### Introduction

Dimensionality Reduction in machine learning is the conversion of data from a high-dimensional space into a low-dimensional space. This is so that the low-dimensional representation recalls certain expressive properties of the original data that is preferably close to its basic dimension. At work in high-dimensional spaces may be unwanted for many reasons for example;

- Raw data are frequently thin as a result of the curse of dimensionality
- Analyzing the data is commonly computationally intractable.

Dimensionality reduction in machine earning is general in arenas that contract with large numbers of observations and big numbers of variables, for example, signal processing, speech recognition, neuroinformatic, and bioinformatics.

### Description

Work straight with high-dimensional data, for example, images come with some difficulties because;

- It is tough to analyze
- Clarification and interpretation is difficult
- Imagining is nearly impossible,

From a practical point of view, the storage of the data vectors can be costly. Though, high-dimensional data a lot has properties that we can exploit. E.g., high-dimensional data is repeatedly over complete, i.e., numerous dimensions are out of work and maybe clarified by a mixture of other dimensions. Also, dimensions in high-dimensional data are frequently connected so that the data owns an intrinsic lower-dimensional construction. Dimensionality reduction exploits structure and correlation. It permits us to work through an extra solid representation of the data, preferably lacking behind the information. We may think of dimensionality reduction as a solidity technique, related to jpeg or mp3, which are compression algorithms for images and music.

### Methods for Dimensionality Reduction

There are many methods that can be used for dimensionality reduction in machine learning. Methods are usually distributed into linear and non-linear approaches and may also be further divided into feature selection and feature extraction. Dimensionality reduction in machine learning might be used for;

- sound reduction
- data visualization
- cluster examination
- or as an in-between step to ease other studies.

#### Feature Selection Methods

Possibly the most common are so-called feature selection systems. These are being used for scoring or statistical methods to select which features to keep and which features to delete. The two highest classes of dimensionality reduction in machine learning features are wrapper methods and filter methods.

**Wrapper methods**

This method wraps a machine learning model, fitting and assessing the model with different subsets of input features. Also, wrap a model by choosing the subset the results in the best model show. The best example of a wrapper feature selection method is RFE.

**Filter methods**

This method is used for counting methods, similar to the link between the feature and the target variable. These are used to select a subset of input features that are most predictive. Examples comprise Pearsonâ€™s correlation and the Chi-Squared test.

#### Matrix Factorization

Methods from linear algebra may be used for dimensionality reduction in machine learning. Exactly, matrix factorization methods can be used to decrease a dataset matrix into its basic parts. Examples contain the Eigen decomposition and singular value decomposition. The shares can then be graded and a subset of those shares may be designated that best captures the salient structure of the matrix, which may be used to represent the dataset. The most common method for ranking the components is principal components analysis (PCA).

### Manifold Learning

Methods from a high-dimensionality reduction in machine learning statistics can as well be used for dimensionality reduction in machine learning. These methods are occasionally referred to as manifold learning”. These are used to create a low-dimensional projection of high-dimensional data, repeatedly for the drives of data visualization. The plan is intended to equally create a low-dimensional representation of the dataset at the same time as best conserving the salient structure or dealings in the data. Illustrations of manifold learning methods include:

- Kohonen Self-Organizing Map (SOM)
- Sammons Mapping
- Multidimensional Scaling (MDS)
- t-distributed Stochastic Neighbor Embedding (t-SNE).

The types in the projection regularly have a tiny relationship with the original columns, for instance, they do not have column names that can be confusing to trainees.

### Autoencoder Methods

Deep learning neural networks may be built to perform dimensionality reduction. One widespread approach is called autoencoders. This includes framing a self-supervised learning problem where a model must replicate the input properly. A network model has used that search to compress the data flow to a jam layer with far fewer dimensions than the unique input data. The part of the model previous to and including the block is mentioned as the encoder, and the part of the model that reads the block output and reconstructs the input is called the decoder. The decoder is rejected and the output from the bottleneck is used right as the reduced dimensionality of the input after training. Inputs changed by this encoder can then be provided for into another model, not essentially a neural network model. The productivity of the encoder is a type of projection. Similar to other projection methods, there is no direct association to the bottleneck output back to the unique input variables, creating them stimulating to interpret.

### Guidelines for Dimensionality Reduction in Machine learning

There is no greatest method for dimensionality reduction in machine learning and no mapping of techniques to problems. As an alternative, the best line is to use systematic controlled experiments to learn what dimensionality reduction methods, once paired with our model of choice, the outcome in the best performance on our dataset.

Following are dimensionality reduction techniques:

- Feature extraction and elimination
- Linear algebra methods
- Manifold

Normally, linear algebra and manifold learning methods take up that all input features have the same scale or distribution. This proposes that it is a decent practice to whichever normalize or standardize data previous to using these methods if the input variables have opposing scales or units.