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A Review of Dimensionality Reduction Methods and their Applications

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Description

Download A Review of Dimensionality Reduction Methods and their Applications. Computer Science students who are writing their projects can get this material to aid their research work.

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 comes 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 where by 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.

Introduction

This project is mainly a survey on dimensionality reduction discussing different motives why we might want to reduce the dimensionality of a dataset. Outlining various works done, methods used and finally their applications in different domains of life.

This project goes further in depth to look at different dimensionality reduction methods and ways in which we can implement a few of them.

Finally, this project goes further to compare these techniques to the extent in which they preserve images and outlines the various applications in random projection.

Assume a data set D contains n points in a high dimensional space, this can be mapped out onto a lower dimensional space with minimal distortion. (see Nsang, Novel Approaches to Dimensionality Reduction and Applications). For example, a data set with 30,000 columns will be difficult to inspect.

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