# What is PCA and its Methodology

In this blog, we would discuss what is PCA and its Methodology. PCA is a statistical technique that is used to reduce the dimensionality of data. It is often used to speed up machine learning algorithms or to make data easier to visualize. PCA works by finding the directions of maximum variance in the data and then projecting the data onto these directions. This can be done by computing the eigenvectors of the covariance matrix of the data. The eigenvectors are the directions of maximum variance and the eigenvalues are the amount of variance in each direction. The eigenvectors with the largest eigenvalues are the directions of maximum variance.

## What is Principal Component Analysis

PCA can be used to reduce the dimensionality of data while still retaining the most important information. For example, if we have a dataset with 1000 features, we can use PCA to reduce it to 100 features while still retaining most of the information. This can be beneficial for machine learning algorithms since they can run faster on lower-dimensional data. Additionally, lower dimensional data is easier to visualize. There are a few drawbacks to PCA. One is that it can be sensitive to outliers. Another is that it can be difficult to interpret the results.

Overall, PCA is a powerful tool that can be used to reduce the dimensionality of data. It is especially useful for machine learning algorithms and data visualization. PCA is often used to make data easier to visualize or to make patterns easier to find. It is a linear transformation that projects data onto a lower-dimensional space. The projection is chosen such that the projected data has the maximum variance. PCA can be used to find patterns in data, reduce the dimensionality of data, or make data easier to visualize.

## Methodology of PCA

Now, we shall look into PCA and its Methodology. PCA is a statistical technique that is used to reduce the dimensionality of data. It is often used to reduce the data to two or three dimensions so that it can be visualized easily. PCA is a linear transformation that projects the data onto a lower dimensional space. The new axes are chosen such that they are orthogonal to each other and the variance of the data is maximized.

The first step in performing PCA is to center the data. This is done by subtracting the mean of each column from the data. Next, the covariance matrix is computed. This is a square matrix that contains the variances of the columns of the centered data. The eigenvectors of the covariance matrix are then computed. These are the vectors that define the new axes of the lower dimensional space.

The eigenvectors are sorted in order of the eigenvalues. The eigenvector with the largest eigenvalue is chosen as the first axis. The eigenvector with the second largest eigenvalue is chosen as the second axis, and so on. The data is then transformed onto the new axes. This is done by multiplying the data by the matrix of eigenvectors. PCA is a powerful tool for dimensionality reduction. It can be used to reduce the data to two or three dimensions so that it can be visualized easily. It can also be used to find the most important features of the data.

This procedure is often used to reduce the dimensionality of data, especially data that has a large number of variables while retaining as much information as possible. The principal components are obtained as the eigenvectors of the covariance matrix of the original data. They are orthogonal to each other and are ranked in order of the amount of variance they explain.

The first principal component explains the maximum amount of variance (and is therefore the most informative), while the last principal component explains the least amount of variance (and is therefore the least informative). The principal components can be used to represent the original data in a lower-dimensional space. This can be useful for visualizing the data, simplifying the data (removing redundancy), or for machine learning (reducing the number of features while retaining as much information as possible).

## Applications of PCA

Till now, we had discussed PCA and its Methodology. Now we shall look into some applications. One of the most popular applications of PCA is dimensionality reduction. In many applications, data sets can have hundreds or even thousands of features. However, most of the features in the data set may be highly correlated and contain similar information.

In these cases, only a small number of the features may contain most of the information in the data set. PCA can be used to find a smaller set of features that still contain most of the information in the data set. This can be useful for visualizations, training machine learning models, or for reducing the storage requirements for data sets. PCA can also be used for outlier detection.

In some cases, data sets may contain outliers that are not representative of the rest of the data. These outliers can often be found by looking at the features that have the largest variance. PCA can also be used to improve the performance of machine learning models. In some cases, the features in a data set may be highly correlated. This can cause problems for machine learning models, as they may overfit the data. PCA can be used to find a set of uncorrelated features that can be used to train the machine learning model.

Also, read – What is Imputation and Implementation Techniques