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Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
We discuss a new approach to data clustering. We find that maximum likelyhood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…
In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…
We review the recent approach of correlation based networks of financial equities. We investigate portfolio of stocks at different time horizons, financial indices and volatility time series and we show that meaningful economic information…
With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
A simple method is proposed to estimate the instantaneous correlations between state variables in a hybrid system from the empirical correlations between observable market quantities such as spot rate, stock price and implied volatility.…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
We discuss a new approach to data clustering. We find that maximum likelihood leads naturally to an Hamiltonian of Potts variables which depends on the correlation matrix and whose low temperature behavior describes the correlation…
We present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical…
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…
Compositional data are characterized by the fact that their elemental information is contained in simple pairwise logratios of the parts that constitute the composition. While pairwise logratios are typically easy to interpret, the number…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
With the growing size of data sets, feature selection becomes increasingly important. Taking interactions of original features into consideration will lead to extremely high dimension, especially when the features are categorical and…
Based on a recent theorem due to the authors, it is shown how the extreme tail dependence between an asset and a factor or index or between two assets can be easily calibrated. Portfolios constructed with stocks with minimal tail dependence…
Principal component analysis is a long-standing go-to method for exploring multivariate data. The principal components are linear combinations of the original variables, ordered by descending variance. The first few components typically…
Although the understanding of and motivation behind individual trading behavior is an important puzzle in finance, little is known about the connection between an investor's portfolio structure and her trading behavior in practice. In this…
I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting…
In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce…