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...

Functional principal component analysis (FPCA) based on the Karhunen–Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation, but also by the actual question of dynamics of...

We present a new algorithm for eliminating excess parameters and improving network generalization after supervised training. The method, "Principal Components Pruning (PCP)", is based on principal component analysis of the node activations of successive layers of the network. It is simple, cheap to implement, and effective. It requires no network retraining, and does not involve calculating the...

In regression problems where the number of predictors greatly exceeds the number of observations, conventional regression techniques may produce unsatisfactory results. We describe a technique called supervised principal components that can be applied to this type of problem. Supervised principal components is similar to conventional principal components analysis except that it uses a subset of...

introduction of human development index (hdi) by undp in early 1990 followed a surge in use of non-parametric and parametric indices for measurement and comparison of countries performance in development, globalization, competition, well-being and etc. the hdi is a composite index of three indicators. its components are to reflect three major dimensions of human development: longevity, knowledg...

In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...