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Dynamic Clustering of n-Dimensional Data on Tangential Space

机译：切向空间上n维数据的动态聚类

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Clustering of n-dimensional data into classes is consistent problem of research, Large number of efficient clustering techniques are in literature and still more are in development. K-means and Spherical K-means are standard clustering methods which are frequently used. Euclidean distance and cosine distance are mainly used by clustering methods. Data distribution is always non-linear and distributed in n-dimensional hyper sphere. Euclidean distance did not take care of topology of the hyper space. Clustering of data using spherical K-means clustering is done through mapping all data points in hyper sphere to the nearest cosine angular distance, but both do not take care of geodesic distance between the points on the surface of the hyper sphere. In this paper new mathematical dynamic clustering approach has been proposed which take care of topology of the data distribution between various clusters and geodesic distance between the points with in the cluster. Theoretical and mathematical results are discussed and empirically verified on the iris data set.
机译：将n维数据聚类到类中一直是研究的问题。文献中有大量有效的聚类技术，并且仍在发展中。 K均值和球形K均值是常用的标准聚类方法。欧几里德距离和余弦距离主要通过聚类方法使用。数据分配始终是非线性的，并且分布在n维超球体中。欧几里得距离并未考虑超空间的拓扑。通过将超球面中的所有数据点映射到最接近的余弦角距离，可以使用球形K均值聚类对数据进行聚类，但是这两者都不考虑超球面表面上各点之间的测地距离。本文提出了一种新的数学动态聚类方法，该方法考虑了各个聚类之间数据分布的拓扑以及聚类中各点之间的测地距离。对虹膜数据集进行了理论和数学结果的讨论并进行了经验验证。

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