Supplementary Material ofDifferentially Private Clustering in High-Dimensional Euclidean Spaces

Differentially Private Clustering in High-Dimensional Euclidean Spaces

We study the problem of clustering sensitive data while preserving the privacy of individuals represented in the dataset, which has broad applications in practical machine learning and data analysis tasks. Although the problem has been widely studied in the context of lowdimensional, discrete spaces, much remains unknown concerning private clustering in highdimensional Euclidean spaces R. In th...

An $\ell_1$-Method for Clustering High-Dimensional Data

In general, the clustering problem is NP–hard, and global optimality cannot be established for non–trivial instances. For high–dimensional data, distance–based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high–dimensional spaces. We propose a distance–based iterative method for clustering data in very high–dimensional space, usin...

Probabilistic Temporal Subspace Clustering: Supplementary Material

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

یادداشتی بر دوگانی AdS/CFT

We study duality of field theories in (d+1) dimensional flat Euclidean space and (d+1) dimensional Euclidean AdS space for both scalar the and vector fields. In the case of the scalar theory, the injective map between conformally coupled massless scalars in two spaces is reviewed. It is shown that for vector fields the injective map exists only in four dimensions. Since Euclidean AdS space is e...