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In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to…
This tutorial reviews the main steps of the principal component analysis of a multivariate data set and its subsequent dimensional reduction on the grounds of identified dominant principal components. The underlying computations are…
We propose a new hybrid symbolic-numerical approach to the center-focus problem. The method allowed us to obtain center conditions for a three-dimensional system of differential equations, which was previously not possible using…
The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…
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.…
Scatter plots are widely recognized as fundamental tools for illustrating the relationship between two numerical variables. Despite this, based on solid theoretical foundations, scatter plots generated from pairs of continuous random…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the…
By using a symbolic method, known in the literature as the classical umbral calculus, the trace of a non-central Wishart random matrix is represented as the convolution of the trace of its central component and of a formal variable…
With the advent of very large redshift surveys of tens to hundreds of thousands of galaxies reliable techniques for automatically determining galaxy redshifts are becoming increasingly important. The most common technique currently in…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. We complement principal loading analysis and propose to rather use a mix of both, the…
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…
A visualization notation is a recurring pattern of symbols used to author specifications of visualizations, from data transformation to visual mapping. Programmatic notations use symbols defined by grammars or domain-specific languages…