Related papers: Hierarchical PCA and Modeling Asset Correlations

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…

Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…

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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…

Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…

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…

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The latent class model is a widely used mixture model for multivariate discrete data. Besides the existence of qualitatively heterogeneous latent classes, real data often exhibit additional quantitative heterogeneity nested within each…

The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Parallel coordinates plot (PCP) is an excellent tool for multivariate visualization and analysis, but it may fail to reveal inherent structures for datasets with a large number of items. In this paper, we propose a suite of novel…

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Hierarchical classification is a crucial task in many applications, where objects are organized into multiple levels of categories. However, conventional classification approaches often neglect inherent inter-class relationships at…

(Abridged) Environmental differences in the stellar populations of early-type galaxies are explored using principal component analysis (PCA), focusing on differences between elliptical galaxies in Hickson Compact Groups (HCGs) and in the…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

We propose improved methods to identify stock groups using the correlation matrix of stock price changes. By filtering out the marketwide effect and the random noise, we construct the correlation matrix of stock groups in which nontrivial…