Alternating Maximization: Unifying Framework for 8 Sparse PCA Formulations and Efficient Parallel Codes

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector; these are obtained by combining the following factors: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two different ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via a natural alternating maximization (AM) method. We show the the AM method is nontrivially equivalent to GPower (Journ\'{e}e et al; JMLR 11:517--553, 2010) for all our formulations. Besides this, we provide 24 efficient parallel SPCA implementations: 3 codes (multi-core, GPU and cluster) for each of the 8 problems. Parallelism in the methods is aimed at i) speeding up computations (our GPU code can be 100 times faster than an efficient serial code written in C++), ii) obtaining solutions explaining more variance and iii) dealing with big data problems (our cluster code is able to solve a 357 GB problem in about a minute).Comment: 29 pages, 9 tables, 7 figures (the paper is accompanied by a release of the open-source code '24am'

A Unifying review of linear gaussian models

Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model.We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

A Tutorial on Bayesian Nonparametric Models

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.Comment: 28 pages, 8 figure

Distributed Training Large-Scale Deep Architectures

Scale of data and scale of computation infrastructures together enable the current deep learning renaissance. However, training large-scale deep architectures demands both algorithmic improvement and careful system configuration. In this paper, we focus on employing the system approach to speed up large-scale training. Via lessons learned from our routine benchmarking effort, we first identify bottlenecks and overheads that hinter data parallelism. We then devise guidelines that help practitioners to configure an effective system and fine-tune parameters to achieve desired speedup. Specifically, we develop a procedure for setting minibatch size and choosing computation algorithms. We also derive lemmas for determining the quantity of key components such as the number of GPUs and parameter servers. Experiments and examples show that these guidelines help effectively speed up large-scale deep learning training

Automated Grain Yield Behavior Classification

A method for classifying grain stress evolution behaviors using unsupervised learning techniques is presented. The method is applied to analyze grain stress histories measured in-situ using high-energy X-ray diffraction microscopy (HEDM) from the aluminum-lithium alloy Al-Li 2099 at the elastic-plastic transition (yield). The unsupervised learning process automatically classified the grain stress histories into four groups: major softening, no work-hardening or softening, moderate work-hardening, and major work-hardening. The orientation and spatial dependence of these four groups are discussed. In addition, the generality of the classification process to other samples is explored

Statistical Traffic State Analysis in Large-scale Transportation Networks Using Locality-Preserving Non-negative Matrix Factorization

Statistical traffic data analysis is a hot topic in traffic management and control. In this field, current research progresses focus on analyzing traffic flows of individual links or local regions in a transportation network. Less attention are paid to the global view of traffic states over the entire network, which is important for modeling large-scale traffic scenes. Our aim is precisely to propose a new methodology for extracting spatio-temporal traffic patterns, ultimately for modeling large-scale traffic dynamics, and long-term traffic forecasting. We attack this issue by utilizing Locality-Preserving Non-negative Matrix Factorization (LPNMF) to derive low-dimensional representation of network-level traffic states. Clustering is performed on the compact LPNMF projections to unveil typical spatial patterns and temporal dynamics of network-level traffic states. We have tested the proposed method on simulated traffic data generated for a large-scale road network, and reported experimental results validate the ability of our approach for extracting meaningful large-scale space-time traffic patterns. Furthermore, the derived clustering results provide an intuitive understanding of spatial-temporal characteristics of traffic flows in the large-scale network, and a basis for potential long-term forecasting.Comment: IET Intelligent Transport Systems (2013