Introduction to Data Mining
Dimensionality reduction is a technique used in data mining to reduce the number of variables in a dataset while still preserving as much of the original information as possible. This technique is particularly useful when working with high-dimensional datasets, where the number of variables is much larger than the number of observations.
There are two main techniques for dimensionality reduction: feature selection and feature extraction.
Feature selection involves selecting a subset of the original variables to use in the analysis. This approach is often used when the original variables have some meaning or relevance to the analysis.
Feature extraction involves creating new variables that are combinations of the original variables. This approach is often used when the original variables are highly correlated or when there are too many variables to work with.
PCA is a popular technique used for feature extraction in dimensionality reduction. It works by finding the linear combinations of the original variables that explain the most variance in the data. These linear combinations are called principal components, and they represent the directions in the data where there is the most variation. By selecting only the top principal components, we can reduce the dimensionality of the data while still preserving as much of the original information as possible.
Suppose we have a dataset with 100 variables and 1000 observations. We want to reduce the dimensionality of the dataset to make it easier to analyze. We can use PCA to find the top principal components and select only those components for further analysis. For example, if we find that the top 10 principal components explain 90% of the variance in the data, we can select only those 10 components and reduce the dataset from 100 variables to 10 variables.
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