2023/12/15 by Ayoub Belhadji, Rémi Gribonval, Belhadji, Ayoub +1
Computer Science · Engineering · #Advanced Image and Video Retrieval Techniques #Algorithm #Artificial intelligence #Cluster analysis #Compressed sensing #Computer science #Deep learning #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Heuristic #Heuristics #Information bottleneck method #Leverage (statistics) #MNIST database #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine learning #Mutual information #Robustness (evolution) #Sketch #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2312.09940
openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Compressive learning is an emerging approach to drastically reduce the memory footprint of large-scale learning, by first summarizing a large dataset into a low-dimensional sketch vector, and then decoding from this sketch the latent information needed for learning. In light of recent progress on information preservation guarantees for sketches based on random features, a major objective is to design easy-to-tune algorithms (called decoders) to robustly and efficiently extract this information. To address the underlying non-convex optimization problems, various heuristics have been proposed. In the case of compressive clustering, the standard heuristic is CL-OMPR, a variant of sliding Frank-Wolfe. Yet, CL-OMPR is hard to tune, and the examination of its robustness was overlooked. In this work, we undertake a scrutinized examination of CL-OMPR to circumvent its limitations. In particular, we show how this algorithm can fail to recover the clusters even in advantageous scenarios. To gain insight, we show how the deficiencies of this algorithm can be attributed to optimization difficulties related to the structure of a correlation function appearing at core steps of the algorithm. To address these limitations, we propose an alternative decoder offering substantial improvements over CL-OMPR. Its design is notably inspired from the mean shift algorithm, a classic approach to detect the local maxima of kernel density estimators. The proposed algorithm can extract clustering information from a sketch of the MNIST dataset that is 10 times smaller than previously.