{"title":"Using Block Coordinate Descent to Learn Sparse Coding Dictionaries with a Matrix Norm Update","authors":"Bradley M. Whitaker, David V. Anderson","doi":"10.1109/ICASSP.2018.8461499","DOIUrl":null,"url":null,"abstract":"Researchers have recently examined a modified approach to sparse coding that encourages dictionaries to learn anomalous features. This is done by incorporating the matrix I-norm, or $\\ell_{1,\\infty}$ mixed matrix norm, into the dictionary update portion of a sparse coding algorithm. However, solving a matrix norm minimization problem in each iteration of the algorithm causes it to run more slowly. The purpose of this paper is to introduce block coordinate descent, a subgradient-like approach to minimizing the matrix norm, to the dictionary update. This approach removes the need to solve a convex optimization program in each iteration and dramatically reduces the time required to learn a dictionary. Importantly, the dictionary learned in this manner can still model anomalous features present in a dataset.","PeriodicalId":6638,"journal":{"name":"2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","volume":"89 1","pages":"2761-2765"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICASSP.2018.8461499","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Researchers have recently examined a modified approach to sparse coding that encourages dictionaries to learn anomalous features. This is done by incorporating the matrix I-norm, or $\ell_{1,\infty}$ mixed matrix norm, into the dictionary update portion of a sparse coding algorithm. However, solving a matrix norm minimization problem in each iteration of the algorithm causes it to run more slowly. The purpose of this paper is to introduce block coordinate descent, a subgradient-like approach to minimizing the matrix norm, to the dictionary update. This approach removes the need to solve a convex optimization program in each iteration and dramatically reduces the time required to learn a dictionary. Importantly, the dictionary learned in this manner can still model anomalous features present in a dataset.