Principal Component Analysis is a dimensionality reduction technique commonly used in machine learning and data analysis. Its primary goal is to transform high-dimensional data into a lower-dimensional representation, capturing the most important information. This reduction in dimensionality can lead to improved computational efficiency, visualization, and often better model performance.

steps to perform PCA:

**Standardize the Data:**If the features in the dataset have different scales, it is important to standardize them by subtracting the mean and dividing by the standard deviation to give each feature equal importance.**Compute the Covariance Matrix:**Calculate the covariance matrix of the standardized data. The covariance matrix provides information about how variables change together.**Compute Eigenvectors and Eigenvalues:**Calculate the eigenvectors and eigenvalues of the covariance matrix. The eigenvectors represent the principal components, and the eigenvalues indicate the amount of variance captured by each principal component.**Sort Eigenvectors by Eigenvalues:**Sort the eigenvectors in descending order based on their corresponding eigenvalues. The higher the eigenvalue, the more variance is captured by the corresponding eigenvector.**Select Principal Components:**Choose the top k eigenvectors to form the new feature space. Typically, it would select the number of principal components that capture a sufficiently high percentage of the total variance.

Example:

Suppose the data on people’s heights and weights. We can find that most of the variation, along a diagonal line, representing a combination of height and weight. PCA helps us focus on this main trend and ignore less important details.