Apply user-specific regularization instead of uniform regularization …

…in Alternating Least Squares (ALS)

mllib/src/main/scala/org/apache/spark/mllib/recommendation/ALS.scala

@@ -488,6 +488,9 @@ class ALS private (
     val tempXtX = DoubleMatrix.zeros(triangleSize)
     val fullXtX = DoubleMatrix.zeros(rank, rank)
 
+    // Count the number of ratings each user gives to provide user-specific regularization
+    val numRatings = Array.fill(numUsers)(0)
+
     // Compute the XtX and Xy values for each user by adding products it rated in each product
     // block
     for (productBlock <- 0 until numBlocks) {
@@ -500,6 +503,7 @@ class ALS private (
         if (implicitPrefs) {
           var i = 0
           while (i < us.length) {
+            numRatings(us(i)) += 1
             // Extension to the original paper to handle rs(i) < 0. confidence is a function
             // of |rs(i)| instead so that it is never negative:
             val confidence = 1 + alpha * abs(rs(i))
@@ -515,6 +519,7 @@ class ALS private (
         } else {
           var i = 0
           while (i < us.length) {
+            numRatings(us(i)) += 1
             userXtX(us(i)).addi(tempXtX)
             SimpleBlas.axpy(rs(i), x, userXy(us(i)))
             i += 1
@@ -531,9 +536,10 @@ class ALS private (
       // Compute the full XtX matrix from the lower-triangular part we got above
       fillFullMatrix(userXtX(index), fullXtX)
       // Add regularization
+      val regParam = numRatings(index) * lambda
       var i = 0
       while (i < rank) {
-        fullXtX.data(i * rank + i) += lambda
+        fullXtX.data(i * rank + i) += regParam
         i += 1
       }
       // Solve the resulting matrix, which is symmetric and positive-definite