Adaptive Metric Dimensionality Reduction
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages the dual benefits of low dimensionality: (1) more efficient algorithms, e.g., for proximity search, and (2) more optimistic generalization bounds.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionGeneralization BoundsMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
A general framework for adaptive nonparametric dimensionality reduction
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such met…
Dimensionality ReductionDataset-Adaptive Dimensionality Reduction
Selecting the appropriate dimensionality reduction (DR) technique and determining its optimal hyperparameter settings that maximize the accuracy of the output projections typically involves extensive trial and error, oft…
Dimensionality ReductionTopiCLEAR: Adaptive embedding clustering for interpretable topic discovery from short texts
Topic discovery is a fundamental technique for text mining that identifies abstract topics within large document collections. A recent approach to topic discovery is to cluster document or sentence embeddings, typically …
Supervised Discriminative Sparse PCA with Adaptive Neighbors for Dimensionality Reduction
Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existi…
ClusteringDimensionality ReductionGeneral ClassificationSupervised dimensionality reductionSpectral Overlap and a Comparison of Parameter-Free, Dimensionality Reduction Quality Metrics
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is of…
Dimensionality ReductionHyperparameter Optimization