Sharif Digital Repository

The meaning and the nature of space and it’s essential properties seems to be one of the oldest problems which has been continuing to occupy human’s mind during centuries. It can be counted as a common ground between philosophy, mathematics, physics and even art. However this thesis concentrates on the philosophical and mathematical attitudes, neglecting the other aspects of the issue. Prima facie, it appears that the concept of space is essentially mingled with geometry, the science which seems to investigate the essentials of space. Taking it for granted, Kant regarded space, and so Euclidean geometry which dominates it, as an indispensible and necessary structure of the human’s mind.... 

Traditional methods for data classification only make use of the labeled data. However, in most of the applications, labeling the unlabeled data is expensive, time consuming and requires expert knowledge. To overcome these problems, Semi-supervised Learning (SSL) methods have become an area of recent research that aim to effectively addressing the problem of limited labeled data.One of the recently introduced SSL methods is the classification based on geometric structure of the data, namely the data manifold. In this approach unlabeled data is utilized to recover the underlying structure of the data. The common assumption is that despite of being represented in a high dimensional space, data...