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The existing methods of boundary points detection cannot differentiate boundary points from outliers as they are affected by the presence of outliers as well as by the size and density of clusters in the dataset. Also, they require tuning of one or more parameters and prior knowledge of the number of outliers in the dataset for tuning. In this research, a boundary points detection method called <jats:italic>BPF<\/jats:italic> is proposed which can effectively differentiate boundary points from outliers and core points. <jats:italic>BPF<\/jats:italic> combines the well-known outlier detection method <jats:italic>Local Outlier Factor<\/jats:italic> (LOF) with <jats:italic>Gravity<\/jats:italic> value to calculate the BPF score. Our proposed algorithm <jats:italic>StaticBPF<\/jats:italic> can detect the top-<jats:italic>m<\/jats:italic> boundary points in the given dataset. Importantly, <jats:italic>StaticBPF<\/jats:italic> requires tuning of only one parameter i.e. the number of nearest neighbors <jats:inline-formula><jats:alternatives><jats:tex-math>$$(k)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>k<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and can employ the same <jats:inline-formula><jats:alternatives><jats:tex-math>$$k$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>k<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> used by LOF for outlier detection. This paper also extends <jats:italic>BPF<\/jats:italic> for streaming data and proposes <jats:italic>StreamBPF<\/jats:italic>. <jats:italic>StreamBPF<\/jats:italic> employs a grid structure for improving <jats:italic>k<\/jats:italic>-nearest neighbor computation and an incremental method of calculating BPF scores of a subset of data points in a sliding window over data streams. In evaluation, the accuracy of <jats:italic>StaticBPF<\/jats:italic> and the runtime efficiency of <jats:italic>StreamBPF<\/jats:italic> are evaluated on synthetic and real data where they generally performed better than their competitors.<\/jats:p>","DOI":"10.1007\/s10115-023-01854-1","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T07:02:50Z","timestamp":1679382170000},"page":"2991-3022","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["BPF: a novel cluster boundary points detection method for static and streaming data"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3573-267X","authenticated-orcid":false,"given":"Vijdan","family":"Khalique","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2984-2258","authenticated-orcid":false,"given":"Hiroyuki","family":"Kitagawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0595-2230","authenticated-orcid":false,"given":"Toshiyuki","family":"Amagasa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,21]]},"reference":[{"key":"1854_CR1","doi-asserted-by":"crossref","unstructured":"Ackermann MR, M\u00e4rtens M, Raupach C et al (2012) Streamkm++ a clustering algorithm for data streams. 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