Sampling-enabled scalable manifold learning unveils the discriminative cluster structure of high-dimensional data

TL;DR

This paper introduces SUDE, a scalable manifold learning method that uses sampling and landmark-based embedding to effectively analyze large-scale, high-dimensional data while preserving cluster structures and global geometry.

Contribution

The paper proposes SUDE, a novel sampling-based manifold learning technique that improves scalability and discriminative embedding for large and high-dimensional datasets.

Findings

SUDE outperforms existing methods in scalability and cluster separation.

It maintains embedding quality even with reduced sampling rates.

SUDE effectively analyzes single-cell and ECG data for pattern detection.

Abstract

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key insights. Although existing techniques have achieved remarkable successes, they suffer from extensive distortions of cluster structure, which hinders the understanding of underlying patterns. Scalability issues also limit their applicability for handling large-scale data. We hence propose a sampling-based Scalable manifold learning technique that enables Uniform and Discriminative Embedding, namely SUDE, for large-scale and high-dimensional data. It starts by seeking a set of landmarks to construct the low-dimensional skeleton of the entire data, and then incorporates the non-landmarks into the learned space based on the constrained locally linear embedding (CLLE). We empirically validated the effectiveness of SUDE on synthetic datasets and real-world benchmarks, and applied it to analyze single-cell data and detect anomalies in electrocardiogram (ECG) signals. SUDE exhibits distinct advantage in scalability with respect to data size and embedding dimension, and has promising performance in cluster separation, integrity, and global structure preservation. The experiments also demonstrate notable robustness in embedding quality as the sampling rate decreases.