A review of dimensionality reduction methods and their applications.

Abstract

In the world we live in today, the reduction in data generally has seen a great rise. This is because of the numerous advantages that come with working with smaller efficient data instead of the original large dataset. With this analogy, we can adopt Dimensionality reduction in computer science emphasizing on reducing computer memory in order to have more storage capacity on a computer. An example of this would be to reduce digital images which are then stored in 2D matrices. Dimensionality reduction is a process whereby given a collection of data points in a high dimensional Euclidean space, it is often helpful to be able to project it into a lower dimensional Euclidean space without suffering great distortion. The result obtained by working in the lower dimensional space becomes a good approximation to the original dataset obtained by working in the high dimensional space. Dimensionality Reduction has two categories: In the first category includes those in which each attribute in the reduced set is a linear combination of the attributes in the original dataset. These include RP and PCA. While the second category includes those in which the set of attributes in the reduced set is a proper subset of the attributes in the original dataset. These include all the other six techniques I implemented such as New Random Approach, Variance Approach, The first Novel Approach, The second Novel Approach, The Third Novel Approach and the LSA-Transform Approach. Also, I compared these techniques mentioned above by how they preserve their images. Furthermore, I looked at the various applications we can use. Dimensionality reduction example includes: Image reduction

Text data Nearest neighbor search K-nearest neighbor search Similarity search in a time series Clustering Classification

MATLAB programming language was used to carry all forms of implementation in this project course.