Modern dimension reduction / Philip D. Waggoner.

Format:

Book

Author/Creator:

Waggoner, Philip D., author.

Series:

Cambridge elements. Elements in quantitative and computational methods for the social sciences 2398-4023

Language:

English

Subjects (All):

Dimension reduction (Statistics).

Physical Description:

1 online resource (86 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern society. All code is publicly accessible on Github.

Contents:

Cover

Title page

Copyright page

Modern Dimension Reduction

Contents

1 Introduction

1.1 Defining the Title

1.2 Running Example: 2019 American National Election Pilot Study

1.3 The Methods

1.4 The Methods Not Covered

1.5 Tidy Programming in R

1.6 Cleaning the Data

1.7 Addressing Missing Data

2 A Classic Approach to Dimension Reduction

2.1 Why PCA?

2.2 What Is PCA Doing?

2.3 Formalizing PCA

2.4 Applying PCA to the ANES Data

2.5 Suggestions for Further Reading

3 Locally Linear Embedding

3.1 Manifolds and Complex Structure

3.2 Formalizing LLE

3.3 Applying LLE to the ANES Data

3.4 A Risk-Averse Workflow

3.5 Suggestions for Further Reading

4 Nonlinear Dimension Reduction for Visualization

4.1 From Linear to Nonlinear Dimension Reduction

4.2 t-SNE

4.3 UMAP

4.4 A Tidy Tangent on UMAP via uwot::umap() and embed

4.5 Suggestions for Further Reading

5 Neural Network-Based Approaches

5.1 A Basic Neural Network Architecture

5.2 Self-Organizing Maps

Defining the Steps of the Algorithm

Applying SOM to the ANES Data

5.3 Autoencoders

Applying Autoencoders to the ANES Data

5.4 Suggestions for Further Reading

6 Final Thoughts on Dimension Reduction

References

Acknowledgments.

Notes:

Title from publisher's bibliographic system (viewed on 26 Jul 2021).

ISBN:

1-108-99164-5

1-108-98176-3

OCLC:

1260473519