Modern Dimension Reduction

by   Philip D. Waggoner, et al.

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.


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Universality laws for randomized dimension reduction, with applications

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Rdimtools: An R package for Dimension Reduction and Intrinsic Dimension Estimation

Discovering patterns of the complex high-dimensional data is a long-stan...

Linearly-scalable learning of smooth low-dimensional patterns with permutation-aided entropic dimension reduction

In many data science applications, the objective is to extract appropria...

Using Dimension Reduction to Improve the Classification of High-dimensional Data

In this work we show that the classification performance of high-dimensi...

Function Preserving Projection for Scalable Exploration of High-Dimensional Data

We present function preserving projections (FPP), a scalable linear proj...

AVIDA: Alternating method for Visualizing and Integrating Data

High-dimensional multimodal data arises in many scientific fields. The i...

Persuasion by Dimension Reduction

How should an agent (the sender) observing multi-dimensional data (the s...

Code Repositories


Replication files for my book "Modern Dimension Reduction"

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