[GitHub] [systemds] gabrielaozegovic commented on a change in pull request #1070: Rewriting ALS functions

[GitBox <gi...@apache.org>]

gabrielaozegovic commented on a change in pull request #1070:
URL: https://github.com/apache/systemds/pull/1070#discussion_r497410970



##########
File path: scripts/builtin/als_cg.dml
##########
@@ -0,0 +1,172 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+#  
+# THIS SCRIPT COMPUTES AN APPROXIMATE FACTORIZATION OF A LOW-RANK MATRIX X INTO TWO MATRICES U AND V
+# USING THE ALTERNATING-LEAST-SQUARES (ALS) ALGORITHM WITH CONJUGATE GRADIENT.
+# MATRICES U AND V ARE COMPUTED BY MINIMIZING A LOSS FUNCTION (WITH REGULARIZATION).
+#
+# INPUT   PARAMETERS:
+# ---------------------------------------------------------------------------------------------
+# NAME    TYPE     DEFAULT  MEANING
+# ---------------------------------------------------------------------------------------------
+# X       String   ---      Location to read the input matrix X to be factorized
+# U       String   ---      Location to write the factor matrix U
+# V       String   ---      Location to write the factor matrix V
+# rank    Int      10       Rank of the factorization
+# reg     String   "L2"	    Regularization: 
+#                           "L2" = L2 regularization;
+#                           "wL2" = weighted L2 regularization
+# lambda  Double   0.000001 Regularization parameter, no regularization if 0.0
+# maxi    Int      50       Maximum number of iterations
+# check   Boolean  TRUE     Check for convergence after every iteration, i.e., updating U and V once
+# thr     Double   0.0001   Assuming check is set to TRUE, the algorithm stops and convergence is declared 
+#                           if the decrease in loss in any two consecutive iterations falls below this threshold; 
+#                           if check is FALSE thr is ignored
+# fmt     String   "text"   The output format of the factor matrices L and R, such as "text" or "csv"
+# ---------------------------------------------------------------------------------------------
+# OUTPUT: 
+# 1- An m x r matrix U, where r is the factorization rank 
+# 2- An r x n matrix V
+#
+# HOW TO INVOKE THIS SCRIPT - EXAMPLE:
+# hadoop jar SystemDS.jar -f ALS-CG.dml -nvargs X=INPUT_DIR/X U=OUTPUT_DIR/U V=OUTPUT_DIR/V rank=10 reg="L2" lambda=0.0001 fmt=csv
+
+
+m_als_cg = function(Matrix[Double] X, Integer rank = 10, String reg = "L2", Double lambda = 0.000001, Integer maxi = 50, Boolean check = TRUE, Double thr = 0.0001, String fmt = "text")
+    return (Matrix[Double] U, Matrix[Double] V)
+    {
+
+    r = rank;
+    max_iter = maxi;
+    fmt0 = fmt;
+
+    ###### MAIN PART ######
+    m = nrow (X);
+    n = ncol (X);
+
+    # initializing factor matrices
+    U = rand (rows = m, cols = r, min = -0.5, max = 0.5); # mxr
+    V = rand (rows = n, cols = r, min = -0.5, max = 0.5); # nxr
+
+    W = (X != 0);
+
+    # check for regularization
+    row_nonzeros = matrix(0,rows=1,cols=1);
+    col_nonzeros = matrix(0,rows=1,cols=1);
+    if( reg == "L2" ) {
+      print ("BEGIN ALS-CG SCRIPT WITH NONZERO SQUARED LOSS + L2 WITH LAMBDA - " + lambda);
+      row_nonzeros = matrix(1, nrow(W), 1);
+      col_nonzeros = matrix(1, ncol(W), 1);
+    }
+    else if( reg == "wL2" ) {
+      print ("BEGIN ALS-CG SCRIPT WITH NONZERO SQUARED LOSS + WEIGHTED L2 WITH LAMBDA - " + lambda);
+      row_nonzeros = rowSums(W);
+      col_nonzeros = t(colSums(W));
+    }
+    else {
+      stop ("wrong regularization! " + reg);
+    }
+
+    # Loss Function with L2:
+    # f (U, V) = 0.5 * sum (W * (U %*% V - X) ^ 2)
+    #          + 0.5 * lambda * (sum (U ^ 2) + sum (V ^ 2))
+    # Loss Function with weighted L2:
+    # f (U, V) = 0.5 * sum (W * (U %*% V - X) ^ 2)
+    #          + 0.5 * lambda * (sum (U ^ 2 * row_nonzeros) + sum (V ^ 2 * col_nonzeros))

Review comment:
       Done.




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