Related papers: A Report on Multilinear PCA Plus Multilinear LDA t…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

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…

With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Graph contrastive learning is usually performed by first conducting Graph Data Augmentation (GDA) and then employing a contrastive learning pipeline to train GNNs. As we know that GDA is an important issue for graph contrastive learning.…

The Machine Learning has various learning algorithms that are better in some or the other aspect when compared with each other but a common error that all algorithms will suffer from is training data with very high dimensional feature set.…

Adversarial images are designed to mislead deep neural networks (DNNs), attracting great attention in recent years. Although several defense strategies achieved encouraging robustness against adversarial samples, most of them fail to…

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…

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…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

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…

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an…

Unsupervised Domain Adaptation (UDA) addresses the problem of performance degradation due to domain shift between training and testing sets, which is common in computer vision applications. Most existing UDA approaches are based on…

Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise…

High dimensional data can contain multiple scales of variance. Analysis tools that preferentially operate at one scale can be ineffective at capturing all the information present in this cross-scale complexity. We propose a multiscale joint…

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…

In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…