[Paper Review] Collaborative Multi-sensor Classification via Sparsity-based Representation

Minh N. Dao, Nam H. Nguyen+2 more|arXiv (Cornell University)|Oct 29, 2014

Sparse and Compressive Sensing Techniques34 references4 citations

TL;DR

This paper proposes a collaborative sparse representation framework for multi-sensor classification that jointly enforces row-sparsity and block-sparsity across heterogeneous sensors, while robustly modeling sparse noise and low-rank interference. It introduces MS-JSR, MS-JSR+E, MS-JSR+L, and kernelized variants (MS-KerJSR, MS-KerGJSR+L), solved via an ADMM-based algorithm with guaranteed convergence, achieving superior classification accuracy on real multi-sensor datasets compared to conventional methods.

ABSTRACT

In this paper, we propose a general collaborative sparse representation framework for multi-sensor classification, which takes into account the correlations as well as complementary information between heterogeneous sensors simultaneously while considering joint sparsity within each sensor's observations. We also robustify our models to deal with the presence of sparse noise and low-rank interference signals. Specifically, we demonstrate that incorporating the noise or interference signal as a low-rank component in our models is essential in a multi-sensor classification problem when multiple co-located sources/sensors simultaneously record the same physical event. We further extend our frameworks to kernelized models which rely on sparsely representing a test sample in terms of all the training samples in a feature space induced by a kernel function. A fast and efficient algorithm based on alternative direction method is proposed where its convergence to an optimal solution is guaranteed. Extensive experiments are conducted on several real multi-sensor data sets and results are compared with the conventional classifiers to verify the effectiveness of the proposed methods.

Motivation & Objective

• To develop a unified framework for collaborative multi-sensor classification that leverages joint sparsity across sensors and within each sensor’s observations.
• To enhance robustness against two common noise types: sparse noise and low-rank interference signals from co-located sensors.
• To integrate group-sparse regularization to exploit structured sparsity patterns across sensor groups.
• To extend the framework into kernel-induced feature spaces for improved nonlinear discrimination.
• To design a fast, convergent optimization algorithm based on the alternating direction method of multipliers (ADMM).

Proposed method

• Formulates a multi-sensor joint sparse representation (MS-JSR) model with row-sparsity constraints across all sensors and within each sensor’s data.
• Extends MS-JSR to handle sparse noise (MS-JSR+E) and low-rank interference (MS-JSR+L), modeling interference as a low-rank matrix.
• Introduces group-sparse regularization (MS-GJSR+L) to enforce both block-sparse and row-sparse coefficient structures.
• Applies kernel mapping to implicitly represent data in a nonlinear feature space, leading to MS-KerJSR and MS-KerGJSR+L models.
• Develops an ADMM-based optimization algorithm with convergence guarantees to solve the non-convex, structured sparsity-regularized problems.
• Uses variable splitting and augmented Lagrangian techniques to decompose the problem into subproblems solvable via closed-form updates.

Experimental results

Research questions

• RQ1 Can joint sparsity across multiple heterogeneous sensors improve classification performance in multi-sensor systems?
• RQ2 How does modeling low-rank interference from co-located sensors enhance robustness in multi-sensor classification?
• RQ3 To what extent does incorporating group-sparse regularization improve classification accuracy compared to standard sparse models?
• RQ4 Does kernelized sparse representation in a feature space lead to better discrimination in nonlinear data scenarios?
• RQ5 Is the proposed ADMM-based algorithm guaranteed to converge to a stationary solution for the structured sparsity problems?

Key findings

• The proposed MS-JSR+L model significantly improves classification accuracy by explicitly modeling low-rank interference, which is common in co-located sensor recordings.
• The integration of group-sparse regularization (MS-GJSR+L) leads to better performance than row-sparse or block-sparse models alone, due to enhanced structural modeling of sensor data.
• Kernelized extensions (MS-KerGJSR+L) outperform linear models on nonlinearly separable data, demonstrating the benefit of nonlinear feature mapping.
• The ADMM-based algorithm converges to a stationary solution, as proven through convergence analysis involving variable sequences and subgradient conditions.
• Experiments on real multi-sensor datasets show that the proposed models consistently outperform conventional classifiers such as SVM and traditional sparse representation methods.
• Robustness to both sparse noise and low-rank interference is empirically validated, with the low-rank model showing particular effectiveness in real-world multi-sensor scenarios.