The expanding role of positional covariance data in modern spacecraft operations leads to a need for better understanding of the time evolution of covariance by mission planners and operators. It is common to see positional covariance information presented as uncertainties in the radial, cross-track and in-track directions. While such a time history does provide some information, it tends to ob...

OF THESIS COVARIANCE REGULARIZATION IN MIXTURE OF GAUSSIANS FOR HIGH-DIMENSIONAL IMAGE CLASSIFICATION In high dimensions, it is rare to find a data set large enough to compute a non-singular covariance matrix. This problem is exacerbated when performing clustering using a mixture of Gaussians (MoG) because now each cluster’s covariance matrix is computed from only a subset of the data set makin...

Mixture of Probabilistic Principal Component Analyzers (MPPCA) is a seminal work in Machine Learning in that it was the first to use PCA to perform clustering and local dimensionality reduction. MPPCA is based upon the mixture of Factor Analyzers (MFA) which is similar to MPPCA except is uses Factor Analysis to estimate the covariance matrix. This algorithm is of interest to me because it is re...

Many similarity measures used for classification involve the inverse of the group covariance matrices. However, the number of observations available in the training set for each group is, in many cases, significantly inferior to the dimension of the feature space, what implies that the sample covariance matrix is singular. A common solution to this problem is to assume the same covariance matri...

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by minimizing the quadratic loss function and joint penalty of `1 norm and variance of its eigenvalues. In contrast to some of the existing methods of covariance...

We propose a test of equality of two covariance matrices based on the maximum standardized difference of scalar covariances of two sample covariance matrices. We derive the tail probability of the asymptotic null distribution of the test statistic by the tube method. However the usual formal tube formula has to be suitably modified, because in this case the index set, around which the tube is f...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 CHAPTER 1: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 CHAPTER 2: ONE-DIMENSIONAL POWER SPECTRUM . . . . . . . . . . . . 17 2.1 Three-Dimensional Power Spectrum . . . . . . . . . . . . . . . . . . . . . 17 2.2 One-Dimensional Power Spectrum . . . . . . . . . . . . . . . . . . . . . . 19 2....

This paper describes our progress in developing visualization techniques to explore covariance, especially within the context of the Inverse Ocean Modeling framework. The size and dimensionality of the data make this an interesting challenge. We describe ways to use common visualization techniques, such as color, to explore covariance. We also introduce a new representation for covariance, in w...