Calcutta Statistical Association Bulletin, Volume 75, Issue 1, Page 60-71, May 2023.
We propose a novel nonparametric cluster validity index which can be used to evaluate the unknown number of existing clusters prevailing a data set, to assess the quality of classification for a clustered set of data members, or to compare the clustering output obtained from different algorithms. Our efficient measure depends only on the observation-wise distances of the non-negative clustered data from their origin given in an arbitrary dimensional space. Its fast implementation makes it appealing for big data analysis, whereas the high-dimensional applicability widens its usefulness. Easy interpretation, simple algorithm, speedy computation and great performance, shown in terms of data study, establish our advised validity index as a strong cluster accuracy measure among the acknowledged ones from the literature.AMS subject classification: 62H30
Quotients of exact categories by pseudo-cluster-tilting subcategories
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Group module structure of symmetrized tensor spaces
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On modules and rings having large absolute direct summands
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Generalized extended Mittag-Leffler function and its properties pertaining to integral transforms and fractional calculus
Kernel density estimation using additive randomized response technique (RRT) models
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Continuous-time locally stationary time series models
We adapt the classical definition of locally stationary processes in discrete time (see e.g. Dahlhaus, ‘Locally stationary processes’, in Time Series Analysis: Methods and Applications (2012)) to the continuous-time setting and obtain equivalent representations in the time and frequency domains. From this, a unique time-varying spectral density is derived using the Wigner–Ville spectrum. As an example, we investigate time-varying Lévy-driven state space processes, including the class of time-varying Lévy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying Lévy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.
Half-isomorphisms of automorphic loops
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