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The reconstruction error is sometimes large even when a large number of eigenmode is used. In this paper, we show that this unexpected error source is the pollution effect of a summation operation in the objective function of the PCA algorithm. The summation operator brings together unrelated parts of the data into the same optimization and the result is the reduction of the accuracy of the overall algorithm. We introduce a domain decomposed PCA that improves the accuracy, and surprisingly also increases the parallelism of the algorithm. To demonstrate the accuracy and parallel efficiency of the proposed algorithm, we consider three applications including a face recognition problem, a brain tumor detection problem using two\u2010 and three\u2010dimensional MRI images.<\/jats:p>","DOI":"10.1002\/nla.2370","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T07:31:06Z","timestamp":1615793466000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Summation pollution of principal component analysis and an improved algorithm for location sensitive data"],"prefix":"10.1002","volume":"28","author":[{"given":"Jingwei","family":"Li","sequence":"first","affiliation":[{"name":"Department of Computer Science University of Colorado Boulder Boulder Colorado USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-0296-8640","authenticated-orcid":false,"given":"Xiao\u2010Chuan","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Computer Science University of Colorado Boulder Boulder Colorado USA"},{"name":"Department of Mathematics University of Macau Macau China"}]}],"member":"311","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.743"},{"issue":"1","key":"e_1_2_9_3_1","first-page":"1","article-title":"Principal components analysis and the reported low intrinsic dimensionality of gene expression microarray data","volume":"6","author":"Lenz M","year":"2016","journal-title":"Sci Rep [Internet]"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1214\/18-AOS1713"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1209854"},{"key":"e_1_2_9_6_1","unstructured":"QuY OstrouchovG SamatovaN GeistA. 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