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The first is standard Multinomial Naive Bayes. The second is an implementation of Transformed Weight-normalized Complement Naive Bayes as introduced by Rennie et al. <a href="http://people.csail.mit.edu/jrennie/papers/icml03-nb.pdf";>[1]</a>. We refer to the former as Bayes and the latter as CBayes.</p> + +<p>Where Bayes has long been a standard in text classification, CBayes is an extension of Bayes that performs particularly well on datasets with skewed classes and has been shown to be competitive with algorithms of higher complexity such as Support Vector Machines.</p> + +<h2 id="implementations">Implementations</h2> +<p>The mahout <code class="highlighter-rouge">math-scala</code> library has an implemetation of both Bayes and CBayes which is further optimized in the <code class="highlighter-rouge">spark</code> module. Currently the Spark optimized version provides CLI drivers for training and testing. Mahout Spark-Naive-Bayes models can also be trained, tested and saved to the filesystem from the Mahout Spark Shell.</p> + +<h2 id="preprocessing-and-algorithm">Preprocessing and Algorithm</h2> + +<p>As described in <a href="http://people.csail.mit.edu/jrennie/papers/icml03-nb.pdf";>[1]</a> Mahout Naive Bayes is broken down into the following steps (assignments are over all possible index values):</p> + +<ul> + <li>Let <code class="highlighter-rouge">\(\vec{d}=(\vec{d_1},...,\vec{d_n})\)</code> be a set of documents; <code class="highlighter-rouge">\(d_{ij}\)</code> is the count of word <code class="highlighter-rouge">\(i\)</code> in document <code class="highlighter-rouge">\(j\)</code>.</li> + <li>Let <code class="highlighter-rouge">\(\vec{y}=(y_1,...,y_n)\)</code> be their labels.</li> + <li>Let <code class="highlighter-rouge">\(\alpha_i\)</code> be a smoothing parameter for all words in the vocabulary; let <code class="highlighter-rouge">\(\alpha=\sum_i{\alpha_i}\)</code>.</li> + <li><strong>Preprocessing</strong>(via seq2Sparse) TF-IDF transformation and L2 length normalization of <code class="highlighter-rouge">\(\vec{d}\)</code> + <ol> + <li><code class="highlighter-rouge">\(d_{ij} = \sqrt{d_{ij}}\)</code></li> + <li><code class="highlighter-rouge">\(d_{ij} = d_{ij}\left(\log{\frac{\sum_k1}{\sum_k\delta_{ik}+1}}+1\right)\)</code></li> + <li><code class="highlighter-rouge">\(d_{ij} =\frac{d_{ij}}{\sqrt{\sum_k{d_{kj}^2}}}\)</code></li> + </ol> + </li> + <li><strong>Training: Bayes</strong><code class="highlighter-rouge">\((\vec{d},\vec{y})\)</code> calculate term weights <code class="highlighter-rouge">\(w_{ci}\)</code> as: + <ol> + <li><code class="highlighter-rouge">\(\hat\theta_{ci}=\frac{d_{ic}+\alpha_i}{\sum_k{d_{kc}}+\alpha}\)</code></li> + <li><code class="highlighter-rouge">\(w_{ci}=\log{\hat\theta_{ci}}\)</code></li> + </ol> + </li> + <li><strong>Training: CBayes</strong><code class="highlighter-rouge">\((\vec{d},\vec{y})\)</code> calculate term weights <code class="highlighter-rouge">\(w_{ci}\)</code> as: + <ol> + <li><code class="highlighter-rouge">\(\hat\theta_{ci} = \frac{\sum_{j:y_j\neq c}d_{ij}+\alpha_i}{\sum_{j:y_j\neq c}{\sum_k{d_{kj}}}+\alpha}\)</code></li> + <li><code class="highlighter-rouge">\(w_{ci}=-\log{\hat\theta_{ci}}\)</code></li> + <li><code class="highlighter-rouge">\(w_{ci}=\frac{w_{ci}}{\sum_i \lvert w_{ci}\rvert}\)</code></li> + </ol> + </li> + <li><strong>Label Assignment/Testing:</strong> + <ol> + <li>Let <code class="highlighter-rouge">\(\vec{t}= (t_1,...,t_n)\)</code> be a test document; let <code class="highlighter-rouge">\(t_i\)</code> be the count of the word <code class="highlighter-rouge">\(t\)</code>.</li> + <li>Label the document according to <code class="highlighter-rouge">\(l(t)=\arg\max_c \sum\limits_{i} t_i w_{ci}\)</code></li> + </ol> + </li> +</ul> + +<p>As we can see, the main difference between Bayes and CBayes is the weight calculation step. Where Bayes weighs terms more heavily based on the likelihood that they belong to class <code class="highlighter-rouge">\(c\)</code>, CBayes seeks to maximize term weights on the likelihood that they do not belong to any other class.</p> + +<h2 id="running-from-the-command-line">Running from the command line</h2> + +<p>Mahout provides CLI drivers for all above steps. Here we will give a simple overview of Mahout CLI commands used to preprocess the data, train the model and assign labels to the training set. An <a href="https://github.com/apache/mahout/blob/master/examples/bin/classify-20newsgroups.sh";>example script</a> is given for the full process from data acquisition through classification of the classic <a href="https://mahout.apache.org/users/classification/twenty-newsgroups.html";>20 Newsgroups corpus</a>.</p> + +<ul> + <li> + <p><strong>Preprocessing:</strong> +For a set of Sequence File Formatted documents in PATH_TO_SEQUENCE_FILES the <a href="https://mahout.apache.org/users/basics/creating-vectors-from-text.html";>mahout seq2sparse</a> command performs the TF-IDF transformations (-wt tfidf option) and L2 length normalization (-n 2 option) as follows:</p> + + <div class="highlighter-rouge"><pre class="highlight"><code> $ mahout seq2sparse + -i ${PATH_TO_SEQUENCE_FILES} + -o ${PATH_TO_TFIDF_VECTORS} + -nv + -n 2 + -wt tfidf +</code></pre> + </div> + </li> + <li> + <p><strong>Training:</strong> +The model is then trained using <code class="highlighter-rouge">mahout spark-trainnb</code>. The default is to train a Bayes model. The -c option is given to train a CBayes model:</p> + + <div class="highlighter-rouge"><pre class="highlight"><code> $ mahout spark-trainnb + -i ${PATH_TO_TFIDF_VECTORS} + -o ${PATH_TO_MODEL} + -ow + -c +</code></pre> + </div> + </li> + <li> + <p><strong>Label Assignment/Testing:</strong> +Classification and testing on a holdout set can then be performed via <code class="highlighter-rouge">mahout spark-testnb</code>. Again, the -c option indicates that the model is CBayes:</p> + + <div class="highlighter-rouge"><pre class="highlight"><code> $ mahout spark-testnb + -i ${PATH_TO_TFIDF_TEST_VECTORS} + -m ${PATH_TO_MODEL} + -c +</code></pre> + </div> + </li> +</ul> + +<h2 id="command-line-options">Command line options</h2> + +<ul> + <li> + <p><strong>Preprocessing:</strong> <em>note: still reliant on MapReduce seq2sparse</em></p> + + <p>Only relevant parameters used for Bayes/CBayes as detailed above are shown. Several other transformations can be performed by <code class="highlighter-rouge">mahout seq2sparse</code> and used as input to Bayes/CBayes. For a full list of <code class="highlighter-rouge">mahout seq2Sparse</code> options see the <a href="https://mahout.apache.org/users/basics/creating-vectors-from-text.html";>Creating vectors from text</a> page.</p> + + <div class="highlighter-rouge"><pre class="highlight"><code> $ mahout seq2sparse + --output (-o) output The directory pathname for output. + --input (-i) input Path to job input directory. + --weight (-wt) weight The kind of weight to use. Currently TF + or TFIDF. Default: TFIDF + --norm (-n) norm The norm to use, expressed as either a + float or "INF" if you want to use the + Infinite norm. Must be greater or equal + to 0. The default is not to normalize + --overwrite (-ow) If set, overwrite the output directory + --sequentialAccessVector (-seq) (Optional) Whether output vectors should + be SequentialAccessVectors. If set true + else false + --namedVector (-nv) (Optional) Whether output vectors should + be NamedVectors. If set true else false +</code></pre> + </div> + </li> + <li> + <p><strong>Training:</strong></p> + + <div class="highlighter-rouge"><pre class="highlight"><code> $ mahout spark-trainnb + --input (-i) input Path to job input directory. + --output (-o) output The directory pathname for output. + --trainComplementary (-c) Train complementary? Default is false. + --master (-ma) Spark Master URL (optional). Default: "local". + Note that you can specify the number of + cores to get a performance improvement, + for example "local[4]" + --help (-h) Print out help +</code></pre> + </div> + </li> + <li> + <p><strong>Testing:</strong></p> + + <div class="highlighter-rouge"><pre class="highlight"><code> $ mahout spark-testnb + --input (-i) input Path to job input directory. + --model (-m) model The path to the model built during training. + --testComplementary (-c) Test complementary? Default is false. + --master (-ma) Spark Master URL (optional). Default: "local". + Note that you can specify the number of + cores to get a performance improvement, + for example "local[4]" + --help (-h) Print out help +</code></pre> + </div> + </li> +</ul> + +<h2 id="examples">Examples</h2> +<ol> + <li><a href="https://github.com/apache/mahout/blob/master/examples/bin/classify-20newsgroups.sh";>20 Newsgroups classification</a></li> + <li><a href="https://github.com/apache/mahout/blob/master/examples/bin/spark-document-classifier.mscala";>Document classification with Naive Bayes in the Mahout shell</a></li> +</ol> + +<h2 id="references">References</h2> + + + </div> + </div> +</div> + <footer class="footer" align="center"> + <div class="container"> + <p> + Copyright © 2014-2016 The Apache Software Foundation, Licensed under + the <a href="http://www.apache.org/licenses/LICENSE-2.0";>Apache License, Version 2.0</a>. + <br /> + Apache Mahout, Mahout, Apache, the Apache feather logo, and the elephant rider logo are either registered trademarks or trademarks of <a href="http://www.apache.org/foundation/marks/";>The Apache Software Foundation</a> in the United States and other countries. + </p> + </div> + </footer> + + <script src="/assets/themes/mahout-retro/js/jquery-1.9.1.min.js"></script> + <script src="/assets/themes/mahout-retro/js/bootstrap.min.js"></script> + <script> + (function() { + var cx = '012254517474945470291:vhsfv7eokdc'; + var gcse = document.createElement('script'); + gcse.type = 'text/javascript'; + gcse.async = true; + gcse.src = (document.location.protocol == 'https:' ? 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