Related papers: Learning RUMs: Reducing Mixture to Single Componen…
This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity…
Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
Standard machine learning models optimized for average performance often fail on minority subgroups and lack robustness to distribution shifts. This challenge worsens when subgroups are latent and affected by complex interactions among…
Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…
A computational approach by an implementation of the Principle Component Analysis (PCA) with K-means and Gaussian Mixture (GM) clustering methods from Machine Learning (ML) algorithms to identify structural and dynamical heterogeneities of…
Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…
This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis (PCA) problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this…
It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…
PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The…
For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized…
This paper proposes a novel sparse principal component analysis algorithm with self-learning ability for successive modes, where synaptic intelligence is employed to measure the importance of variables and a regularization term is added to…
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to…