Related papers: CA-PCA: Manifold Dimension Estimation, Adapted for…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…
Word embeddings have become the basic building blocks for several natural language processing and information retrieval tasks. Pre-trained word embeddings are used in several downstream applications as well as for constructing…
In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive…
Developing a reliable and practical face recognition system is a long-standing goal in computer vision research. Existing literature suggests that pixel-wise face alignment is the key to achieve high-accuracy face recognition. By assuming a…
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…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…
Principal component analysis (PCA) is one of the most popular dimension reduction methods. The usual PCA is known to be sensitive to the presence of outliers, and thus many robust PCA methods have been developed. Among them, the Tyler's…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
For multimode processes, one generally establishes local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is…
Principal Component Analysis (PCA) is a pivotal technique widely utilized in the realms of machine learning and data analysis. It aims to reduce the dimensionality of a dataset while minimizing the loss of information. In recent years,…
We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…
Principal component analysis (PCA) is an essential algorithm for dimensionality reduction in many data science domains. We address the problem of performing a federated PCA on private data distributed among multiple data providers while…
In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random…
While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…