Scores and loadings matrices are discussed including properties such as orthogonality orthonormality illustrated by a simple numerical example.

Canonical Correlation is one of the most general of the multivariate techniques. It is used to investigate the overall correlation between two sets of variables (p’ and q’). The basic principle behind canonical correlation is determining how much variance in one set of variables is accounted for by the other set along one or more axes. If there is more than one axis, they must be orthogonal. Un...

This work proposes an extension of the functional principal components analysis, or Karhunen-Loève expansion, which can take into account non-parametrically the effects of an additional covariate. Such models can also be interpreted as non-parametric mixed effects models for functional data. We propose estimators based on kernel smoothers and a data-driven selection procedure of the smoothing p...

This paper deals with Principal Components Analysis (PCA) of data spread over a network where central coordination and synchronous communication between networking nodes are forbidden. We propose an asynchronous and decentralized PCA algorithm dedicated to large scale problems, where ”large” simultaneously applies to dimensionality, number of observations and network size. It is based on the in...

We present a new neural model that extends the classical competitive learning by performing a principal components analysis (PCA) at each neuron. This model represents an improvement with respect to known local PCA methods, because it is not needed to present the entire data set to the network on each computing step. This allows a fast execution while retaining the dimensionality-reduction prop...

DI MIAO: CLASS-SENSITIVE PRINCIPAL COMPONENTS ANALYSIS (Under the direction of J. S. Marron and Jason P. Fine) Research in a number of fields requires the analysis of complex datasets. Principal Components Analysis (PCA) is a popular exploratory method. However it is driven entirely by variation in the dataset without using any predefined class label information. Linear classifiers make up a fa...

To my father iii ACKNOWLEDGEMENTS My journey through the PhD program has been a long one, taking me from robotics, to computer vision, to machine learning, and finally to theory. Making so many transitions slowed my graduation, no doubt, but it also allowed me to work with leaders across several research fields and has given me a better perspective on the The most important man in my PhD career...

maryam sadat salamati1, hossein zeinali2 ,ehdi yousefi3     1- ardestan branch, islamic azad university, ardestan, iran   2- esfahan agricultural and natural research center, isfahan, iran   3- assist. prof, payam noor university, isfahan, iran             received: 10 february 2011 accepted: 26 may 2011     * corresponding author: e-mail: [email protected]       abstract     in order to...

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