Clustering-based Low-Rank Matrix Approximation: An Adaptive Theoretical Analysis with Application to Data Compression
Low-rank matrix approximation (LoRMA) is a fundamental tool for compressing high-resolution data matrices by extracting important features while suppressing redundancy. Low-rank methods, such as global singular value decomposition (SVD), apply uniform compression across the entire data matrix, often ignoring important local variations and leading to the loss of fine structural details. To address these limitations, we introduce an adaptive LoRMA, which partitions data matrix into overlapping patches, groups structurally similar patches into several clusters using k-means, and performs SVD within each cluster. We derive the overall compression factor accounting for patch overlap and analyze how patch size influences compression efficiency and computational cost. While the proposed adaptive LoRMA method is applicable to any data exhibiting high local variation, we focus on medical imaging due to its pronounced local variability. We evaluate and compare our adaptive LoRMA against global SVD across four imaging modalities: MRI, ultrasound, CT scan, and chest X-ray. Results demonstrate that adaptive LoRMA effectively preserves structural integrity, edge details, and diagnostic relevance, as measured by peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), mean squared error (MSE), intersection over union (IoU), and edge preservation index (EPI). Adaptive LoRMA significantly minimizes block artifacts and residual errors, particularly in pathological regions, consistently outperforming global SVD in terms of PSNR, SSIM, IoU, EPI, and achieving lower MSE. Adaptive LoRMA prioritizes clinically salient regions while allowing aggressive compression in non-critical regions, optimizing storage efficiency. Although adaptive LoRMA requires higher processing time, its diagnostic fidelity justifies the overhead for high-compression applications.
Code (0)
등록된 구현이 없습니다.
Tasks
Data CompressionDiagnosticSSIMMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Robust Subspace Clustering via Smoothed Rank Approximation
Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank e…
ClusteringFace ClusteringMotion SegmentationA Review of Nonnegative Matrix Factorization Methods for Clustering
Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first…
ClusteringTransport Clustering: Solving Low-Rank Optimal Transport via Clustering
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank op…
Scalable Spectral Clustering with Nystrom Approximation: Practical and Theoretical Aspects
Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding base…
ClusteringA Nested Matrix-Tensor Model for Noisy Multi-view Clustering
In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observ…
Clustering