Locality Preserving Markovian Transition for Instance Retrieval

TL;DR

This paper introduces the LPMT framework that combines diffusion, locality embedding, and thermodynamic Markovian transitions to improve instance retrieval by better modeling data manifolds and maintaining local discriminative signals.

Contribution

The paper proposes a novel LPMT framework integrating diffusion, locality embedding, and thermodynamic transitions for enhanced manifold distance measurement in retrieval tasks.

Findings

LPMT outperforms existing methods in diverse retrieval tasks.

The combination of BCD, LSE, and TMT improves local and global retrieval accuracy.

Experimental results demonstrate the effectiveness of LPMT in maintaining local signals over multiple steps.

Abstract

Diffusion-based re-ranking methods are effective in modeling the data manifolds through similarity propagation in affinity graphs. However, positive signals tend to diminish over several steps away from the source, reducing discriminative power beyond local regions. To address this issue, we introduce the Locality Preserving Markovian Transition (LPMT) framework, which employs a long-term thermodynamic transition process with multiple states for accurate manifold distance measurement. The proposed LPMT first integrates diffusion processes across separate graphs using Bidirectional Collaborative Diffusion (BCD) to establish strong similarity relationships. Afterwards, Locality State Embedding (LSE) encodes each instance into a distribution for enhanced local consistency. These distributions are interconnected via the Thermodynamic Markovian Transition (TMT) process, enabling efficient global retrieval while maintaining local effectiveness. Experimental results across diverse tasks confirm the effectiveness of LPMT for instance retrieval.