Principal Component Analysis (also known as PCA) is a commonly used statistical technique in the field of data science for dimensionality reduction and for understanding key driving variables in datasets.
Often, in real-world datasets, many features (i.e., columns in a data table) are correlated to each other. This multicollinearity can produce issues when attempting to create predictive models. PCA is a method used to overcome these multicollinearity issues. Additionally, PCA can transform a high-dimensional dataset into a lower-dimensional one while retaining as much of the original variance as possible -- this is a process known as dimensionality reduction.
Below is an example of how to perform PCA in Python using the sklearn library and the famous iris dataset:
from sklearn.decomposition import PCA from sklearn import datasets # Load iris dataset iris = datasets.load_iris() X = iris.data # Perform dimensionality reduction using PCA pca = PCA(n_components=2) principalComponents = pca.fit_transform(X)
In the code above, n_components=2 means that we want to reduce the dataset to a 2-dimensional dataset.
One of the key aspects of PCA is the concept of 'explained variance'. After performing dimensionality reduction using PCA, each principal component will explain a certain percentage of the original dataset's variance. The 'explained variance ratio' is an array that shows this relationship:
# Explained variance ratio print('Explained Variance: {}'.format(pca.explained_variance_ratio_))
The 'explained variance ratio' is an important factor when determining the number of principal components needed to represent the original data effectively.
In sum, Principal Component Analysis is an efficient tool used in data science to transform high-dimensional datasets into lower dimensions, capturing most of the information from the original data. Its ability to handle multicollinearity makes it valuable in creating predictive models.