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Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…

Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches.…

Retrieval-augmented generation (RAG) enhances large language models (LLMs) with external knowledge but still suffers from long contexts and disjoint retrieval-generation optimization. In this work, we propose CLaRa (Continuous Latent…

Generative Adversarial Networks (GANs) have emerged as a significant player in generative modeling by mapping lower-dimensional random noise to higher-dimensional spaces. These networks have been used to generate high-resolution images and…

Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…

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…

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

In this paper, we implement an information-theoretic approach to travel behaviour analysis by introducing a generative modelling framework to identify informative latent characteristics in travel decision making. It involves developing a…

Autonomous materials science, where active learning is used to navigate large compositional phase space, has emerged as a powerful vehicle to rapidly explore new materials. A crucial aspect of autonomous materials science is exploring new…

Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…

The increasing prevalence of Large Language Models (LMs) in critical applications highlights the need for controlled language generation strategies that are not only computationally efficient but that also enjoy performance guarantees. To…

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…

We propose a kernel-PCA based method to detect anomaly in chemical sensors. We use temporal signals produced by chemical sensors to form vectors to perform the Principal Component Analysis (PCA). We estimate the kernel-covariance matrix of…

We introduce a new framework for manipulating and interacting with deep generative models that we call network bending. We present a comprehensive set of deterministic transformations that can be inserted as distinct layers into the…

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…

Explainable AI aims to overcome the black-box nature of complex ML models like neural networks by generating explanations for their predictions. Explanations often take the form of a heatmap identifying input features (e.g. pixels) that are…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…