |
| <p>The code to reproduce these measurements is available in the <a href="https://github.com/apache/datasketches-characterization">Datasketches/characterization repository</a></p> |
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