SvenCelin commented on a change in pull request #1071: URL: https://github.com/apache/systemds/pull/1071#discussion_r497408892
########## File path: scripts/builtin/ppca.dml ########## @@ -0,0 +1,154 @@ +#------------------------------------------------------------- +# +# 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 performs Probabilistic Principal Component Analysis (PCA) on the given input data. +# It is based on paper: sPCA: Scalable Principal Component Analysis for Big Data on Distributed +# Platforms. Tarek Elgamal et.al. + +# INPUT PARAMETERS: +# --------------------------------------------------------------------------------------------- +# NAME TYPE DEFAULT MEANING +# --------------------------------------------------------------------------------------------- +# X String --- location to read the matrix X input matrix +# k Int --- indicates dimension of the new vector space constructed from eigen vectors +# tolobj Int 0.00001 objective function tolerance value to stop ppca algorithm +# tolrecerr Int 0.02 reconstruction error tolerance value to stop the algorithm +# iter Int 10 maximum number of iterations +# fmt String 'text' output format of results PPCA such as "text" or "csv" +# hadoop jar SystemDS.jar -f PPCA.dml -nvargs X=/INPUT_DIR/X C=/OUTPUT_DIR/C V=/OUTPUT_DIR/V k=2 tol=0.2 iter=100 +# --------------------------------------------------------------------------------------------- +# OUTPUT PARAMETERS: +# --------------------------------------------------------------------------------------------- +# NAME TYPE DEFAULT MEANING +# --------------------------------------------------------------------------------------------- +# C Matrix --- principal components +# V Matrix --- eigenvalues / eigenvalues of principal components +# + + +m_pcaa = function(Matrix[Double] X, int iter = 10, double tolobj = 0.00001, double tolrecerr = 0.02, String fmt0 = "text") return(Matrix[Double] PC, Matrix[Double] V) + { + k = ncol(X) + n = nrow(X); + m = ncol(X); + + #initializing principal components matrix + C = rand(rows=m, cols=k, pdf="normal"); + ss = rand(rows=1, cols=1, pdf="normal"); + ss = as.scalar(ss); + ssPrev = ss; + + # best selected principle components - with the lowest reconstruction error + PC = C; + + # initilizing reconstruction error + RE = tolrecerr+1; + REBest = RE; + + Z = matrix(0,rows=1,cols=1); + + #Objective function value + ObjRelChng = tolobj+1; + + # mean centered input matrix - dim -> [n,m] + Xm = X - colMeans(X); + + #I -> k x k + ITMP = matrix(1,rows=k,cols=1); + I = diag(ITMP); + + i = 0; + while (i < iter & ObjRelChng > tolobj & RE > tolrecerr){ + #Estimation step - Covariance matrix + #M -> k x k + M = t(C) %*% C + I*ss; + + #Auxilary matrix with n latent variables + # Z -> n x k + Z = Xm %*% (C %*% inv(M)); + + #ZtZ -> k x k + ZtZ = t(Z) %*% Z + inv(M)*ss; + + #XtZ -> m x k + XtZ = t(Xm) %*% Z; + + #Maximization step + #C -> m x k + ZtZ_sum = sum(ZtZ); #+n*inv(M)); + C = XtZ/ZtZ_sum; + + #ss2 -> 1 x 1 + ss2 = trace(ZtZ * (t(C) %*% C)); + + #ss3 -> 1 x 1 + ss3 = sum((Z %*% t(C)) %*% t(Xm)); + + #Frobenius norm of reconstruction error -> Euclidean norm + #Fn -> 1 x 1 + Fn = sum(Xm*Xm); + + #ss -> 1 x 1 + ss = (Fn + ss2 - 2*ss3)/(n*m); + + #calculating objective function relative change + ObjRelChng = abs(1 - ss/ssPrev); + #print("Objective Relative Change: " + ObjRelChng + ", Objective: " + ss); 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. For queries about this service, please contact Infrastructure at: [email protected]
