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Syst."],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Data distribution presents sparsity in a high-dimensional space, thus difficulty affording sufficient information to distinguish anomalies from normal instances. Moreover, a high-dimensional space may exist many subspaces, obviously, anomalies can exist in any subspaces. This also creates trouble for anomaly mining. Consequently, it is a challenge for anomaly mining in a high-dimensional space. To address this, here proposed a deep hypersphere method fused with probabilistic approach for anomaly mining. In the proposed method, the deep neural network is used as a feature extractor to capture those layered low-dimensional features from the data lying in a high-dimensional space. To promote the ability of the deep neural network to capture these features, the probability approach of sample binary-classification is fused into the loss function, thereby forming the probability deep neural network Then, the hypersphere is used as an anomalous detector. In the low-dimensional features extracted by the deep neural network, the anomalous detector separates anomaly features from normal features. Finally, experimental results on synthetic and real-world data sets show that the proposed method not only outperforms the state-of-the-art methods in the precision of mined anomalies, but also this hybrid method consisting of deep neural networks and traditional detection methods has outstanding capabilities of mining high-dimensional anomalies. We find that deep neural networks fusing the probabilistic method of sample multi-classification can capture these desired low-dimensional features; moreover, these captured low-dimensional features present more obvious layered characteristics. We also demonstrate that as long as these captured features represent a fewer anomaly instances, it can sufficiently identify anomalies from normal instances.<\/jats:p>","DOI":"10.1007\/s40747-022-00695-9","type":"journal-article","created":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T10:34:41Z","timestamp":1648204481000},"page":"4205-4220","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Anomaly detection for high-dimensional space using deep hypersphere fused with probability approach"],"prefix":"10.1007","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9741-9526","authenticated-orcid":false,"given":"Jian","family":"Zheng","sequence":"first","affiliation":[]},{"given":"Jingyi","family":"Li","sequence":"additional","affiliation":[]},{"given":"Cong","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Jianfeng","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Jiang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Hongling","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,24]]},"reference":[{"issue":"4","key":"695_CR1","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1109\/TNNLS.2018.2861743","volume":"30","author":"Yu Kui","year":"2019","unstructured":"Kui Yu, Chen H (2019) Markov Boundary-Based Outlier Mining. 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