Related papers: Non-Gaussian Component Analysis with Log-Density G…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
This work studies information-computation gaps for statistical problems. A common approach for providing evidence of such gaps is to show sample complexity lower bounds (that are stronger than the information-theoretic optimum) against…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose…
Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Decentralized learning over distributed datasets can have significantly different data distributions across the agents. The current state-of-the-art decentralized algorithms mostly assume the data distributions to be Independent and…
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of…
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…
Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…
Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…
In this paper, we propose a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product (SLRP) model for dominant eigenspace…
We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2)…
We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our…
Dimension reduction is a common strategy in multivariate data analysis which seeks a subspace which contains all interesting features needed for the subsequent analysis. Non-Gaussian component analysis attempts for this purpose to divide…
In independent component analysis it is assumed that the observed random variables are linear combinations of latent, mutually independent random variables called the independent components. Our model further assumes that only the…
Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…