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A learning algorithm combining functional discriminant coordinates and functional principal components

Tomasz Górecki, Mirosław Krzyśko (2014)

Discussiones Mathematicae Probability and Statistics

A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.

A novel robust principal component analysis method for image and video processing

Guoqiang Huan, Ying Li, Zhanjie Song (2016)

Applications of Mathematics

The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the 1 -norm. However, the sparse noise has clustering effect in practice so using a certain p -norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery...

A review of canonical coordinates and an alternative to correspondence analysis using Hellinger distance.

C. Radhakrishna Rao (1995)


In this paper a general theory of canonical coordinates is developed for reduction of dimensionality in multivariate data, assessing the loss of information and plotting higher dimensional data in two or three dimensions for visual displays. The theory is applied to data in two way tables with variables in one category and samples (individual or populations) in the other. Two types of data are considered, one with continuous measurements on the variables and another with frequencies of attributes....

An alternating minimization algorithm for Factor Analysis

Valentina Ciccone, Augusto Ferrante, Mattia Zorzi (2019)


The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem. This algorithm appears to perform extremely well and is extremely fast even when the given covariance matrix has a very large dimension. The effectiveness of the algorithm is assessed through simulation studies and by applications to three real benchmark datasets...

Anàlisi de matrius quadrades no simètriques: un enfocament integral usant anàlisi de correspondències.

Josep Daunis i Estadella, Tomàs Aluja Banet, Santiago Thió Fernández de Henestrosa (2002)


In this paper a new integrated approach to the analysis of square non-symmetric tables is introduced by means of cortrespondence analysis. The application of correspondence analysis to such tables is not successful due to the strong role played by the diagonal values: overloaded diagonals and structural zeros. Two main families of methods of resolution are integrated in this paper. The resulting method is applied to the study of commuting between the 41 Catalan counties.

Análisis en componentes principales de un proceso estocástico con funciones muestrales escalonadas.

Ana María Aguilera del Pino, Francisco A. Ocaña Lara, Mariano J. Valderrama Bonnet (1996)


El ACP de un número finito de variables puede ser generalizado para manejar datos que evolucionan en el tiempo. El objetivo de este trabajo es la estimación de los factores principales de procesos aleatorios con funciones muestrales escalonadas. Ante la imposibilidad de obtener una solución exacta a este problema, proponemos estimar el ACP de un proceso de este tipo a partir del ACP del proceso cuyas trayectorias se obtienen como proyección de las originales en el subespacio de las funciones constantes...

Análisis factorial de tablas mixtas: nuevas equivalencias entre ACP normado y ACM.

M.ª Isabel Landaluce Calvo (1997)


En este trabajo se pone de manifiesto que es posible el Análisis Factorial de tablas mixtas sin modificar la naturaleza de ninguno de los dos conjuntos, cualitativo y cuantitativo, que las integran. Se propone codificar de manera apropiada las indicadoras de cada variable cualitativa tratando de respetar, en la medida de lo posible, la estructura inicial de ésta última y posteriormente aplicar un Análisis en Componentes Principales (ACP) Normado al conjunto de variables. Los factores obtenidos para...

Análisis factorial múltiple como técnica de estudio de la estabilidad de los resultados de un análisis de componentes principales.

Elena Abascal Fernández, M.ª Isabel Landaluce Calvo (2002)


Una característica de los métodos factoriales es que siempre producen resultados y éstos no son una simple descripción, sino que ponen de manifiesto la estructura existente entre los datos, de ahí la necesidad de estudiar la validez de los resultados. Es preciso analizar la naturaleza de esta estructura y estudiar la estabilidad de los resultados. Consideramos que el mejor criterio es el análisis de la estabilidad de los mapas obtenidos en el análisis factorial.El Análisis Factorial Múltiple (AFM),...

Analysis of correlation based dimension reduction methods

Yong Joon Shin, Cheong Hee Park (2011)

International Journal of Applied Mathematics and Computer Science

Dimension reduction is an important topic in data mining and machine learning. Especially dimension reduction combined with feature fusion is an effective preprocessing step when the data are described by multiple feature sets. Canonical Correlation Analysis (CCA) and Discriminative Canonical Correlation Analysis (DCCA) are feature fusion methods based on correlation. However, they are different in that DCCA is a supervised method utilizing class label information, while CCA is an unsupervised method....

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