Modern Dimension Reduction
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.
Code (1)
Tasks
Dimensionality ReductionSimilar Papers 제목 키워드 기반
Randomized Dimension Reduction on Massive Data
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approache…
Dimensionality ReductionregressionDetermining Principal Component Cardinality through the Principle of Minimum Description Length
PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the numbe…
Dimensionality ReductionModel SelectionregressionDimensionality Reduction on Riemannian Manifolds in Data Analysis
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlin…
Dimensionality ReductionFair Recommendation by Geometric Interpretation and Analysis of Matrix Factorization
Matrix factorization-based recommender system is in effect an angle preserving dimensionality reduction technique. Since the frequency of items follows power-law distribution, most vectors in the original dimension of us…
Dimensionality ReductionRecommendation SystemsDiRe-JAX: A JAX based Dimensionality Reduction Algorithm for Large-scale Data
DiRe - JAX is a new dimensionality reduction toolkit designed to address some of the challenges faced by traditional methods like UMAP and tSNE such as loss of global structure and computational efficiency. Built on the …
Computational EfficiencyDimensionality Reduction