Sharif Digital Repository

This thesis is devoted to study some asymptotic behaviors of Poisson Voronoi tessellation in the Euclidean space as dimension of the space tends to infinity. First we use Blaschke-Petkantschin formula to prove that the variance of volume of the typical cell tends to zero exponentially in dimension. It is also shown that the volume of intersection of the typical cell with the co-centered ball of volume converges in distribution to the constant . Next we consider the linear contact distribution function of the Poisson Voronoi tessellation and compute the limit when dimension goes to infinity. As a byproduct, the chord length distribution and the geometric covariogram of the typical cell are... 

Genome sequences, high dimensional digital pictures and on-line text news are all examples of high dimensional data sets. As technology keeps advancing new challenges arise from applications of high dimensional datasets. Amongst these challenges, the problem of constraint clustering for high dimensional data is of great importance. This problem deals with 2 major challenges.The first challenge is the concentration effect of Lp norms, which means as the dimensionality increases, ratio of distance between the closest points to the distance of furthest points approaches 1. This in turn makes the concept of nearest neighbour meaning less. It also means the discriminative property of such... 

Sparse representation has attracted much attention over the past decade. The main idea is that natural signals have information contents much lower than their ambient dimensions,and as such, they can be represented by using only a few basis signals (also called atoms). In other words, a natural signal of length n, which in general needs n atoms to be represented, can be written as a linear combination of s atoms, where s ≪ n. To achieve a sparser representation, i.e., a smaller s, the number of atoms is chosen much larger than n. In this way, there are more choices to represent a signal and we can choose the sparsest possible combination. The set of atoms is called a dictionary. Here, two... 

Human action recognition is one of the most attended topics in computer vision and robotics.One of the flavors of this problem relates to the situation in which the task of action recognition is carried out by data from several cameras. Different approaches have been proposed for combining information. Various reduction methods have been introduced to decrease the processing load. All of the methods in this particular field of study can be divided into two linear and non-linear methods. In the linear methods, we don’t pay attention to the non-linear structure of the data, and these kind of approaches are not reliable. Furthermore, combining different actions data is done before the dimension...