dimensionality_reduction/

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Published: Feb 27, 2017 License: Apache-2.0

README

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

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.

Directories

Path Synopsis
Sample program to illustrate the calculation of principal components.
Sample program to illustrate the calculation of principal components.
Sample program to visualize the impact of dimensionality reduction.
Sample program to visualize the impact of dimensionality reduction.
Sample program to project iris data on to principal components.
Sample program to project iris data on to principal components.
exercises
exercise1
Sample program to project iris data on to 3 principal components.
Sample program to project iris data on to 3 principal components.
template1
Sample program to project iris data on to 3 principal components.
Sample program to project iris data on to 3 principal components.

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