What is PCA and cluster analysis?
Cluster analysis groups observations while PCA groups variables rather than observations. PCA can be used as a final method (by adding rotation to perform factor analysis) or to reduce the number of variables to conduct another analysis, such as regression or other data mining (classifying etc.) techniques.
What does clustering do in regression?
In Regression Clustering (RC), K (>1) regression functions are applied to the dataset simultaneously which guide the clustering of the dataset into K subsets each with a simpler distribution matching its guiding function. Each function is regressed on its own subset of data with a much smaller residue error.
Are PCA and cluster analysis linked?
It is a common practice to apply PCA (principal component analysis) before a clustering algorithm (such as k-means). It is believed that it improves the clustering results in practice (noise reduction).
What’s the difference between PCA and linear regression?
With Linear Regression, we are trying to find a straight line that best fits the data. So if we took a very simple example of univariate regression, predicting one variable with another, how would my PCA transformation look from the best-fit line derived through linear regression. Let’s dive in and find out.
What happens when we regress y ~ y in PCA?
When we regress y~x, it is the vertical distances that are minimized based on the Least Squares method (or the metric we choose). This is highlighted in the brown lines in the plot above. So what happens when we regress x~y?
How to decrease the number of variables in PCA?
If you want to decrease the number variables using PCA, you should look at the lambda values that describe the variations in the principle components, then, select the a few components with the largest corresponding lambda values (eg the first four). Do a scaling if necessary.
How to visualize PCA data in a plot?
So you can transform a 1000-feature dataset into 2D so you can visualize it in a plot or you could bring it down to x features where x<<1000 while preserving most of the variance in the data. I’ve previously explored Facial image compression and reconstruction using PCA using scikit-learn.