# Collective Matrix Factorization (CMF) Collective matrix factorization (CMF) finds joint low-rank representations for a collection of matrices with shared row or column entities. This package learns a variational Bayesian approximation for CMF, supporting multiple likelihood potentials and missing data, while identifying both factors shared by multiple matrices and factors private for each matrix. package ## Details This package implements a variational Bayesian approximation for CMF, following the presentation in "Group-sparse embeddings in collective matrix factorization" (see references below). The main functionality is provided by the function `CMF()` that is used for learning the model, and by the function `predictCMF()` that estimates missing entries based on the learned model. These functions take as input lists of matrices in a specific sparse format that stores only the observed entries but that explicitly stores zeroes (unlike most sparse matrix representations). For converting between regular matrices and this sparse format see `matrix_to_triplets()` and `triplets_to_matrix()`. The package can also be used to learn Bayesian canonical correlation analysis (CCA) and group factor analysis (GFA) models, both of which are special cases of CMF. This is likely to be useful for people looking for CCA and GFA solutions supporting missing data and non-Gaussian likelihoods. ## Examples ```r require("CMF") # Create data for a circular setup with three matrices and three # object sets of varying sizes. X <- list() D <- c(10, 20, 30) inds <- matrix(0, nrow = 3, ncol = 2) # Matrix 1 is between sets 1 and 2 and has continuous data inds[1, ] <- c(1, 2) X[[1]] <- matrix( rnorm(D[inds[1, 1]] * D[inds[1, 2]], 0, 1), nrow = D[inds[1, 1]] ) # Matrix 2 is between sets 1 and 3 and has binary data inds[2, ] <- c(1, 3) X[[2]] <- matrix( round(runif(D[inds[2, 1]] * D[inds[2, 2]], 0, 1)), nrow = D[inds[2, 1]] ) # Matrix 3 is between sets 2 and 3 and has count data inds[3, ] <- c(2, 3) X[[3]] <- matrix( round(runif(D[inds[3, 1]] * D[inds[3, 2]], 0, 6)), nrow = D[inds[3, 1]] ) # Convert the data into the right format triplets <- lapply(X, matrix_to_triplets) # Missing entries correspond to missing rows in the triple representation # so they can be removed from training data by simply taking a subset # of the rows. train <- list() test <- list() keep_for_training <- c(100, 200, 300) for (m in 1:3) { subset <- sample(nrow(triplets[[m]]), keep_for_training[m]) train[[m]] <- triplets[[m]][subset, ] test[[m]] <- triplets[[m]][-subset, ] } # Learn the model with the correct likelihoods K <- 4 likelihood <- c("gaussian", "bernoulli", "poisson") opts <- getCMFopts() opts$iter.max <- 500 # Less iterations for faster computation model <- CMF(train, inds, K, likelihood, D, test = test, opts = opts) # Check the predictions # Note that the data created here has no low-rank structure, # so we should not expect good accuracy. print(test[[1]][1:3, ]) print(model$out[[1]][1:3, ]) # predictions for the test set using the previously learned model out <- predictCMF(test, model) print(out$out[[1]][1:3, ]) print(out$error[[1]]) # ...this should be the same as the output provided by CMF() print(model$out[[1]][1:3, ]) ``` ## References Arto Klami, Guillaume Bouchard, and Abhishek Tripathi. Group-sparse embeddings in collective matrix factorization. arXiv:1312.5921, 2013. Arto Klami, Seppo Virtanen, and Samuel Kaski. Bayesian canonical correlation analysis. Journal of Machine Learning Research, 14(1):965--1003, 2013. Seppo Virtanen, Arto Klami, Suleiman A. Khan, and Samuel Kaski. Bayesian group factor analysis. In Proceedings of the 15th International Conference on Artificial Intelligence and Statistics, volume 22 of JMLR:W&CP, pages 1269-1277, 2012. ## Author(s) Arto Klami arto.klami@cs.helsinki.fi and Lauri Väre Maintainer: Felix Held felix.held@gmail.se

CMF-package