What Principal Component Analysis (PCA) Meaning, Applications & Example
A technique that reduces data dimensionality by finding principal components.
What is Principal Component Analysis (PCA)?
Principal Component Analysis (PCA) is a dimensionality reduction technique used to reduce the number of variables in a dataset while preserving as much of the original data’s variability as possible. It transforms the data into a new coordinate system, where the greatest variance comes to lie on the first few principal components (new axes). PCA is commonly used to simplify data, speed up computations, and highlight important patterns in data.
How PCA Works
- Standardization: PCA starts by standardizing the data, making sure each feature has a mean of 0 and a standard deviation of 1, so that all features contribute equally.
- Covariance Matrix: PCA calculates the covariance matrix to understand how variables relate to one another.
- Eigenvalues and Eigenvectors: The covariance matrix is decomposed into eigenvalues and eigenvectors, which represent the variance (importance) and directions (principal components) of the data.
- Projection: The data is then projected onto the new set of principal components, reducing the number of dimensions while retaining most of the data’s variability.
Applications of PCA
- Data Visualization: PCA is commonly used to reduce high-dimensional data to two or three principal components for visual exploration of complex datasets, making it easier to identify patterns or clusters.
- Noise Reduction : By keeping only the most important principal components, PCA can help reduce noise and improve the performance of machine learning models.
- Feature Selection : PCA can be used to select a smaller set of features (principal components) that capture the most variance, improving the efficiency of downstream models.
Example of PCA
In image compression, PCA can be used to reduce the number of dimensions in an image dataset. For instance, given a dataset of high-resolution images, PCA can compress the images by focusing on the most important components, reducing file size while retaining key visual information. This results in faster storage and processing of images while minimizing the loss of important details.