gabrielaozegovic commented on a change in pull request #1070: URL: https://github.com/apache/systemds/pull/1070#discussion_r497412816
########## File path: scripts/builtin/als_ds.dml ########## @@ -0,0 +1,160 @@ +#------------------------------------------------------------- +# +# 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. +# +#------------------------------------------------------------- + +# +# ALS algorithm using a direct solve method for individual least squares problems. This script +# computes an approximate factorization of a low-rank matrix V into two matrices L and R. +# Matrices L and R are computed by minimizing a loss function (with regularization). +# +# INPUT PARAMETERS: +# --------------------------------------------------------------------------------------------- +# NAME TYPE DEFAULT MEANING +# --------------------------------------------------------------------------------------------- +# V String --- Location to read the input matrix V to be factorized +# L String --- Location to write the factor matrix L +# R String --- Location to write the factor matrix R +# 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 FALSE Check for convergence after every iteration, i.e., updating L and R 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 L, where r is the factorization rank +# 2- An r x n matrix R +# + +m_als_ds = function(Matrix[Double] V, Integer rank = 10, String reg = "L2", Double lambda = 0.000001, Integer maxi = 50, Boolean check = FALSE, Double thr = 0.0001, String fmt = "text") + return (Matrix[Double] L, Matrix[Double] R) + { + + r = rank; + max_iter = maxi; + fmt0 = fmt; + + # check the input matrix V, if some rows or columns contain only zeros remove them from V + V_nonzero_ind = V != 0; + row_nonzeros = rowSums (V_nonzero_ind); + col_nonzeros = t (colSums (V_nonzero_ind)); + orig_nonzero_rows_ind = row_nonzeros != 0; + orig_nonzero_cols_ind = col_nonzeros != 0; + num_zero_rows = nrow (V) - sum (orig_nonzero_rows_ind); + num_zero_cols = ncol (V) - sum (orig_nonzero_cols_ind); + if (num_zero_rows > 0) { + print ("Matrix V contains empty rows! These rows will be removed."); + V = removeEmpty (target = V, margin = "rows"); + } + if (num_zero_cols > 0) { + print ("Matrix V contains empty columns! These columns will be removed."); + V = removeEmpty (target = V, margin = "cols"); + } + if (num_zero_rows > 0 | num_zero_cols > 0) { + print ("Recomputing nonzero rows and columns!"); + V_nonzero_ind = V != 0; + row_nonzeros = rowSums (V_nonzero_ind); + col_nonzeros = t (colSums (V_nonzero_ind)); + } + + ###### MAIN PART ###### + m = nrow (V); + n = ncol (V); + + # initializing factor matrices + L = rand (rows = m, cols = r, min = -0.5, max = 0.5); + R = rand (rows = n, cols = r, min = -0.5, max = 0.5); + + # initializing transformed matrices + Vt = t(V); + + # check for regularization + if (reg == "L2") { + print ("BEGIN ALS SCRIPT WITH NONZERO SQUARED LOSS + L2 WITH LAMBDA - " + lambda); + } else if (reg == "wL2") { + print ("BEGIN ALS SCRIPT WITH NONZERO SQUARED LOSS + WEIGHTED L2 WITH LAMBDA - " + lambda); + } else { + stop ("wrong regularization! " + reg); + } + + loss_init = 0.0; # only used if check is TRUE + if (check) { + loss_init = sum (V_nonzero_ind * (V - (L %*% t(R)))^2) + lambda * (sum ((L^2) * row_nonzeros) + sum ((R^2) * col_nonzeros)); + print ("----- Initial train loss: " + loss_init + " -----"); + } + + lambda_I = diag (matrix (lambda, rows = r, cols = 1)); + it = 0; + converged = FALSE; + while ((it < max_iter) & (!converged)) { + it = it + 1; + # keep R fixed and update L + parfor (i in 1:m) { + R_nonzero_ind = t(V[i,] != 0); + R_nonzero = removeEmpty (target=R * R_nonzero_ind, margin="rows"); + A1 = (t(R_nonzero) %*% R_nonzero) + (as.scalar(row_nonzeros[i,1]) * lambda_I); # coefficient matrix + L[i,] = t(solve (A1, t(V[i,] %*% R))); + } + + # keep L fixed and update R + parfor (j in 1:n) { + L_nonzero_ind = t(Vt[j,] != 0) + L_nonzero = removeEmpty (target=L * L_nonzero_ind, margin="rows"); + A2 = (t(L_nonzero) %*% L_nonzero) + (as.scalar(col_nonzeros[j,1]) * lambda_I); # coefficient matrix + R[j,] = t(solve (A2, t(Vt[j,] %*% L))); + } + + # check for convergence + if (check) { + loss_cur = sum (V_nonzero_ind * (V - (L %*% t(R)))^2) + lambda * (sum ((L^2) * row_nonzeros) + sum ((R^2) * col_nonzeros)); + loss_dec = (loss_init - loss_cur) / loss_init; + print ("Train loss at iteration (R) " + it + ": " + loss_cur + " loss-dec " + loss_dec); + if (loss_dec >= 0 & loss_dec < thr | loss_init == 0) { + print ("----- ALS converged after " + it + " iterations!"); + converged = TRUE; + } + loss_init = loss_cur; + } + } # end of while loop + + if (check) { + print ("----- Final train loss: " + loss_init + " -----"); + } + + if (!converged) { + print ("Max iteration achieved but not converged!"); + } + + # inject 0s in L if original V had empty rows + if (num_zero_rows > 0) { + L = removeEmpty (target = diag (orig_nonzero_rows_ind), margin = "cols") %*% L; + } + # inject 0s in R if original V had empty rows + if (num_zero_cols > 0) { + R = removeEmpty (target = diag (orig_nonzero_cols_ind), margin = "cols") %*% R; + } + Rt = t (R); + + } Review comment: Done. ########## 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). Review comment: I changed the description to normal text. ########## File path: scripts/builtin/als_ds.dml ########## @@ -0,0 +1,160 @@ +#------------------------------------------------------------- +# +# 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. +# +#------------------------------------------------------------- + +# +# ALS algorithm using a direct solve method for individual least squares problems. This script Review comment: Done. ---------------------------------------------------------------- This is an automated message from the Apache Git Service. To respond to the message, please log on to GitHub and use the URL above to go to the specific comment. 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