# REVIEW OF DIMENSIONALITY REDUCTION METHODS AND THEIR APPLICATION

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## REVIEW OF DIMENSIONALITY REDUCTION METHODS AND THEIR APPLICATION

Chapter one
1.1 Project Objective
This project is primarily a survey on dimensionality reduction, exploring various reasons why we might desire to lower the dimensionality of a dataset. Outlining many works completed, methods used, and their applications in various fields of life.

This project delves deeper into several dimensionality reduction approaches and how we may implement some of them. Finally, this research compares these strategies based on how well they retain images and discusses the numerous applications of random projection.

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1.2 Background Of the study

Assume a data collection D has n points in a high-dimensional space; this can be mapped to a lower-dimensional space with little distortion. (See Nsang’s Novel Approaches to Dimensionality Reduction and Applications).

For example, inspecting a dataset with 30,000 columns will be challenging. Obtaining 1,500 columns will undoubtedly be beneficial, as it will make it much easier to analyse the results acquired when compared to the initial data set of 30,000 columns.

Such that, after analysing the dataset, the result obtained is a good approximation when compared to the result acquired by analysing the original dataset.

Some advantages of reducing the dimensionality (d) of a given set of n points include:
1. Dimensionality reduction will operate as a catalyst in speeding up a given algorithm whose runtime is exponentially proportional to the dimension of the working space.

For example, if the dimensionality of the data set, d, is too high, a sophisticated control system will be required to prevent overfitting of the training data in machine learning.

2. “High-dimensionality data sets may limit the variation of available data processing methods” (Nsang, Novel Approaches to Dimensionality Reduction and Applications).

These include picture data clustering, text file analysis, and so on. Dimensionality might be high due to product variety, phraseology, or a big image window, as seen in previous examples.

3. High-dimensional data sets tend to displace sporadically. As a result, an algorithm will take a lengthy time to identify any structure in the provided data set.

4. Dimensionality reduction includes noise and other irrelevant image specifications. This is due to the variability in the high-dimensional data collection.

5. Dimensionality reduction makes data visualisation easier by reducing it to low dimensions such as 2D or 3D.

6. Finally, dimensionality reduction allows us to save time and, most crucially, memory space.

Even if multiple expensive programmed approaches can generate identical models from the same high-dimensional datasets, dimensionality reduction is still suggested as the first step before any data modelling.

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