Related papers: Principal Curvatures Estimation with Applications …

We present a new self-supervised paradigm on point cloud sequence understanding. Inspired by the discriminative and generative self-supervised methods, we design two tasks, namely point cloud sequence based Contrastive Prediction and…

We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with…

Conventional domain adaptation typically transfers knowledge from a source domain to a stationary target domain. However, in many real-world cases, target data usually emerge sequentially and have continuously evolving distributions.…

RNA sequencing (RNA-seq) is the conventional genome-scale approach used to capture the expression levels of all detectable genes in a biological sample. This is now regularly used for population-based studies designed to identify genetic…

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

In this article, we study curvature-like feature value of data sets in Euclidean spaces. First, we formulate such curvature functions with desirable properties under the manifold hypothesis. Then we make a test property for the validity of…

Principal component analysis (PCA) is a commonly used pattern analysis method that maps high-dimensional data into a lower-dimensional space maximizing the data variance, that results in the promotion of separability of data. Inspired by…

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…

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,…

In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…

Machine learning models for molecular property prediction generally rely on representations -- such as SMILES strings and molecular graphs -- that overlook the surface-local phenomena driving intermolecular behavior. 3D-based approaches…

Numerous tools have been recently developed to predict disease phenotypes using single-cell RNA sequencing (RNA-seq) data. CloudPred is an end-to-end differentiable learning algorithm coupled with a biologically informed mixture model,…

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary…

Principal Component Analysis (PCA) is a dimensionality reduction technique widely used to reduce the computational cost associated with numerical simulations of combustion phenomena. However, PCA, which transforms the thermo-chemical state…

A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…

While several convolution-like operators have recently been proposed for extracting features out of point clouds, down-sampling an unordered point cloud in a deep neural network has not been rigorously studied. Existing methods down-sample…

Since its selection as the method of the year in 2013, single-cell technologies have become mature enough to provide answers to complex research questions. With the growth of single-cell profiling technologies, there has also been a…

Single-cell RNA sequencing (scRNA-seq) has revolutionized our ability to analyze gene expression at the resolution of individual cells, providing unprecedented insights into cellular heterogeneity and complex biological systems. This paper…

In this paper, we propose PCPNet, a deep-learning based approach for estimating local 3D shape properties in point clouds. In contrast to the majority of prior techniques that concentrate on global or mid-level attributes, e.g., for shape…

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…