Related papers: Modularity Component Analysis versus Principal Com…
The present paper attempts to generate visual clustering and data extraction of cell formation problem using both principal component analysis (PCA) and self organizing map (SOM) from input of sequence based machine-part incidence matrix.…
Software module clustering is an unsupervised learning method used to cluster software entities (e.g., classes, modules, or files) with similar features. The obtained clusters may be used to study, analyze, and understand the software…
Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…
In areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be…
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…
This paper investigates the intrinsic group structures within the framework of large-dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. To this…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
We investigate the adaptation and performance of modularity-based algorithms, designed in the scope of complex networks, to analyze the mesoscopic structure of correlation matrices. Using a multi-resolution analysis we are able to describe…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
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…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
The increasing needs of clustering massive datasets and the high cost of running clustering algorithms poses difficult problems for users. In this context it is important to determine if a data set is clusterable, that is, it may be…
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…
For data assumed to come from a finite mixture with an unknown number of components, it has become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. The…
Through a study of multi-gas mixture datasets, we show that in multi-component spectral analysis, the number of functional or non-functional principal components required to retain the essential information is the same as the number of…
Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of $q$ communities, the number of eigenvectors corresponding to the $q$ largest eigenvalues form a "community"…
Mixtures of linear mixed models are widely used for modelling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients…
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…