Similarity Search Over Graphs Using Localized Spectral Analysis

TL;DR

This paper introduces a novel spectral analysis algorithm for similarity search over graphs, embedding multi-dimensional data into a low-dimensional space to effectively identify similar data points relative to a reference.

Contribution

The paper proposes a localized spectral kernel method that selects specific eigenvectors for improved similarity detection in graph-structured data.

Findings

Effective separation of similar and dissimilar data points

Low-dimensional embedding enhances computational efficiency

Outperforms traditional kernel methods in similarity tasks

Abstract

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the algorithm uses kernel method that embeds the data points into a low dimensional manifold. Unlike other kernel methods, which consider the entire data for the embedding, our method selects a specific set of kernel eigenvectors. The eigenvectors are chosen to separate between the data points and the reference data point so that similar data points can be easily identified as being distinct from most of the members in the dataset.