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Posted to commits@flink.apache.org by mx...@apache.org on 2015/07/01 12:01:23 UTC
[31/54] [partial] flink-web git commit: Revert "[hotfix] Manual build
of docs"
http://git-wip-us.apache.org/repos/asf/flink-web/blob/f0ac0cdb/content/docs/0.9/libs/index.html
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http://git-wip-us.apache.org/repos/asf/flink-web/blob/f0ac0cdb/content/docs/0.9/libs/ml/als.html
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- </ul>
- </li>
- <li><a href="#parameters" id="markdown-toc-parameters">Parameters</a></li>
- <li><a href="#examples" id="markdown-toc-examples">Examples</a></li>
-</ul>
-
-<h2 id="description">Description</h2>
-
-<p>The alternating least squares (ALS) algorithm factorizes a given matrix $R$ into two factors $U$ and $V$ such that $R \approx U^TV$.
-The unknown row dimension is given as a parameter to the algorithm and is called latent factors.
-Since matrix factorization can be used in the context of recommendation, the matrices $U$ and $V$ can be called user and item matrix, respectively.
-The $i$th column of the user matrix is denoted by $u_i$ and the $i$th column of the item matrix is $v_i$.
-The matrix $R$ can be called the ratings matrix with <script type="math/tex">(R)_{i,j} = r_{i,j}</script>.</p>
-
-<p>In order to find the user and item matrix, the following problem is solved:</p>
-
-<script type="math/tex; mode=display">\arg\min_{U,V} \sum_{\{i,j\mid r_{i,j} \not= 0\}} \left(r_{i,j} - u_{i}^Tv_{j}\right)^2 +
-\lambda \left(\sum_{i} n_{u_i} \left\lVert u_i \right\rVert^2 + \sum_{j} n_{v_j} \left\lVert v_j \right\rVert^2 \right)</script>
-
-<p>with $\lambda$ being the regularization factor, <script type="math/tex">n_{u_i}</script> being the number of items the user $i$ has rated and <script type="math/tex">n_{v_j}</script> being the number of times the item $j$ has been rated.
-This regularization scheme to avoid overfitting is called weighted-$\lambda$-regularization.
-Details can be found in the work of <a href="http://dx.doi.org/10.1007/978-3-540-68880-8_32">Zhou et al.</a>.</p>
-
-<p>By fixing one of the matrices $U$ or $V$, we obtain a quadratic form which can be solved directly.
-The solution of the modified problem is guaranteed to monotonically decrease the overall cost function.
-By applying this step alternately to the matrices $U$ and $V$, we can iteratively improve the matrix factorization.</p>
-
-<p>The matrix $R$ is given in its sparse representation as a tuple of $(i, j, r)$ where $i$ denotes the row index, $j$ the column index and $r$ is the matrix value at position $(i,j)$.</p>
-
-<h2 id="operations">Operations</h2>
-
-<p><code>ALS</code> is a <code>Predictor</code>.
-As such, it supports the <code>fit</code> and <code>predict</code> operation.</p>
-
-<h3 id="fit">Fit</h3>
-
-<p>ALS is trained on the sparse representation of the rating matrix:</p>
-
-<ul>
- <li><code>fit: DataSet[(Int, Int, Double)] => Unit</code></li>
-</ul>
-
-<h3 id="predict">Predict</h3>
-
-<p>ALS predicts for each tuple of row and column index the rating:</p>
-
-<ul>
- <li><code>predict: DataSet[(Int, Int)] => DataSet[(Int, Int, Double)]</code></li>
-</ul>
-
-<h2 id="parameters">Parameters</h2>
-
-<p>The alternating least squares implementation can be controlled by the following parameters:</p>
-
-<table class="table table-bordered">
- <thead>
- <tr>
- <th class="text-left" style="width: 20%">Parameters</th>
- <th class="text-center">Description</th>
- </tr>
- </thead>
-
- <tbody>
- <tr>
- <td><strong>NumFactors</strong></td>
- <td>
- <p>
- The number of latent factors to use for the underlying model.
- It is equivalent to the dimension of the calculated user and item vectors.
- (Default value: <strong>10</strong>)
- </p>
- </td>
- </tr>
- <tr>
- <td><strong>Lambda</strong></td>
- <td>
- <p>
- Regularization factor. Tune this value in order to avoid overfitting or poor performance due to strong generalization.
- (Default value: <strong>1</strong>)
- </p>
- </td>
- </tr>
- <tr>
- <td><strong>Iterations</strong></td>
- <td>
- <p>
- The maximum number of iterations.
- (Default value: <strong>10</strong>)
- </p>
- </td>
- </tr>
- <tr>
- <td><strong>Blocks</strong></td>
- <td>
- <p>
- The number of blocks into which the user and item matrix are grouped.
- The fewer blocks one uses, the less data is sent redundantly.
- However, bigger blocks entail bigger update messages which have to be stored on the heap.
- If the algorithm fails because of an OutOfMemoryException, then try to increase the number of blocks.
- (Default value: <strong>None</strong>)
- </p>
- </td>
- </tr>
- <tr>
- <td><strong>Seed</strong></td>
- <td>
- <p>
- Random seed used to generate the initial item matrix for the algorithm.
- (Default value: <strong>0</strong>)
- </p>
- </td>
- </tr>
- <tr>
- <td><strong>TemporaryPath</strong></td>
- <td>
- <p>
- Path to a temporary directory into which intermediate results are stored.
- If this value is set, then the algorithm is split into two preprocessing steps, the ALS iteration and a post-processing step which calculates a last ALS half-step.
- The preprocessing steps calculate the <code>OutBlockInformation</code> and <code>InBlockInformation</code> for the given rating matrix.
- The results of the individual steps are stored in the specified directory.
- By splitting the algorithm into multiple smaller steps, Flink does not have to split the available memory amongst too many operators.
- This allows the system to process bigger individual messages and improves the overall performance.
- (Default value: <strong>None</strong>)
- </p>
- </td>
- </tr>
- </tbody>
- </table>
-
-<h2 id="examples">Examples</h2>
-
-<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="c1">// Read input data set from a csv file</span>
-<span class="k">val</span> <span class="n">inputDS</span><span class="k">:</span> <span class="kt">DataSet</span><span class="o">[(</span><span class="kt">Int</span>, <span class="kt">Int</span>, <span class="kt">Double</span><span class="o">)]</span> <span class="k">=</span> <span class="n">env</span><span class="o">.</span><span class="n">readCsvFile</span><span class="o">[(</span><span class="kt">Int</span>, <span class="kt">Int</span>, <span class="kt">Double</span><span class="o">)](</span>
- <span class="n">pathToTrainingFile</span><span class="o">)</span>
-
-<span class="c1">// Setup the ALS learner</span>
-<span class="k">val</span> <span class="n">als</span> <span class="k">=</span> <span class="nc">ALS</span><span class="o">()</span>
-<span class="o">.</span><span class="n">setIterations</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
-<span class="o">.</span><span class="n">setNumFactors</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span>
-<span class="o">.</span><span class="n">setBlocks</span><span class="o">(</span><span class="mi">100</span><span class="o">)</span>
-<span class="o">.</span><span class="n">setTemporaryPath</span><span class="o">(</span><span class="s">"hdfs://tempPath"</span><span class="o">)</span>
-
-<span class="c1">// Set the other parameters via a parameter map</span>
-<span class="k">val</span> <span class="n">parameters</span> <span class="k">=</span> <span class="nc">ParameterMap</span><span class="o">()</span>
-<span class="o">.</span><span class="n">add</span><span class="o">(</span><span class="nc">ALS</span><span class="o">.</span><span class="nc">Lambda</span><span class="o">,</span> <span class="mf">0.9</span><span class="o">)</span>
-<span class="o">.</span><span class="n">add</span><span class="o">(</span><span class="nc">ALS</span><span class="o">.</span><span class="nc">Seed</span><span class="o">,</span> <span class="mi">42L</span><span class="o">)</span>
-
-<span class="c1">// Calculate the factorization</span>
-<span class="n">als</span><span class="o">.</span><span class="n">fit</span><span class="o">(</span><span class="n">inputDS</span><span class="o">,</span> <span class="n">parameters</span><span class="o">)</span>
-
-<span class="c1">// Read the testing data set from a csv file</span>
-<span class="k">val</span> <span class="n">testingDS</span><span class="k">:</span> <span class="kt">DataSet</span><span class="o">[(</span><span class="kt">Int</span>, <span class="kt">Int</span><span class="o">)]</span> <span class="k">=</span> <span class="n">env</span><span class="o">.</span><span class="n">readCsvFile</span><span class="o">[(</span><span class="kt">Int</span>, <span class="kt">Int</span><span class="o">)](</span><span class="n">pathToData</span><span class="o">)</span>
-
-<span class="c1">// Calculate the ratings according to the matrix factorization</span>
-<span class="k">val</span> <span class="n">predictedRatings</span> <span class="k">=</span> <span class="n">als</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">testingDS</span><span class="o">)</span></code></pre></div>
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-
-
-
-<p>The Flink community highly appreciates all sorts of contributions to FlinkML.
-FlinkML offers people interested in machine learning to work on a highly active open source project which makes scalable ML reality.
-The following document describes how to contribute to FlinkML.</p>
-
-<ul id="markdown-toc">
- <li><a href="#getting-started" id="markdown-toc-getting-started">Getting Started</a></li>
- <li><a href="#pick-a-topic" id="markdown-toc-pick-a-topic">Pick a Topic</a></li>
- <li><a href="#testing" id="markdown-toc-testing">Testing</a></li>
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- <li><a href="#contributing" id="markdown-toc-contributing">Contributing</a></li>
-</ul>
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-<h2 id="getting-started">Getting Started</h2>
-
-<p>In order to get started first read Flink’s <a href="http://flink.apache.org/how-to-contribute.html">contribution guide</a>.
-Everything from this guide also applies to FlinkML.</p>
-
-<h2 id="pick-a-topic">Pick a Topic</h2>
-
-<p>If you are looking for some new ideas you should first look into our <a href="vision_roadmap.html#Roadmap">roadmap</a>, then you should check out the list of <a href="https://issues.apache.org/jira/issues/?jql=component%20%3D%20%22Machine%20Learning%20Library%22%20AND%20project%20%3D%20FLINK%20AND%20resolution%20%3D%20Unresolved%20ORDER%20BY%20priority%20DESC">unresolved issues on JIRA</a>.
-Once you decide to contribute to one of these issues, you should take ownership of it and track your progress with this issue.
-That way, the other contributors know the state of the different issues and redundant work is avoided.</p>
-
-<p>If you already know what you want to contribute to FlinkML all the better.
-It is still advisable to create a JIRA issue for your idea to tell the Flink community what you want to do, though.</p>
-
-<h2 id="testing">Testing</h2>
-
-<p>New contributions should come with tests to verify the correct behavior of the algorithm.
-The tests help to maintain the algorithm’s correctness throughout code changes, e.g. refactorings.</p>
-
-<p>We distinguish between unit tests, which are executed during Maven’s test phase, and integration tests, which are executed during maven’s verify phase.
-Maven automatically makes this distinction by using the following naming rules:
-All test cases whose class name ends with a suffix fulfilling the regular expression <code>(IT|Integration)(Test|Suite|Case)</code>, are considered integration tests.
-The rest are considered unit tests and should only test behavior which is local to the component under test.</p>
-
-<p>An integration test is a test which requires the full Flink system to be started.
-In order to do that properly, all integration test cases have to mix in the trait <code>FlinkTestBase</code>.
-This trait will set the right <code>ExecutionEnvironment</code> so that the test will be executed on a special <code>FlinkMiniCluster</code> designated for testing purposes.
-Thus, an integration test could look the following:</p>
-
-<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">class</span> <span class="nc">ExampleITSuite</span> <span class="k">extends</span> <span class="nc">FlatSpec</span> <span class="k">with</span> <span class="nc">FlinkTestBase</span> <span class="o">{</span>
- <span class="n">behavior</span> <span class="n">of</span> <span class="s">"An example algorithm"</span>
-
- <span class="n">it</span> <span class="n">should</span> <span class="s">"do something"</span> <span class="n">in</span> <span class="o">{</span>
- <span class="o">...</span>
- <span class="o">}</span>
-<span class="o">}</span></code></pre></div>
-
-<p>The test style does not have to be <code>FlatSpec</code> but can be any other scalatest <code>Suite</code> subclass.
-See <a href="http://scalatest.org/user_guide/selecting_a_style">ScalaTest testing styles</a> for more information.</p>
-
-<h2 id="documentation">Documentation</h2>
-
-<p>When contributing new algorithms, it is required to add code comments describing the way the algorithm works and its parameters with which the user can control its behavior.
-Additionally, we would like to encourage contributors to add this information to the online documentation.
-The online documentation for FlinkML’s components can be found in the directory <code>docs/libs/ml</code>.</p>
-
-<p>Every new algorithm is described by a single markdown file.
-This file should contain at least the following points:</p>
-
-<ol>
- <li>What does the algorithm do</li>
- <li>How does the algorithm work (or reference to description)</li>
- <li>Parameter description with default values</li>
- <li>Code snippet showing how the algorithm is used</li>
-</ol>
-
-<p>In order to use latex syntax in the markdown file, you have to include <code>mathjax: include</code> in the YAML front matter.</p>
-
-<div class="highlight"><pre><code class="language-java" data-lang="java"><span class="o">---</span>
-<span class="nl">mathjax:</span> <span class="n">include</span>
-<span class="nl">htmlTitle:</span> <span class="n">FlinkML</span> <span class="o">-</span> <span class="n">Example</span> <span class="n">title</span>
-<span class="nl">title:</span> <span class="o"><</span><span class="n">a</span> <span class="n">href</span><span class="o">=</span><span class="s">"../ml"</span><span class="o">></span><span class="n">FlinkML</span><span class="o"></</span><span class="n">a</span><span class="o">></span> <span class="o">-</span> <span class="n">Example</span> <span class="n">title</span>
-<span class="o">---</span></code></pre></div>
-
-<p>In order to use displayed mathematics, you have to put your latex code in <code>$$ ... $$</code>.
-For in-line mathematics, use <code>$ ... $</code>.
-Additionally some predefined latex commands are included into the scope of your markdown file.
-See <code>docs/_include/latex_commands.html</code> for the complete list of predefined latex commands.</p>
-
-<h2 id="contributing">Contributing</h2>
-
-<p>Once you have implemented the algorithm with adequate test coverage and added documentation, you are ready to open a pull request.
-Details of how to open a pull request can be found <a href="http://flink.apache.org/how-to-contribute.html#contributing-code--documentation">here</a>.</p>
-
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-
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http://git-wip-us.apache.org/repos/asf/flink-web/blob/f0ac0cdb/content/docs/0.9/libs/ml/distance_metrics.html
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- <h1><a href="../ml">FlinkML</a> - Distance Metrics</h1>
-
-
-
-<ul id="markdown-toc">
- <li><a href="#description" id="markdown-toc-description">Description</a></li>
- <li><a href="#built-in-implementations" id="markdown-toc-built-in-implementations">Built-in Implementations</a></li>
- <li><a href="#custom-implementation" id="markdown-toc-custom-implementation">Custom Implementation</a></li>
-</ul>
-
-<h2 id="description">Description</h2>
-
-<p>Different metrics of distance are convenient for different types of analysis. Flink ML provides
-built-in implementations for many standard distance metrics. You can create custom
-distance metrics by implementing the <code>DistanceMetric</code> trait.</p>
-
-<h2 id="built-in-implementations">Built-in Implementations</h2>
-
-<p>Currently, FlinkML supports the following metrics:</p>
-
-<table class="table table-bordered">
- <thead>
- <tr>
- <th class="text-left" style="width: 20%">Metric</th>
- <th class="text-center">Description</th>
- </tr>
- </thead>
-
- <tbody>
- <tr>
- <td><strong>Euclidean Distance</strong></td>
- <td>
- $$d(\x, \y) = \sqrt{\sum_{i=1}^n \left(x_i - y_i \right)^2}$$
- </td>
- </tr>
- <tr>
- <td><strong>Squared Euclidean Distance</strong></td>
- <td>
- $$d(\x, \y) = \sum_{i=1}^n \left(x_i - y_i \right)^2$$
- </td>
- </tr>
- <tr>
- <td><strong>Cosine Similarity</strong></td>
- <td>
- $$d(\x, \y) = 1 - \frac{\x^T \y}{\Vert \x \Vert \Vert \y \Vert}$$
- </td>
- </tr>
- <tr>
- <td><strong>Chebyshev Distance</strong></td>
- <td>
- $$d(\x, \y) = \max_{i}\left(\left \vert x_i - y_i \right\vert \right)$$
- </td>
- </tr>
- <tr>
- <td><strong>Manhattan Distance</strong></td>
- <td>
- $$d(\x, \y) = \sum_{i=1}^n \left\vert x_i - y_i \right\vert$$
- </td>
- </tr>
- <tr>
- <td><strong>Minkowski Distance</strong></td>
- <td>
- $$d(\x, \y) = \left( \sum_{i=1}^{n} \left( x_i - y_i \right)^p \right)^{\rfrac{1}{p}}$$
- </td>
- </tr>
- <tr>
- <td><strong>Tanimoto Distance</strong></td>
- <td>
- $$d(\x, \y) = 1 - \frac{\x^T\y}{\Vert \x \Vert^2 + \Vert \y \Vert^2 - \x^T\y}$$
- with $\x$ and $\y$ being bit-vectors
- </td>
- </tr>
- </tbody>
- </table>
-
-<h2 id="custom-implementation">Custom Implementation</h2>
-
-<p>You can create your own distance metric by implementing the <code>DistanceMetric</code> trait.</p>
-
-<div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">class</span> <span class="nc">MyDistance</span> <span class="k">extends</span> <span class="nc">DistanceMetric</span> <span class="o">{</span>
- <span class="k">override</span> <span class="k">def</span> <span class="n">distance</span><span class="o">(</span><span class="n">a</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">,</span> <span class="n">b</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">)</span> <span class="k">=</span> <span class="o">...</span> <span class="c1">// your implementation for distance metric</span>
-<span class="o">}</span>
-
-<span class="k">object</span> <span class="nc">MyDistance</span> <span class="o">{</span>
- <span class="k">def</span> <span class="n">apply</span><span class="o">()</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">MyDistance</span><span class="o">()</span>
-<span class="o">}</span>
-
-<span class="k">val</span> <span class="n">myMetric</span> <span class="k">=</span> <span class="nc">MyDistance</span><span class="o">()</span></code></pre></div>
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