Related papers: Discrete Component Analysis
This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…
We study the problem of distributed information bottleneck, in which multiple encoders separately compress their observations in a manner such that, collectively, the compressed signals preserve as much information as possible about another…
Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
Data discretization, also known as binning, is a frequently used technique in computer science, statistics, and their applications to biological data analysis. We present a new method for the discretization of real-valued data into a finite…
With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the…
We propose a new method to impute missing values in mixed datasets. It is based on a principal components method, the factorial analysis for mixed data, which balances the influence of all the variables that are continuous and categorical…
We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence,…
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots,X_K$ are processed separately so as to learn as much information as possible about some ground truth $Y$. We investigate this…
This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition…
This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…
This work presents an unsupervised deep discriminant analysis for clustering. The method is based on deep neural networks and aims to minimize the intra-cluster discrepancy and maximize the inter-cluster discrepancy in an unsupervised…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Local differential privacy is a differential privacy paradigm in which individuals first apply a privacy mechanism to their data (often by adding noise) before transmitting the result to a curator. The noise for privacy results in…
Distributed data analysis without revealing the individual data has recently attracted significant attention in several applications. A collaborative data analysis through sharing dimensionality reduced representations of data has been…
Discrete mixture models are routinely used for density estimation and clustering. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Recent advances have sparked significant interest in the development of privacy-preserving Principal Component Analysis (PCA). However, many existing approaches rely on restrictive assumptions, such as assuming sub-Gaussian data or being…