Dimensionality Reduction for Distributed Vision Systems Using Random Projection

2010 ◽  
Author(s):  
Vildana Sulic ◽  
Janez Pers ◽  
Matej Kristan ◽  
Stanislav Kovacic
Keyword(s):  
Dimensionality Reduction ◽  
Random Projection ◽  
Vision Systems ◽  
Distributed Vision

scholarly journals Dimensionality reduction for k-distance applied to persistent homology

2021 ◽  
Author(s):  
Shreya Arya ◽  
Jean-Daniel Boissonnat ◽  
Kunal Dutta ◽  
Martin Lotz
Keyword(s):  
Dimensionality Reduction ◽  
Persistent Homology ◽  
Random Projection ◽  
Distance Functions ◽  
Random Projections ◽  
Annual Symposium ◽  
Gaussian Width ◽  
College Park ◽  
Low Dimensional ◽  
Open Question

AbstractGiven a set P of n points and a constant k, we are interested in computing the persistent homology of the Čech filtration of P for the k-distance, and investigate the effectiveness of dimensionality reduction for this problem, answering an open question of Sheehy (The persistent homology of distance functions under random projection. In Cheng, Devillers (eds), 30th Annual Symposium on Computational Geometry, SOCG’14, Kyoto, Japan, June 08–11, p 328, ACM, 2014). We show that any linear transformation that preserves pairwise distances up to a $$(1\pm {\varepsilon })$$ ( 1 ± ε ) multiplicative factor, must preserve the persistent homology of the Čech filtration up to a factor of $$(1-{\varepsilon })^{-1}$$ ( 1 - ε ) - 1 . Our results also show that the Vietoris-Rips and Delaunay filtrations for the k-distance, as well as the Čech filtration for the approximate k-distance of Buchet et al. [J Comput Geom, 58:70–96, 2016] are preserved up to a $$(1\pm {\varepsilon })$$ ( 1 ± ε ) factor. We also prove extensions of our main theorem, for point sets (i) lying in a region of bounded Gaussian width or (ii) on a low-dimensional submanifold, obtaining embeddings having the dimension bounds of Lotz (Proc R Soc A Math Phys Eng Sci, 475(2230):20190081, 2019) and Clarkson (Tighter bounds for random projections of manifolds. In Teillaud (ed) Proceedings of the 24th ACM Symposium on Computational Geom- etry, College Park, MD, USA, June 9–11, pp 39–48, ACM, 2008) respectively. Our results also work in the terminal dimensionality reduction setting, where the distance of any point in the original ambient space, to any point in P, needs to be approximately preserved.

A Dimensionality Reduction-Based Transformation to Support Business Collaboration

2011 ◽  
pp. 79-102
Author(s):  
Stanley R.M. Oliveira ◽  
Osmar R. Zaiane
Keyword(s):  
Dimensionality Reduction ◽  
Data Clustering ◽  
Privacy Preservation ◽  
Clustering Algorithms ◽  
Random Projection ◽  
Mathematical Foundation ◽  
Privacy Concerns ◽  
Privacy Requirements ◽  
Data Owner ◽  
Privacy Issues

While the sharing of data is known to be beneficial in data mining applications and widely acknowledged as advantageous in business, this information sharing can become controversial and thwarted by privacy regulations and other privacy concerns. Data clustering for instance could be more accurate if more information is available, hence the data sharing. Any solution needs to balance the clustering requirements and the privacy issues. Rather than simply hindering data owners from sharing information for data analysis, a solution could be designed to meet privacy requirements and guarantee valid data clustering results. To achieve this dual goal, this chapter introduces a method for privacy-preserving clustering, called Dimensionality Reduction-Based Transformation (DRBT). This method relies on the intuition behind random projection to protect the underlying attribute values subjected to cluster analysis. It is shown analytically and empirically that transforming a dataset using DRBT, a data owner can achieve privacy preservation and get accurate clustering with little overhead of communication cost. Such a method presents the following advantages: it is independent of distance-based clustering algorithms; it has a sound mathematical foundation; and it does not require CPU-intensive operations.

scholarly journals A Novel Two-Stage Spectrum-Based Approach for Dimensionality Reduction: A Case Study on the Recognition of Handwritten Numerals

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Amin Shayegan ◽  
Saeed Aghabozorgi ◽  
Ram Gopal Raj
Keyword(s):  
Principal Component Analysis ◽  
Pattern Recognition ◽  
Feature Selection ◽  
Dimensionality Reduction ◽  
Feature Vector ◽  
Principal Component ◽  
Random Projection ◽  
Component Analysis ◽  
Two Stage ◽  
Linear Discriminant

Dimensionality reduction (feature selection) is an important step in pattern recognition systems. Although there are different conventional approaches for feature selection, such as Principal Component Analysis, Random Projection, and Linear Discriminant Analysis, selecting optimal, effective, and robust features is usually a difficult task. In this paper, a new two-stage approach for dimensionality reduction is proposed. This method is based on one-dimensional and two-dimensional spectrum diagrams of standard deviation and minimum to maximum distributions for initial feature vector elements. The proposed algorithm is validated in an OCR application, by using two big standard benchmark handwritten OCR datasets, MNIST and Hoda. In the beginning, a 133-element feature vector was selected from the most used features, proposed in the literature. Finally, the size of initial feature vector was reduced from 100% to 59.40% (79 elements) for the MNIST dataset, and to 43.61% (58 elements) for the Hoda dataset, in order. Meanwhile, the accuracies of OCR systems are enhanced 2.95% for the MNIST dataset, and 4.71% for the Hoda dataset. The achieved results show an improvement in the precision of the system in comparison to the rival approaches, Principal Component Analysis and Random Projection. The proposed technique can also be useful for generating decision rules in a pattern recognition system using rule-based classifiers.

Sign in / Sign up

Export Citation Format

Share Document