It is well known that dimensionality reduction based on multivariate analysis methods and their kernelized extensions can be formulated as generalized eigenvalue problems of scatter matrices, Gram matrices or their augmented matrices. This paper provides a generic and theoretical framework of multivariate analysis introducing a new expression for scatter matrices and Gram matrices, called Gener...

The tannins are polyphenolic compounds with complex structures formed by the secondary metabolism in various plants. Among the oldest applications of tannins is leather tanning. Tanning properties are due to the ability of these polyphenols to form complexes with proteins. In this study were analysed six different types of commercially polyphenolic extracts by Fourier transform infrared spectro...

This study presents the application of multivariate analyses to analyze micro-Raman spectral imaging data in reference to the adhesive/dentin interface as well as comparison with univariate analysis. The univariate statistical methods, such as mapping of specific functional group peak intensities, do not always detect functional group positions and quantities due to peak overlapping. A comprehe...

We discuss the use of orthogonal wavelet transforms in multivariate data analysis methods such as clustering and dimensionality reduction. Wavelet transforms allow us to introduce multiresolution approximation, and multiscale nonparametric regression or smoothing, in a natural and integrated way into the data analysis. Applications illustrate the powerfulness of this new perspective on data ana...

We describe the use of the wavelet transform for multivariate data analysis problems. In prediction, a multiscale transform of time-varying data can allow forecasts of each scale, followed by combining of the individual forecasts. The use of a wavelet transform with noise modeling for point pattern clustering can lead to the result, which initially appears counter-intuitive, of clustering in co...

Recently, interest has been increasing in crime analytics in which time series clustering research has been playing an important role, particularly for finding useful similar trends in crime. Time series clustering technique has potential for large volume of data analysis. Multivariate time series data relating to various areas such as finance, health sector, environmental research, and crime i...

Tree-dependent component analysis (TCA) is a generalization of independent component analysis (ICA), the goal of which is to model the multivariate data by a linear transformation of latent variables, while latent variables fit by a tree-structured graphical model. In contrast to ICA, TCA allows dependent structure of latent variables and also consider non-spanning trees (forests). In this pape...