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The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-driven approaches…
Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
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…
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
For numerous reasons there raises a need for dimension reduction that preserves certain characteristics of data. In this work we focus on data coming from a mixture of Gaussian distributions and we propose a method that preserves…
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…
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)…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In…
Principal Component Analysis (PCA) aims to find subspaces spanned by the so-called principal components that best represent the variance in the dataset. The deflation method is a popular meta-algorithm that sequentially finds individual…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
A computational approach by an implementation of the Principle Component Analysis (PCA) with K-means and Gaussian Mixture (GM) clustering methods from Machine Learning (ML) algorithms to identify structural and dynamical heterogeneities of…
Detection of change-points in a sequence of high-dimensional observations is a very challenging problem, and this becomes even more challenging when the sample size (i.e., the sequence length) is small. In this article, we propose some…
As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…