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href="http://github.com/apache/mahout";>Github</a></li>--> - </div><!-- /.container-fluid --> + + + <!--</ul>--> + </div><!-- /.navbar-collapse --> + </div> </nav> -<body> + <div class="container mt-5 pb-4"> -<div id="wrap"> - <body class=""> + <div class="row"> - <div class="container"> - <h1 id="introduction-to-item-based-recommendations-with-hadoop">Introduction to Item-Based Recommendations with Hadoop</h1> + <div class="col-lg-8"> + <h1 id="introduction-to-item-based-recommendations-with-hadoop">Introduction to Item-Based Recommendations with Hadoop</h1> <p>##Overview</p> @@ -248,8 +208,9 @@ <p>Assuming your <em>JAVA_HOME</em> is appropriately set and Mahout was installed properly weâre ready to configure our syntax. Enter the following command:</p> -<pre><code>$ mahout recommenditembased -s SIMILARITY_LOGLIKELIHOOD -i /path/to/input/file -o /path/to/desired/output --numRecommendations 25 +<div class="highlighter-rouge"><pre class="highlight"><code>$ mahout recommenditembased -s SIMILARITY_LOGLIKELIHOOD -i /path/to/input/file -o /path/to/desired/output --numRecommendations 25 </code></pre> +</div> <p>Running the command will execute a series of jobs the final product of which will be an output file deposited to the directory specified in the command syntax. The output file will contain two columns: the <em>userID</em> and an array of <em>itemIDs</em> and scores.</p> @@ -257,30 +218,26 @@ <p>The output file generated in our simple example can be transformed using your tool of choice and consumed by downstream applications. There exist a variety of configuration options for Mahoutâs item based recommender to accommodate custom business requirements; exploring and testing various configurations to suit your needs will doubtless lead to additional questions. Our user community is accessible via our <a href="https://mahout.apache.org/general/mailing-lists,-irc-and-archives.html";>mailing list</a> and the book <em>Mahout In Action</em> is a fantastic (but slightly outdated) starting point.</p> - </div> - + </div> -</div> -<div id="footer"> - <div class="container"> - <p>© 2017 Apache Mahout - with help from <a href="http://jekyllbootstrap.com"; target="_blank" title="The Definitive Jekyll Blogging Framework">Jekyll Bootstrap</a> - and <a href="http://getbootstrap.com"; target="_blank">Bootstrap</a> - </p> </div> -</div> - - +</div> + <footer class="footer bg-light"> + <div class="container text-center small"> + Copyright © 2014-2017 The Apache Software Foundation, Licensed under the Apache License, Version 2.0. + </div> +</footer> + <script src="/assets/vendor/jquery/jquery-slim.min.js"></script> + <script src="/assets/vendor/popper/popper.min.js"></script> + <script src="/assets/vendor/bootstrap/js/bootstrap.min.js"></script> + <script src="/assets/header.js"></script> + <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; type="text/javascript"></script> -<!-- Latest compiled and minified JavaScript, requires jQuery 1.x (2.x not supported in IE8) --> -<!-- Placed at the end of the document so the pages load faster --> -<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js";></script> -<script src="/assets/themes/mahout3/js/bootstrap.min.js"></script> </body> -</html> +</html>
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href="http://github.com/apache/mahout";>Github</a></li>--> - </div><!-- /.container-fluid --> + + + <!--</ul>--> + </div><!-- /.navbar-collapse --> + </div> </nav> -<body> + <div class="container mt-5 pb-4"> -<div id="wrap"> - <body class=""> + <div class="row"> - <div class="container"> - <p><a name="MatrixFactorization-Intro"></a></p> + <div class="col-lg-8"> + <p><a name="MatrixFactorization-Intro"></a></p> <h1 id="introduction-to-matrix-factorization-for-recommendation-mining">Introduction to Matrix Factorization for Recommendation Mining</h1> <p>In the mathematical discipline of linear algebra, a matrix decomposition @@ -213,39 +173,43 @@ There are many different matrix decompositions, each finds use among a particula <p>In mahout, the SVDRecommender provides an interface to build recommender based on matrix factorization. The idea behind is to project the users and items onto a feature space and try to optimize U and M so that U * (M^t) is as close to R as possible:</p> -<pre><code> U is n * p user feature matrix, +<div class="highlighter-rouge"><pre class="highlight"><code> U is n * p user feature matrix, M is m * p item feature matrix, M^t is the conjugate transpose of M, R is n * m rating matrix, n is the number of users, m is the number of items, p is the number of features </code></pre> +</div> <p>We usually use RMSE to represent the deviations between predictions and atual ratings. RMSE is defined as the squared root of the sum of squared errors at each known user item ratings. So our matrix factorization target could be mathmatically defined as:</p> -<pre><code> find U and M, (U, M) = argmin(RMSE) = argmin(pow(SSE / K, 0.5)) +<div class="highlighter-rouge"><pre class="highlight"><code> find U and M, (U, M) = argmin(RMSE) = argmin(pow(SSE / K, 0.5)) SSE = sum(e(u,i)^2) e(u,i) = r(u, i) - U[u,] * (M[i,]^t) = r(u,i) - sum(U[u,f] * M[i,f]), f = 0, 1, .. p - 1 K is the number of known user item ratings. </code></pre> +</div> <p><a name="MatrixFactorization-Factorizers"></a></p> <p>Mahout has implemented matrix factorization based on</p> -<pre><code>(1) SGD(Stochastic Gradient Descent) +<div class="highlighter-rouge"><pre class="highlight"><code>(1) SGD(Stochastic Gradient Descent) (2) ALSWR(Alternating-Least-Squares with Weighted-λ-Regularization). </code></pre> +</div> <h2 id="sgd">SGD</h2> <p>Stochastic gradient descent is a gradient descent optimization method for minimizing an objective function that is written as a su of differentiable functions.</p> -<pre><code> Q(w) = sum(Q_i(w)), +<div class="highlighter-rouge"><pre class="highlight"><code> Q(w) = sum(Q_i(w)), </code></pre> +</div> <p>where w is the parameters to be estimated, Q(w) is the objective function that could be expressed as sum of differentiable functions, @@ -253,14 +217,16 @@ So our matrix factorization target could be mathmatically defined as:</p> <p>In practice, w is estimated using an iterative method at each single sample until an approximate miminum is obtained,</p> -<pre><code> w = w - alpha * (d(Q_i(w))/dw), where aplpha is the learning rate, +<div class="highlighter-rouge"><pre class="highlight"><code> w = w - alpha * (d(Q_i(w))/dw), where aplpha is the learning rate, (d(Q_i(w))/dw) is the first derivative of Q_i(w) on w. </code></pre> +</div> <p>In matrix factorization, the RatingSGDFactorizer class implements the SGD with w = (U, M) and objective function Q(w) = sum(Q(u,i)),</p> -<pre><code> Q(u,i) = sum(e(u,i) * e(u,i)) / 2 + lambda * [(U[u,] * (U[u,]^t)) + (M[i,] * (M[i,]^t))] / 2 +<div class="highlighter-rouge"><pre class="highlight"><code> Q(u,i) = sum(e(u,i) * e(u,i)) / 2 + lambda * [(U[u,] * (U[u,]^t)) + (M[i,] * (M[i,]^t))] / 2 </code></pre> +</div> <p>where Q(u, i) is the objecive function for user u and item i, e(u, i) is the error between predicted rating and actual rating, @@ -270,7 +236,7 @@ So our matrix factorization target could be mathmatically defined as:</p> <p>The algorithm is sketched as follows:</p> -<pre><code> init U and M with randomized value between 0.0 and 1.0 with standard Gaussian distribution +<div class="highlighter-rouge"><pre class="highlight"><code> init U and M with randomized value between 0.0 and 1.0 with standard Gaussian distribution for(iter = 0; iter < numIterations; iter++) { @@ -292,6 +258,7 @@ So our matrix factorization target could be mathmatically defined as:</p> } } </code></pre> +</div> <h2 id="svd">SVD++</h2> @@ -301,18 +268,20 @@ So our matrix factorization target could be mathmatically defined as:</p> <p>The complete model is a sum of 3 sub-models with complete prediction formula as follows:</p> -<pre><code>pr(u,i) = b[u,i] + fm + nm //user u and item i +<div class="highlighter-rouge"><pre class="highlight"><code>pr(u,i) = b[u,i] + fm + nm //user u and item i pr(u,i) is the predicted rating of user u on item i, b[u,i] = U + b(u) + b(i) fm = (q[i,]) * (p[u,] + pow(|N(u)|, -0.5) * sum(y[j,])), j is an item in N(u) nm = pow(|R(i;u;k)|, -0.5) * sum((r[u,j0] - b[u,j0]) * w[i,j0]) + pow(|N(i;u;k)|, -0.5) * sum(c[i,j1]), j0 is an item in R(i;u;k), j1 is an item in N(i;u;k) </code></pre> +</div> <p>The associated regularized squared error function to be minimized is:</p> -<pre><code>{sum((r[u,i] - pr[u,i]) * (r[u,i] - pr[u,i])) - lambda * (b(u) * b(u) + b(i) * b(i) + ||q[i,]||^2 + ||p[u,]||^2 + sum(||y[j,]||^2) + sum(w[i,j0] * w[i,j0]) + sum(c[i,j1] * c[i,j1]))} -</code></pre> +<div class="highlighter-rouge"><pre class="highlight"><code><span class="p">{</span><span class="err">sum((r[u,i]</span><span class="w"> </span><span class="err">-</span><span class="w"> </span><span class="err">pr[u,i])</span><span class="w"> </span><span class="err">*</span><span class="w"> </span><span class="err">(r[u,i]</span><span class="w"> </span><span class="err">-</span><span class="w"> </span><span class="err">pr[u,i]))</span><span class="w"> </span><span class="err">-</span><span class="w"> </span><span class="err">lambda</span><span class="w"> </span><span class="err">*</span><span class="w"> </span><span class="err">(b(u)</span><span class="w"> </span><span class="err">*</span><span class="w"> </span><span class="err">b(u)</span><span class="w"> </span><span class="err">+</span><span class="w"> </span><span class="err">b(i)</span><span class="w"> </span><span class="err">*</span><span class="w"> </span><span class="err">b(i)</span><span class="w"> </span><span class=" err">+</span><span class="w"> </span><span class="err">||q[i,]||^2</span><span class="w"> </span><span class="err">+</span><span class="w"> </span><span class="err">||p[u,]||^2</span><span class="w"> </span><span class="err">+</span><span class="w"> </span><span class="err">sum(||y[j,]||^2)</span><span class="w"> </span><span class="err">+</span><span class="w"> </span><span class="err">sum(w[i,j0]</span><span class="w"> </span><span class="err">*</span><span class="w"> </span><span class="err">w[i,j0])</span><span class="w"> </span><span class="err">+</span><span class="w"> </span><span class="err">sum(c[i,j1]</span><span class="w"> </span><span class="err">*</span><span class="w"> </span><span class="err">c[i,j1]))</span><span class="p">}</span><span class="w"> +</span></code></pre> +</div> <p>b[u,i] is the baseline estimate of user uâs predicted rating on item i. U is usersâ overall average rating and b(u) and b(i) indicate the observed deviations of user u and item iâs ratings from average.</p> @@ -351,12 +320,13 @@ please refer to the paper <a href="http://research.yahoo.com/files/kdd08koren.pd <p>The update to q, p, y in each gradient descent step is:</p> -<pre><code> err(u,i) = r[u,i] - pr[u,i] +<div class="highlighter-rouge"><pre class="highlight"><code> err(u,i) = r[u,i] - pr[u,i] q[i,] = q[i,] + alpha * (err(u,i) * (p[u,] + pow(|N(u)|, -0.5) * sum(y[j,])) - lamda * q[i,]) p[u,] = p[u,] + alpha * (err(u,i) * q[i,] - lambda * p[u,]) for j that is an item in N(u): y[j,] = y[j,] + alpha * (err(u,i) * pow(|N(u)|, -0.5) * q[i,] - lambda * y[j,]) </code></pre> +</div> <p>where alpha is the learning rate of gradient descent, N(u) is the items that user u has expressed preference.</p> @@ -374,8 +344,9 @@ vanilla SGD.</p> <p>ALSWR is an iterative algorithm to solve the low rank factorization of user feature matrix U and item feature matrix M.<br /> The loss function to be minimized is formulated as the sum of squared errors plus <a href="http://en.wikipedia.org/wiki/Tikhonov_regularization";>Tikhonov regularization</a>:</p> -<pre><code> L(R, U, M) = sum(pow((R[u,i] - U[u,]* (M[i,]^t)), 2)) + lambda * (sum(n(u) * ||U[u,]||^2) + sum(n(i) * ||M[i,]||^2)) +<div class="highlighter-rouge"><pre class="highlight"><code> L(R, U, M) = sum(pow((R[u,i] - U[u,]* (M[i,]^t)), 2)) + lambda * (sum(n(u) * ||U[u,]||^2) + sum(n(i) * ||M[i,]||^2)) </code></pre> +</div> <p>At the beginning of the algorithm, M is initialized with the average item ratings as its first row and random numbers for the rest row.</p> @@ -385,14 +356,16 @@ the cost function similarly. The iteration stops until a certain stopping criter <p>To solve the matrix U when M is given, each userâs feature vector is calculated by resolving a regularized linear least square error function using the items the user has rated and their feature vectors:</p> -<pre><code> 1/2 * d(L(R,U,M)) / d(U[u,f]) = 0 +<div class="highlighter-rouge"><pre class="highlight"><code> 1/2 * d(L(R,U,M)) / d(U[u,f]) = 0 </code></pre> +</div> <p>Similary, when M is updated, we resolve a regularized linear least square error function using feature vectors of the users that have rated the item and their feature vectors:</p> -<pre><code> 1/2 * d(L(R,U,M)) / d(M[i,f]) = 0 +<div class="highlighter-rouge"><pre class="highlight"><code> 1/2 * d(L(R,U,M)) / d(M[i,f]) = 0 </code></pre> +</div> <p>The ALSWRFactorizer class is a non-distributed implementation of ALSWR using multi-threading to dispatch the computation among several threads. Mahout also offers a <a href="https://mahout.apache.org/users/recommender/intro-als-hadoop.html";>parallel map-reduce implementation</a>.</p> @@ -405,30 +378,26 @@ Mahout also offers a <a href="https://mahout.apache.org/users/recommender/intro- <p><a href="http://www.hpl.hp.com/personal/Robert_Schreiber/papers/2008%20AAIM%20Netflix/netflix_aaim08%28submitted%29.pdf";>ALSWR</a></p> - </div> - + </div> -</div> -<div id="footer"> - <div class="container"> - <p>© 2017 Apache Mahout - with help from <a href="http://jekyllbootstrap.com"; target="_blank" title="The Definitive Jekyll Blogging Framework">Jekyll Bootstrap</a> - and <a href="http://getbootstrap.com"; target="_blank">Bootstrap</a> - </p> </div> -</div> - - +</div> + <footer class="footer bg-light"> + <div class="container text-center small"> + Copyright © 2014-2017 The Apache Software Foundation, Licensed under the Apache License, Version 2.0. + </div> +</footer> + <script src="/assets/vendor/jquery/jquery-slim.min.js"></script> + 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Overview</h1> <p>Recommenders have changed over the years. Mahout contains a long list of them, which you can still use. But to get the best out of our more modern aproach weâll need to think of the Recommender as a âmodel creationâ componentâsupplied by Mahoutâs new spark-itemsimilarity job, and a âservingâ componentâsupplied by a modern scalable search engine, like Solr.</p> @@ -231,30 +191,26 @@ and <a href="http://occamsmachete.com/ml/2014/09/09/mahout-on-spark-whats-new-i <p>See the page describing <a href="http://mahout.apache.org/users/recommender/intro-cooccurrence-spark.html";><em>spark-itemsimilarity</em></a> for more details.</p> - </div> - + </div> -</div> -<div id="footer"> - <div class="container"> - <p>© 2017 Apache Mahout - with help from <a href="http://jekyllbootstrap.com"; target="_blank" title="The Definitive Jekyll Blogging Framework">Jekyll Bootstrap</a> - and <a href="http://getbootstrap.com"; target="_blank">Bootstrap</a> - </p> </div> -</div> - - +</div> + <footer class="footer bg-light"> + <div class="container text-center small"> + Copyright © 2014-2017 The Apache Software Foundation, Licensed under the Apache License, Version 2.0. + </div> +</footer> + <script src="/assets/vendor/jquery/jquery-slim.min.js"></script> + <script src="/assets/vendor/popper/popper.min.js"></script> + <script src="/assets/vendor/bootstrap/js/bootstrap.min.js"></script> + <script src="/assets/header.js"></script> + <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; type="text/javascript"></script> -<!-- Latest compiled and minified JavaScript, requires jQuery 1.x (2.x not supported in IE8) --> -<!-- Placed at the end of the document so the pages load faster --> -<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js";></script> -<script src="/assets/themes/mahout3/js/bootstrap.min.js"></script> </body> -</html> +</html>
