Related papers: $\sigma$-PCA: a building block for neural learning…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…
In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data.…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…
In this work we apply the principal component analysis (PCA) method with kernel trick to study classification of phases and phase transition in classical XY models in frustrated lattices. Comparing to our previous work with linear PCA…
Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for…
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
Principal Component Analysis (PCA)-based techniques can separate data into different uncorrelated components and facilitate the statistical analysis as a pre-processing step. Independent Component Analysis (ICA) can separate statistically…
This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in…
Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…
Unified representation learning for multi-source data integration faces two important challenges: blockwise missingness and blockwise signal heterogeneity. The former arises from sources observing different, yet potentially overlapping,…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…