[mlpack-svn] r10226 - mlpack/trunk/src/mlpack/methods/linear_regression

[fastlab-svn at coffeetalk-1.cc.gatech.edu]

Author: jcline3
Date: 2011-11-09 17:27:13 -0500 (Wed, 09 Nov 2011)
New Revision: 10226

Modified:
   mlpack/trunk/src/mlpack/methods/linear_regression/linear_regression.cpp
Log:
Better comments, coding style improvements


Modified: mlpack/trunk/src/mlpack/methods/linear_regression/linear_regression.cpp
===================================================================
--- mlpack/trunk/src/mlpack/methods/linear_regression/linear_regression.cpp	2011-11-09 22:06:22 UTC (rev 10225)
+++ mlpack/trunk/src/mlpack/methods/linear_regression/linear_regression.cpp	2011-11-09 22:27:13 UTC (rev 10226)
@@ -10,30 +10,34 @@
   /*
    * We want to calculate the a_i coefficients of:
    * \sum_{i=0}^n (a_i * x_i^i)
-   * We add a row of ones to get a_0, where x_0^0 = 1, the intercept.
+   * In order to get the intercept value, we will add a row of ones.
    */
 
-  // The number of rows
+  // We store the number of rows of the predictors.
+  // Reminder: Armadillo stores the data transposed from how we think of it,
+  //           that is, columns are actually rows (see: column major order).
   size_t n_cols;
-
   n_cols = predictors.n_cols;
 
-  // Add a row of ones, to get the intercept
+  // Here we add the row of ones to the predictors.
   arma::rowvec ones;
   ones.ones(n_cols);
-  predictors.insert_rows(0,ones);
+  predictors.insert_rows(0, ones);
 
-  // Set the parameters to the correct size, all zeros.
+  // We set the parameters to the correct size and initialize them to zero.
   parameters.zeros(n_cols);
 
-  // Compute the QR decomposition
+  // We compute the QR decomposition of the predictors.
+  // We transpose the predictors because they are in column major order.
   arma::mat Q, R;
-  arma::qr(Q,R,arma::trans(predictors));
+  arma::qr(Q, R, arma::trans(predictors));
 
-  // Compute the parameters, R*B=Q^T*responses
-  arma::solve( parameters, R, arma::trans(Q)*responses);
+  // We compute the parameters, B, like so: 
+  // R * B = Q^T * responses
+  // B = Q^T * responses * R^-1
+  arma::solve(parameters, R, arma::trans(Q) * responses);
 
-  // Remove the added row.
+  // We now remove the row of ones we added so the user's data is unmodified.
   predictors.shed_row(0);
 }
 
@@ -48,26 +52,27 @@
 
 void LinearRegression::predict(arma::rowvec& predictions, const arma::mat& points)
 {
-  // The number of columns and rows
+  // We get the number of columns and rows of the dataset.
   size_t n_cols, n_rows;
   n_cols = points.n_cols;
   n_rows = points.n_rows;
 
-  // Sanity check
+  // We want to be sure we have the correct number of dimensions in the dataset.
   assert(n_rows == parameters.n_rows - 1);
 
   predictions.zeros(n_cols);
-  // Set to a_0
+  // We set all the predictions to the intercept value initially.
   predictions += parameters(0);
 
-  // Iterate through the dimensions
-  for(size_t i = 1; i < n_rows+1; ++i)
+  // Now we iterate through the dimensions of the data and parameters.
+  for(size_t i = 1; i < n_rows + 1; ++i)
   {
-    // Iterate through the datapoints
+    // Now we iterate through each row, or point, of the data.
     for(size_t j = 0; j < n_cols; ++j)
     {
-      // Add in the next term: a_i * x_i
-      predictions(j) += parameters(i) * points(i-1,j);
+      // Increment each prediction value by x_i * a_i, or the next dimensional 
+      // coefficient and x value. 
+      predictions(j) += parameters(i) * points(i - 1, j);
 
     }
   }