Some properties and applications of Menger probabilistic inner product spaces

Xiao, Jianjun; Zhu, Xinghua

doi:10.1016/j.fss.2022.04.018

Cited by 1 publication

(1 citation statement)

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“…However, there are various spaces in mathematics, such as metric space, vector space, normed linear space, and inner product space. Among these spaces, the inner product space adds a "structure" [47], i.e., inner product, in which the angles and lengths of vectors are discussed and it can possess the properties of nonnegativity such as non-degeneracy, conjugate symmetry, first-variable linearity and secondvariable conjugate linearity. Therefore, in this paper, our objective is to explore samples in the inner product space and a framework that can potentially preserve the structure of the data space by integrating the structure of different elements in the higher-dimensional space into the lower-dimensional space via inner product operations.…”

Section: Inner Product Spacementioning

confidence: 99%

Unsupervised Feature Selection with Latent Relationship Penalty Term

Ma,

Huang,

et al. 2023

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With the exponential growth of high dimensional unlabeled data, unsupervised feature selection (UFS) has attracted considerable attention due to its excellent performance in machine learning. Existing UFS methods implicitly assigned the same attribute score to each sample, which disregarded the distinctiveness of features and weakened the clustering performance of UFS methods to some extent. To alleviate these issues, a novel UFS method is proposed, named unsupervised feature selection with latent relationship penalty term (LRPFS). Firstly, latent learning is innovatively designed by assigning explicitly an attribute score to each sample according to its unique importance in clustering results. With this strategy, the inevitable noise interference can be removed effectively while retaining the intrinsic structure of data samples. Secondly, an appropriate sparse model is incorporated into the penalty term to further optimize its roles as follows: (1) It imposes potential constraints on the feature matrix to guarantee the uniqueness of the solution. (2) The interconnection between data instances is established by a pairwise relationship situation. Extensive experiments on benchmark datasets demonstrate that the proposed method is superior to relevant state-of-the-art algorithms with an average improvement of 10.17% in terms of accuracy.

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Section: Inner Product Spacementioning

confidence: 99%