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For instance, these tools are applied in biology to describe spiking patterns of neuronal populations or the genetic profiles of different cell types. Here, we show that when data include noise points that are randomly scattered within a high-dimensional space, a \u201cscattering noise problem\u201d occurs in the low-dimensional embedding where noise points overlap with the cluster points. We show that a simple transformation of the original distance matrix by computing a distance between neighbor distances alleviates this problem and identifies the noise points as a separate cluster. We apply this technique to high-dimensional neuronal spike sequences, as well as the representations of natural images by convolutional neural network units, and find an improvement in the constructed low-dimensional embedding. Thus, we present an improved dimensionality reduction technique for high-dimensional data containing noise points.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010764","type":"journal-article","created":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T18:39:16Z","timestamp":1671561556000},"page":"e1010764","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":14,"title":["Improved visualization of high-dimensional data using the distance-of-distance transformation"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5117-8154","authenticated-orcid":true,"given":"Jinke","family":"Liu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4044-0970","authenticated-orcid":true,"given":"Martin","family":"Vinck","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,12,20]]},"reference":[{"issue":"5","key":"pcbi.1010764.ref001","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1016\/j.neuron.2017.05.025","article-title":"Neural manifolds for the control of movement","volume":"94","author":"JA Gallego","year":"2017","journal-title":"Neuron"},{"issue":"11","key":"pcbi.1010764.ref002","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1038\/nn.3776","article-title":"Dimensionality reduction for large-scale neural recordings","volume":"17","author":"JP Cunningham","year":"2014","journal-title":"Nature neuroscience"},{"key":"pcbi.1010764.ref003","first-page":"1","article-title":"High-dimensional geometry of population responses in visual cortex","author":"C Stringer","year":"2019","journal-title":"Nature"},{"issue":"6","key":"pcbi.1010764.ref004","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1038\/nbt.2594","article-title":"viSNE enables visualization of high dimensional single-cell data and reveals phenotypic heterogeneity of leukemia","volume":"31","author":"EaD Amir","year":"2013","journal-title":"Nature biotechnology"},{"issue":"04","key":"pcbi.1010764.ref005","doi-asserted-by":"crossref","first-page":"1750017","DOI":"10.1142\/S0219720017500172","article-title":"Application of t-SNE to human genetic data","volume":"15","author":"W Li","year":"2017","journal-title":"Journal of bioinformatics and computational biology"},{"issue":"1","key":"pcbi.1010764.ref006","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1038\/nbt.4314","article-title":"Dimensionality reduction for visualizing single-cell data using UMAP","volume":"37","author":"E Becht","year":"2019","journal-title":"Nature biotechnology"},{"issue":"1","key":"pcbi.1010764.ref007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-019-13056-x","article-title":"The art of using t-SNE for single-cell transcriptomics","volume":"10","author":"D Kobak","year":"2019","journal-title":"Nature communications"},{"issue":"Nov","key":"pcbi.1010764.ref008","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"Lvd Maaten","year":"2008","journal-title":"Journal of machine learning research"},{"key":"pcbi.1010764.ref009","first-page":"857","volume-title":"Advances in neural information processing systems","author":"GE Hinton","year":"2003"},{"key":"pcbi.1010764.ref010","doi-asserted-by":"crossref","unstructured":"McInnes L, Healy J, Melville J. 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Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:14091556. 2014;."},{"issue":"3","key":"pcbi.1010764.ref016","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1088\/0143-0807\/29\/3\/023","article-title":"The mean distance to the nth neighbour in a uniform distribution of random points: an application of probability theory","volume":"29","author":"P Bhattacharyya","year":"2008","journal-title":"European Journal of Physics"},{"key":"pcbi.1010764.ref017","volume-title":"bioRxiv","author":"B Sotomayor-Gomez","year":"2020"},{"issue":"6013","key":"pcbi.1010764.ref018","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1126\/science.1195870","article-title":"Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment","volume":"331","author":"P Berkes","year":"2011","journal-title":"Science"},{"issue":"9","key":"pcbi.1010764.ref019","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1038\/s41593-019-0460-x","article-title":"The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep","volume":"22","author":"R Chaudhuri","year":"2019","journal-title":"Nature neuroscience"},{"issue":"12","key":"pcbi.1010764.ref020","doi-asserted-by":"crossref","first-page":"e1000260","DOI":"10.1371\/journal.pbio.1000260","article-title":"Distributed fading memory for stimulus properties in the primary visual cortex","volume":"7","author":"D Nikoli\u0107","year":"2009","journal-title":"PLoS biology"},{"issue":"3","key":"pcbi.1010764.ref021","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.neuron.2009.03.014","article-title":"Spontaneous events outline the realm of possible sensory responses in neocortical populations","volume":"62","author":"A Luczak","year":"2009","journal-title":"Neuron"},{"issue":"6437","key":"pcbi.1010764.ref022","doi-asserted-by":"crossref","first-page":"eaav7893","DOI":"10.1126\/science.aav7893","article-title":"Spontaneous behaviors drive multidimensional, brainwide activity","volume":"364","author":"C Stringer","year":"2019","journal-title":"Science"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1010764","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010764","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T18:30:52Z","timestamp":1672857052000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010764"}},"subtitle":[],"editor":[{"given":"Emma Claire","family":"Robinson","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,12,20]]},"references-count":22,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12,20]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010764","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1010764","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,20]]}}}