scholarly journals Nonlinear Laplacian spectral analysis: capturing intermittent and low-frequency spatiotemporal patterns in high-dimensional data

2012 ◽  
Vol 6 (3) ◽  
pp. 180-194 ◽  
Author(s):  
Dimitrios Giannakis ◽  
Andrew J. Majda
Keyword(s):  
Spectral Analysis ◽  
High Dimensional Data ◽  
Low Frequency ◽  
Spatiotemporal Patterns ◽  
High Dimensional

scholarly journals On landmark selection and sampling in high-dimensional data analysis

2009 ◽  
Vol 367 (1906) ◽  
pp. 4295-4312 ◽  
Author(s):  
Mohamed-Ali Belabbas ◽  
Patrick J. Wolfe
Keyword(s):  
Spectral Analysis ◽  
Partial Information ◽  
Selection Process ◽  
High Dimensional Data ◽  
Video Data ◽  
High Dimensional ◽  
Dimensional Manifold ◽  
Performance Bounds ◽  
Landmark Selection ◽  
Low Dimensional

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here, we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nyström extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.

A Fast Clustering Algorithm for Large-scale and High Dimensional Data

2009 ◽  
Vol 35 (7) ◽  
pp. 859-866
Author(s):  
Ming LIU ◽  
Xiao-Long WANG ◽  
Yuan-Chao LIU
Keyword(s):  
Large Scale ◽  
Clustering Algorithm ◽  
High Dimensional Data ◽  
High Dimensional

Approximate Cluster Heat Maps of Large High-Dimensional Data

2018 ◽  
Author(s):  
Punit Rathore ◽  
James C. Bezdek ◽  
Dheeraj Kumar ◽  
Sutharshan Rajasegarar ◽  
Marimuthu Palaniswami
Keyword(s):  
High Dimensional Data ◽  
High Dimensional ◽  
Heat Maps

scholarly journals The Generalized Bayes Method for High-Dimensional Data Recognition with Applications to Audio Signal Recognition

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 19
Author(s):  
Hsiuying Wang
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Conventional Method ◽  
High Dimensional Data ◽  
Audio Signal ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Signal Recognition ◽  
Bayes Method ◽  
Generalized Bayes

High-dimensional data recognition problem based on the Gaussian Mixture model has useful applications in many area, such as audio signal recognition, image analysis, and biological evolution. The expectation-maximization algorithm is a popular approach to the derivation of the maximum likelihood estimators of the Gaussian mixture model (GMM). An alternative solution is to adopt a generalized Bayes estimator for parameter estimation. In this study, an estimator based on the generalized Bayes approach is established. A simulation study shows that the proposed approach has a performance competitive to that of the conventional method in high-dimensional Gaussian mixture model recognition. We use a musical data example to illustrate this recognition problem. Suppose that we have audio data of a piece of music and know that the music is from one of four compositions, but we do not know exactly which composition it comes from. The generalized Bayes method shows a higher average recognition rate than the conventional method. This result shows that the generalized Bayes method is a competitor to the conventional method in this real application.

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