Generalizable Spectral Embedding with an Application to UMAP
Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability (i.e., out-of-sample extension), scalability, and eigenvectors separation. In this paper, we introduce GrEASE: Generalizable and Efficient Approximate Spectral Embedding, a novel deep-learning approach designed to address these limitations. GrEASE incorporates an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability, allowing for the computation of the Laplacian's eigenvectors on unseen data. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate GrEASE's ability to consistently approximate and generalize SE, while ensuring scalability. Additionally, we show how GrEASE can be leveraged to enhance existing methods. Specifically, we focus on UMAP, a leading visualization technique, and introduce NUMAP, a generalizable version of UMAP powered by GrEASE. Our codes are publicly available.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Accelerating UMAP for Large-Scale Datasets Through Spectral Coarsening
This paper introduces an innovative approach to dramatically accelerate UMAP using spectral data compression.The proposed method significantly reduces the size of the dataset, preserving its essential manifold structure …
ScaleMAP: Preserving Local Density and Neighborhood Structure in Low-Dimensional Embeddings
Nonlinear dimensionality-reduction methods such as UMAP and PaCMAP adaptively normalize local distances during graph construction, erasing neighborhood scale from the data. This distorts more than relative cluster sizes:…
UMAP Is Spectral Clustering on the Fuzzy Nearest-Neighbor Graph
UMAP (Uniform Manifold Approximation and Projection) is among the most widely used algorithms for non linear dimensionality reduction and data visualisation. Despite its popularity, and despite being presented through th…
Dimensionality ReductionContrastive LearningAutoencoded UMAP-Enhanced Clustering for Unsupervised Learning
We propose a novel approach to unsupervised learning by constructing a non-linear embedding of the data into a low-dimensional space followed by any conventional clustering algorithm. The embedding promotes clusterabilit…
ClusteringFastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling
Exploratory analysis of high-dimensional data rarely stops at a single embedding. In practice, analysts rerun dimensionality reduction after changing preprocessing, subsets, or hyperparameters, and standard nonlinear met…
Dimensionality Reduction