dimensionality_reduction/

Dimensionality Reduction

Data scientists use dimensionality reduction to transfrom high-dimensional data sets into more compact, low-dimensional data sets. This process can be very useful when there is redundancy and correlation between features, when a data set includes irrelevant features, and when computational or modeling constraints necessitate lower dimensions. Principal Component Analysis is a widely used dimensionality reduction technique that we will explore here.

Notes

• Principal components are (as stated here):
  • a sequence of projections of the data,
  • mutually uncorrelated, and
  • ordered in variance.
• The axis corresponding to the principal eigenvector/component is the one along which the data is most “spread out” (i.e., the axis along which the variance of the data is maximized).
• A PCA transformation, replaces high-dimensionality data by its projection onto it's most important axes.
• Although PCA is widely used, there are a variety of dimensionality reduction techniques

Links

A tutorial on principal component analysis Another tutorial on principal component analysis A survey of dimensionality reduction techniques

Code Review

github.com/gonum/stat docs
Calculate Principal Components Determine a Number of Target Dimensions
Project the Data

Exercises

Exercise 1

Project the iris data set features on to three dimensions rather than four. Output the results.

Template | Answer

All material is licensed under the Apache License Version 2.0, January 2004.