Related papers: CDPA: Common and Distinctive Pattern Analysis betw…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Conditional diffusion models (CDMs) have shown impressive performance across a range of generative tasks. Their ability to model the full data distribution has opened new avenues for analysis-by-synthesis in downstream discriminative…

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding.…

Domain adaptation is transfer learning which aims to generalize a learning model across training and testing data with different distributions. Most previous research tackle this problem in seeking a shared feature representation between…

In many real-world datasets, rows may have distinct characteristics and require different modeling approaches for accurate predictions. In this paper, we propose an adaptive modeling approach for row-type dependent predictive…

Separating high-dimensional data like images into independent latent factors, i.e independent component analysis (ICA), remains an open research problem. As we show, existing probabilistic deep generative models (DGMs), which are…

Due to the susceptibility of Artificial Intelligence (AI) to data perturbations and adversarial examples, it is crucial to perform a thorough robustness evaluation before any Machine Learning (ML) model is deployed. However, examining a…

We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…

While supervised learning has achieved remarkable success, obtaining large-scale labeled datasets in biomedical imaging is often impractical due to high costs and the time-consuming annotations required from radiologists. Semi-supervised…

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses…

This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of…

Domain Adaptive Object Detection (DAOD) transfers knowledge from a labeled source domain to an unannotated target domain under closed-set assumption. Universal DAOD (UniDAOD) extends DAOD to handle open-set, partial-set, and closed-set…

Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the…

Multi-source data fusion, in which multiple data sources are jointly analyzed to obtain improved information, has considerable research attention. For the datasets of multiple medical institutions, data confidentiality and…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

The reconstruction and prediction of full-state flows from sparse data are of great scientific and engineering significance yet remain challenging, especially in applications where data are sparse and/or subjected to noise. To this end,…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

Diffusion Policy (DP) enables robots to learn complex behaviors by imitating expert demonstrations through action diffusion. However, in practical applications, hardware limitations often degrade data quality, while real-time constraints…

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…