Related papers: Joint Characterization of Multiscale Information i…
Nonlinear data visualization using t-distributed stochastic neighbor embedding (t-SNE) enables the representation of complex single-cell transcriptomic landscapes in two or three dimensions to depict biological populations accurately.…
The t-distributed Stochastic Neighbor Embedding (t-SNE) is a powerful and popular method for visualizing high-dimensional data. It minimizes the Kullback-Leibler (KL) divergence between the original and embedded data distributions. In this…
Nowadays, as data becomes increasingly complex and distributed, data analyses often involve several related datasets that are stored on different servers and probably owned by different stakeholders. While there is an emerging need to…
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
Running machine learning analytics over geographically distributed datasets is a rapidly arising problem in the world of data management policies ensuring privacy and data security. Visualizing high dimensional data using tools such as…
This paper presents a comprehensive overview of several multidimensional reduction methods focusing on Multidimensional Principal Component Analysis (MPCA), Multilinear Orthogonal Neighborhood Preserving Projection (MONPP), Multidimensional…
We address shortcomings of principal component analysis (PCA) for visualizing high-dimensional data lying on a nonlinear low-dimensional manifold via two-dimensional scatterplots, focusing on a fossil teeth dataset from the early mammalian…
Integrative analysis of disparate data blocks measured on a common set of experimental subjects is one major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual…
Convolutional Neural Networks (CNNs) have advanced significantly in visual representation learning and recognition. However, they face notable challenges in performance and computational efficiency when dealing with real-world, multi-scale…
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…
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
We introduce Principal Component Analysis guided Quantile Sampling (PCA QS), a novel sampling framework designed to preserve both the statistical and geometric structure of large scale datasets. Unlike conventional PCA, which reduces…
We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…
Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…
Convolutional neural networks (CNNs) have been applied to learn spatial features for high-resolution (HR) synthetic aperture radar (SAR) image classification. However, there has been little work on integrating the unique statistical…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample.…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to…
Data classification techniques partition the data or feature space into smaller sub-spaces, each corresponding to a specific class. To classify into subspaces, physical features e.g., distance and distributions are utilized. This approach…