| <!DOCTYPE html> |
| <!-- Start _layouts/doc_page.html--> |
| <html lang="en"> |
| |
| <head> |
| <!-- Start _include/site_head.html --> |
| <meta charset="UTF-8" /> |
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> |
| <meta name="description" content=""> |
| <meta name="author" content="datasketches"> |
| |
| <title>DataSketches | </title> |
| |
| <link rel="shortcut icon" href="/img/favicon.png"> |
| |
| <!-- original source: https://maxcdn.bootstrapcdn.com/font-awesome/4.1.0/css/font-awesome.min.css --> |
| <link rel="stylesheet" href="/css/font-awesome.min.css"> |
| <!-- original source: https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css --> |
| <link rel="stylesheet" href="/css/bootstrap.min.css"> |
| |
| <link rel="stylesheet" href="/css/fonts.css" type="text/css"> |
| |
| <link rel="stylesheet" href="/css/main.css"> |
| <link rel="stylesheet" href="/css/header.css"> |
| <link rel="stylesheet" href="/css/footer.css"> |
| <link rel="stylesheet" href="/css/syntax.css"> |
| <link rel="stylesheet" href="/css/docs.css"> |
| |
| <script type="text/x-mathjax-config"> |
| MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]},showMathMenu:false,showMathMenuMSIE:false,showProcessingMessages:false}); |
| </script> |
| |
| <!-- original source: https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMX_HTML-full --> |
| <script type="text/javascript" src="/js/MathJax.js?config=TeX-AMS_HTML"></script> |
| |
| <!-- original source: https://code.jquery.com/jquery.min.js --> |
| <script src="/js/jquery.min.js"></script> |
| |
| <!-- original source: https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js --> |
| <script src="/js/bootstrap.min.js"></script> <!-- 3.2.0--> |
| <!-- End _include/site_head.html --> |
| |
| </head> |
| |
| <body> |
| <!-- Start _include/nav_bar.html --> |
| <div class="navbar navbar-inverse navbar-static-top ds-nav"> |
| <div class="container"> |
| <div class="navbar-header"> |
| <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse"> |
| <span class="sr-only">Toggle navigation</span> |
| <span class="icon-bar"></span> |
| <span class="icon-bar"></span> |
| <span class="icon-bar"></span> |
| </button> |
| <a href="/" style="padding-top: 0px; padding-bottom: 0px;"> |
| <span class="ds-small-h-logo"></span></a> |
| </div> |
| <div class="navbar-collapse collapse"> |
| <ul class="nav navbar-nav navbar-right"> |
| <li> |
| <a href="/docs/Background/TheChallenge.html"> |
| <span class="fa fa-info-circle"></span> DOCUMENTATION</a> |
| </li> |
| <li> |
| <a href="/docs/Community/Downloads.html"> |
| <span class="fa fa-download"></span> DOWNLOAD</a> |
| </li> |
| <!-- |
| <li> |
| <a href="/docs/Architecture/Components.html"> |
| <span class="fa fa-github"></span> GITHUB</a> |
| </li> |
| --> |
| <li> |
| <a href="/docs/Community/Research.html"> |
| <span class="fa fa-paper-plane"></span> RESEARCH</a> |
| </li> |
| <li> |
| <a href="/docs/Community/index.html" style="padding-top: 0; padding-bottom: 0;"> |
| <img class="ds-small-man" src="/img/datasketches-ManWhite.svg"/>COMMUNITY</a> |
| </li> |
| <li> |
| <ul class="nav navbar-nav navbar-right ds-nav"> |
| <li class="dropdown ds-nav" > |
| <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="false" style="padding-top: 0; padding-bottom: 0;"><img class="apache-logo" src="/img/feather.svg"/>Apache <span class="caret"></span></a> |
| <ul class="dropdown-menu ds-nav"> |
| <li><a href="https://www.apache.org/" target="_blank">Foundation</a></li> |
| <li><a href="https://www.apache.org/events/current-event" target="_blank">Events</a></li> |
| <li><a href="https://www.apache.org/licenses/" target="_blank">License</a></li> |
| <li><a href="https://privacy.apache.org/policies/privacy-policy-public.html" target="_blank">Privacy Policy</a></li> |
| <li><a href="https://www.apache.org/foundation/thanks.html" target="_blank">Thanks</a></li> |
| <li><a href="https://www.apache.org/security/" target="_blank">Security</a></li> |
| <li><a href="https://www.apache.org/foundation/sponsorship.html" target="_blank">Sponsorship</a></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
| </div> |
| </div> |
| <!-- End _include/nav_bar.html --> |
| |
| |
| <!-- Start _include/javadocs.html --> |
| <div class="ds-header"> |
| <div class="container"> |
| <h4>API Snapshots: |
| <a href="https://apache.github.io/datasketches-java/4.2.0/">Java Core</a>, |
| <a href="https://apache.github.io/datasketches-cpp/5.0.0/">C++ Core</a>, |
| <a href="https://apache.github.io/datasketches-python/main/">Python</a>, |
| <a href="https://apache.github.io/datasketches-memory/master/">Memory</a>, |
| <a href="/api/pig/snapshot/apidocs/index.html">Pig</a>, |
| <a href="/api/hive/snapshot/apidocs/index.html">Hive</a>, |
| </h4> |
| </div> |
| </div> |
| <!-- End _include/javadocs.html --> |
| |
| |
| <div class="container"> |
| <div class="row"> |
| <!-- Start ToC Block --> |
| <div class="col-md-3"> |
| <div class="searchbox" style="position:relative"> |
| <gcse:searchbox-only></gcse:searchbox-only> |
| </div> |
| <!-- Start _includes/toc.html --> |
| <!-- Computer Generated File, Do Not Edit! --> |
| <link rel="stylesheet" href="/css/toc.css"> |
| <div id="toc" class="nav toc hidden-print"> |
| |
| <p id="background"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_background">Background</a> |
| </p> |
| <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> |
| </div> |
| |
| <p id="architecture-and-design"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_architecture_and_design">Architecture And Design</a> |
| </p> |
| <div class="collapse" id="collapse_architecture_and_design"> |
| <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> |
| |
| <p id="memory-component"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_memory_component">Memory Component</a> |
| </p> |
| <div class="collapse" id="collapse_memory_component"> |
| <li><a href="/docs/Memory/MemoryComponent.html">•Memory Component</a></li> |
| <li><a href="/docs/Memory/MemoryPerformance.html">•Memory Component Performance</a></li> |
| </div> |
| <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> |
| </div> |
| |
| <p id="sketch-families"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_sketch_families">Sketch Families</a> |
| </p> |
| <div class="collapse" id="collapse_sketch_families"> |
| |
| <p id="distinct-counting"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_distinct_counting">Distinct Counting</a> |
| </p> |
| <div class="collapse" id="collapse_distinct_counting"> |
| <li><a href="/docs/DistinctCountFeaturesMatrix.html">•Features Matrix</a></li> |
| <li><a href="/docs/DistinctCountMeritComparisons.html">•Figures-of-Merit Comparison</a></li> |
| |
| <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> |
| |
| <p id="cpc-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_cpc_examples">CPC Examples</a> |
| </p> |
| <div class="collapse" id="collapse_cpc_examples"> |
| <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> |
| |
| <p id="hyperloglog-sketches"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_hyperloglog_sketches">HyperLogLog Sketches</a> |
| </p> |
| <div class="collapse" id="collapse_hyperloglog_sketches"> |
| <li><a href="/docs/HLL/HLL.html">•HLL Sketch</a></li> |
| <li><a href="/docs/HLL/HllMap.html">•HLL Map Sketch</a></li> |
| |
| <p id="hll-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_hll_examples">HLL Examples</a> |
| </p> |
| <div class="collapse" id="collapse_hll_examples"> |
| <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> |
| |
| <p id="hll-studies"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_hll_studies">HLL Studies</a> |
| </p> |
| <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> |
| </p> |
| <div class="collapse" id="collapse_theta_sketches"> |
| <li><a href="/docs/Theta/ThetaSketchFramework.html">•Theta Sketch Framework</a></li> |
| |
| <p id="theta-examples"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_examples">Theta Examples</a> |
| </p> |
| <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> |
| |
| <p id="kmv-tutorial"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_kmv_tutorial">KMV Tutorial</a> |
| </p> |
| <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> |
| |
| <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> |
| </p> |
| <div class="collapse" id="collapse_system_integrations"> |
| <li><a href="/docs/SystemIntegrations/ApacheDruidIntegration.html">•Using Sketches in ApacheDruid</a></li> |
| <li><a href="/docs/SystemIntegrations/ApacheHiveIntegration.html">•Using Sketches in Apache Hive</a></li> |
| <li><a href="/docs/SystemIntegrations/ApachePigIntegration.html">•Using Sketches in Apache Pig</a></li> |
| <li><a href="/docs/SystemIntegrations/PostgreSQLIntegration.html">•Using Sketches in PostgreSQL</a></li> |
| </div> |
| |
| <p id="community"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_community">Community</a> |
| </p> |
| <div class="collapse" id="collapse_community"> |
| <li><a href="/docs/Community/index.html">•Community</a></li> |
| <li><a href="/docs/Community/Downloads.html">•Downloads</a></li> |
| <li><a href="/docs/Community/NewCommitterProcess.html">•Committer Process</a></li> |
| <li><a href="/docs/Community/ReleaseProcessForCppComponents.html">•Release Process For CPP Components</a></li> |
| <li><a href="/docs/Community/ReleaseProcessForJavaComponents.html">•Release Process For Java Components</a></li> |
| <li><a href="/docs/Community/Transitioning.html">•Transitioning from prior GitHub Site</a></li> |
| </div> |
| |
| <p id="research"> |
| <a data-toggle="collapse" class="menu collapsed" href="#collapse_research">Research</a> |
| </p> |
| <div class="collapse" id="collapse_research"> |
| <li><a href="/docs/Community/Research.html">•Research</a></li> |
| </div> |
| </div> |
| <!-- End _includes/toc.html --> |
| |
| |
| <!-- Start _includes/tocScript.html --> |
| <script> |
| (function () { |
| |
| var findLineItem = function (path) { |
| return document.querySelector(`#toc [href="${path}"]`); |
| }; |
| |
| function findNavItem(path) { |
| return document.querySelector(`.nav [href="${path}"]`); |
| } |
| |
| var highlighLineItem = function (element) { |
| element.classList.add('highlight'); |
| }; |
| |
| var checkHasClass = function (element, className) { |
| return element.className.split(' ').find(function (item) { return item === className || '' }) |
| } |
| |
| var findAllCollapseParents = function (element) { |
| var collapseMenus = []; |
| var elementPointer = element; |
| while (elementPointer !== document.body) { |
| if (checkHasClass(elementPointer, 'collapse')) { |
| collapseMenus.push(elementPointer); |
| } |
| elementPointer = elementPointer.parentElement |
| } |
| return collapseMenus |
| }; |
| |
| var openMenuItem = function (element) { |
| // $(element).collapse('show') would start a transition, adding `in` class instead. |
| element.classList.add('in'); |
| }; |
| |
| var openAllFromList = function (elementList) { |
| elementList.forEach(openMenuItem); |
| }; |
| |
| var highlightAndOpenMenu = function () { |
| // Highlight & expand nav item in the TOC |
| var currentLineItem = findLineItem(document.location.pathname); |
| highlighLineItem(currentLineItem); |
| openAllFromList(findAllCollapseParents(currentLineItem)); |
| |
| // Highlight nav item in top navigation |
| highlighLineItem(findNavItem(document.location.pathname)); |
| }; |
| |
| $(highlightAndOpenMenu); |
| |
| }()); |
| </script> |
| <!-- End _includes/tocScript.html --> |
| |
| </div> |
| <!-- End ToC Block --> |
| <div class="col-md-9 doc-content"> |
| <!-- |
| Licensed to the Apache Software Foundation (ASF) under one |
| or more contributor license agreements. See the NOTICE file |
| distributed with this work for additional information |
| regarding copyright ownership. The ASF licenses this file |
| to you under the Apache License, Version 2.0 (the |
| "License"); you may not use this file except in compliance |
| with the License. You may obtain a copy of the License at |
| |
| http://www.apache.org/licenses/LICENSE-2.0 |
| |
| Unless required by applicable law or agreed to in writing, |
| software distributed under the License is distributed on an |
| "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY |
| KIND, either express or implied. See the License for the |
| specific language governing permissions and limitations |
| under the License. |
| --> |
| <h1 id="druid-approximate-histogram-study">Druid Approximate Histogram Study</h1> |
| |
| <p>The goal of this article is to compare the accuracy performance of the Druid built-in Approximate Histogram to an exact, brute-force computation using actual data extracted from one of our back-end servers.</p> |
| |
| <p>Please get familiar with the <a href="/docs/Quantiles/Definitions.html">Definitions</a> for quantiles.</p> |
| |
| <p>Compare this study with the DataSketches <a href="/docs/QuantilesStudies/QuantilesStreamAStudy.html">Quantiles StreamA Study</a> with the same input data.</p> |
| |
| <h2 id="versions">Versions</h2> |
| |
| <ul> |
| <li>Druid <a href="https://github.com/apache/druid/blob/master/extensions-core/histogram/src/main/java/org/apache/druid/query/aggregation/histogram/ApproximateHistogram.java">ApproximateHistogram.java Nov 6, 2018</a></li> |
| </ul> |
| |
| <h2 id="the-paper">The Paper</h2> |
| |
| <p>The implementation of this Approximate Histogram was based on the February, 2010 |
| <a href="http://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf">paper</a> |
| by Yael Ben-Haim and Elad Tom-Tov of the IBM Haifa Research Lab. However, it should be noted that the authors of the paper specifially mention two caveats:</p> |
| |
| <ul> |
| <li>“The second category, to which our algorithm belongs, consists of heuristics that work well empirically and demand low amounts of space, but lack any rigorous accuracy analysis.” Page 856, section 2.4.1.</li> |
| <li>“…when the data distribution is highly skewed, the accuracy of [our] on-line histogram decays …[so] practitioners may prefer to resort to guaranteed accuracy algorithms.” Page 857, first paragraph.</li> |
| </ul> |
| |
| <p>Unfortunately, a lot of the data that we tend to analyze is highly skewed so these caveats don’t bode well for this study. Nonetheless, we thought it would be useful to test it anyway.</p> |
| |
| <h2 id="the-input-data">The Input Data</h2> |
| <p>The data file used for this evaluation, <em>streamA.txt</em>, is real data extracted from one of our back-end servers. It represents one hour of web-site time-spent data measured in milliseconds. The data in this file has a smooth and well-behaved value distribution with a wide dynamic range. It is a text file and consists of consecutive strings of numeric values separated by a line-feeds. Its size is about 2GB.</p> |
| |
| <h2 id="creating-the-exact-cdf-and-histograms-for-comparison">Creating the Exact CDF and Histograms For Comparison</h2> |
| <p>In order to measure the accuracy of the Approximate Histogram, we need an exact, brute-force analysis of <em>streamA.txt</em>.</p> |
| |
| <p>The process for creating these comparison standards can be found <a href="/docs/QuantilesStudies/ExactQuantiles.html">here</a>.</p> |
| |
| <h2 id="the-results">The Results</h2> |
| |
| <p><img class="doc-img-full" src="/docs/img/quantiles/DruidAH_StreamA_CDF.png" alt="Druid Approx Hist CDF of ranks to quantiles" /></p> |
| |
| <p>The green dots in the above plot represents the Exact cumulative distribution (CDF) of ranks to quantile values. The black circles in the upper right corner of the plot represent the values returned from the Approximate Histogram <em>getQuantiles(float[])</em> function.</p> |
| |
| <p>The plot reveals a dramatic failure of the Approximate Histogram. Below rank = 0.89, the returned array had all zeros.</p> |
| |
| <p>The next plot is the Histogram generated from the values returned by the <em>Histogram</em> class generated by the <em>toHistogram(float[])</em> function.</p> |
| |
| <p><img class="doc-img-full" src="/docs/img/quantiles/DruidAH_StreamA_PMF1.png" alt="Druid Approx Hist PMF of values to counts" /></p> |
| |
| <p>Compared to the true histogram (green bars) the histogram produced by the AH algorithm is highly distorted. Note that the green spike at the low end is caused by zeros in the raw data, which is a common occurrence in a lot of data we collect. To make the distortion easier to visualize the same data are plotted using lines instead of bars as in the following:</p> |
| |
| <p><img class="doc-img-full" src="/docs/img/quantiles/DruidAH_StreamA_PMF2.png" alt="Druid Approx Hist PMF of values to counts" /></p> |
| |
| <p>Note that the Approximate Histogram tool gives the user no warning that these serious distortions might be occurring, it just fails silently.</p> |
| |
| <p>Users would be well-advised to not use this tool for serious analysis.</p> |
| |
| <h2 id="the-evaluation-source">The Evaluation Source</h2> |
| <p>The following are used to create the plots above.</p> |
| |
| <ul> |
| <li><a href="https://github.com/DataSketches/characterization/blob/master/src/main/java/org/apache/datasketches/characterization/quantiles/DruidAppHistStreamAProfile.java">Approximate Histogram profiler</a></li> |
| <li><a href="https://github.com/DataSketches/characterization/blob/master/src/main/resources/quantiles/DruidAHStreamAJob.conf">AH profiler config</a></li> |
| <li><a href="https://github.com/DataSketches/characterization/blob/master/streamA.txt.zip">StreamA Data file</a> This is stored using git-lfs.</li> |
| </ul> |
| |
| <p>Run the above profilers as a java application and supply the config file as the single argument. The program will check if the data file has been unzipped, and if not it will unzip it for you.</p> |
| |
| |
| </div> <!-- End content --> |
| </div> <!-- End row --> |
| </div> <!-- End Container --> |
| |
| <!-- Start _include/page_footer.html --> |
| <footer class="ds-footer"> |
| <div class="container"> |
| <div class="text-center"> |
| <p> |
| <div>Copyright © 2024 <a href="https://www.apache.org">Apache Software Foundation</a>, |
| Licensed under the Apache License, Version 2.0. All Rights Reserved. |
| | <a href="https://privacy.apache.org/policies/privacy-policy-public.html">Privacy Policy</a><br/> |
| Apache DataSketches, Apache, the Apache feather logo, and the Apache DataSketches project logos are trademarks of The Apache Software Foundation.<br/> |
| All other marks mentioned may be trademarks or registered trademarks of their respective owners. |
| </div> |
| </p> |
| </div> |
| </div> |
| </footer> |
| <!-- End _include/page_footer.html --> |
| |
| </body> |
| |
| </html> |
| <!-- End _layouts/doc_page.html--> |
