High-Dimensional Clustering via Random Projections

2021 ◽  
Author(s):  
Laura Anderlucci ◽  
Francesca Fortunato ◽  
Angela Montanari
Keyword(s):  
High Dimensional ◽  
Random Projections ◽  
High Dimensional Clustering

A conditional limit theorem for high-dimensional ℓᵖ-spheres

2018 ◽  
Vol 55 (4) ◽  
pp. 1060-1077 ◽  
Author(s):  
Steven S. Kim ◽  
Kavita Ramanan
Keyword(s):  
Limit Theorem ◽  
Large Deviation ◽  
Convex Geometry ◽  
Rare Event ◽  
High Dimensional ◽  
Random Projections ◽  
Dimensional Euclidean Space ◽  
High Dimensions ◽  
Geometric Setting ◽  
Conditional Limit

Abstract The study of high-dimensional distributions is of interest in probability theory, statistics, and asymptotic convex geometry, where the object of interest is the uniform distribution on a convex set in high dimensions. The ℓp-spaces and norms are of particular interest in this setting. In this paper we establish a limit theorem for distributions on ℓp-spheres, conditioned on a rare event, in a high-dimensional geometric setting. As part of our proof, we establish a certain large deviation principle that is also relevant to the study of the tail behavior of random projections of ℓp-balls in a high-dimensional Euclidean space.

scholarly journals Accelerating high-dimensional clustering with lossless data reduction

2017 ◽  
Vol 33 (18) ◽  
pp. 2867-2872 ◽  
Author(s):  
Bahjat F Qaqish ◽  
Jonathon J O’Brien ◽  
Jonathan C Hibbard ◽  
Katie J Clowers
Keyword(s):  
Data Reduction ◽  
High Dimensional ◽  
High Dimensional Clustering

scholarly journals Random projections and Hotelling’s T2 statistics for change detection in high-dimensional data streams

2013 ◽  
Vol 23 (2) ◽  
pp. 447-461 ◽  
Author(s):  
Ewa Skubalska-Rafajłowicz
Keyword(s):  
Discrete Time ◽  
Data Streams ◽  
Random Projection ◽  
Image Sequences ◽  
High Dimensional ◽  
Random Projections ◽  
Random Subspace ◽  
Noisy Image ◽  
Method Of Dimensionality Reduction ◽  
Diagnostic Properties

The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of Rn. We examine the random projection method using artificial noisy image sequences as examples.

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