FCM (fuzzy c-means algorithm) based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. The added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Clustering Algorithm Based on Mahalanobis distance by t...

The rival penalized competitive learning (RPCL) algorithm has been developed to make the clustering analysis on a set of sample data in which the number of clusters is unknown, and recent theoretical analysis shows that it can be constructed by minimizing a special kind of cost function on the sample data. In this paper, we use the Mahalanobis distance instead of the Euclidean distance in the c...

The relations between two distance matrices on the same nite set are analyzed via metric scaling by correlating principal axis Some applications are given and illustrated with examples Introduction Dissimilarities similarities and distances are fundamental concepts in mul tidimensional scaling and related topics Euclidean and Mahalanobis dis tance also play a basic role in techniques such as re...

Background: Lycianthes moziniana (Capsiceae, Solanaceae) is an endemic and widespread species in Mexico. Morphological molecular evidence suggested three varieties (L. var. margaretiana, L. oaxacana).
 Hypotheses: integrated by differentiated lineages corresponding to the identified.
 Studied species: (Dunal) Bitter.
 Study sites dates: Mexico from 2017 2021.
 Methods: We me...

In this thesis, we consider the clustering of time series data; specifically, time series that can be modeled in the state space framework. Of primary focus is the pairwise discrepancy between two state space time series. The state space model can be formulated in terms of two equations: the state equation, based on a latent process, and the observation equation. Because the unobserved state pr...