相关论文: A co-kurtosis PCA based dimensionality reduction w…

For a linear system, the response to a stimulus is often superposed by its responses to other decomposed stimuli. In quantum mechanics, a state is the superposition of multiple eigenstates. Here, by taking advantage of the phase difference,…

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a…

When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…

Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data in a coordinated way, even though their effect is invisible…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Recent advances in photoacoustic (PA) imaging have enabled detailed images of microvascular structure and quantitative measurement of blood oxygenation or perfusion. Standard reconstruction methods for PA imaging are based on solving an…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

High-resolution stellar spectra offer valuable insights into atmospheric parameters and chemical compositions. However, their inherent complexity and high-dimensionality present challenges in fully utilizing the information they contain. In…

At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. Various methods have been proposed to extend PCA to the union of subspace (UoS) setting for clustering data that comes from multiple subspaces…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

This paper considers the problem of nonstationary process monitoring under frequently varying operating conditions. Traditional approaches generally misidentify the normal dynamic deviations as faults and thus lead to high false alarms.…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local…

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…