scholarly journals Model-based regression clustering for high-dimensional data: application to functional data

2016 ◽  
Vol 11 (2) ◽  
pp. 243-279 ◽  
Author(s):  
Emilie Devijver
Keyword(s):  
Functional Data ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Model Based ◽  
Data Application

scholarly journals Smoothed Linear Modeling for Smooth Spectral Data

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Douglas M. Hawkins ◽  
Edgard M. Maboudou-Tchao
Keyword(s):  
Spectral Data ◽  
Functional Data ◽  
High Dimensional Data ◽  
Basis Functions ◽  
High Dimensional ◽  
Data Sets ◽  
Linear Modeling ◽  
Linear Discriminant ◽  
Smooth Basis ◽  
Prediction Problems

Classification and prediction problems using spectral data lead to high-dimensional data sets. Spectral data are, however, different from most other high-dimensional data sets in that information usually varies smoothly with wavelength, suggesting that fitted models should also vary smoothly with wavelength. Functional data analysis, widely used in the analysis of spectral data, meets this objective by changing perspective from the raw spectra to approximations using smooth basis functions. This paper explores linear regression and linear discriminant analysis fitted directly to the spectral data, imposing penalties on the values and roughness of the fitted coefficients, and shows by example that this can lead to better fits than existing standard methodologies.

scholarly journals Model-based clustering of high-dimensional data streams with online mixture of probabilistic PCA

2013 ◽  
Vol 7 (3) ◽  
pp. 281-300 ◽  
Author(s):  
Anastasios Bellas ◽  
Charles Bouveyron ◽  
Marie Cottrell ◽  
Jérôme Lacaille
Keyword(s):  
Data Streams ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Model Based Clustering ◽  
Probabilistic Pca ◽  
Model Based

scholarly journals Model-based Clustering using Automatic Differentiation: Confronting Misspecification and High-Dimensional Data

2019 ◽  
Author(s):  
Siva Rajesh Kasa ◽  
Vaibhav Rajan
Keyword(s):  
Automatic Differentiation ◽  
High Dimensional Data ◽  
Penalized Likelihood ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Adjusted Rand Index ◽  
Penalty Term ◽  
Model Based Clustering ◽  
Model Based ◽  
Leibler Divergence

AbstractWe study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based optimization using Automatic Differentiation (AD). Our simulation studies show that EM has better clustering performance, measured by Adjusted Rand Index, compared to GD in cases of misspecification, whereas on high dimensional data GD outperforms EM. We observe that both with EM and GD there are many solutions with high likelihood but poor cluster interpretation. To address this problem we design a new penalty term for the likelihood based on the Kullback Leibler divergence between pairs of fitted components. Closed form expressions for the gradients of this penalized likelihood are difficult to derive but AD can be done effortlessly, illustrating the advantage of AD-based optimization. Extensions of this penalty for high dimensional data and for model selection are discussed. Numerical experiments on synthetic and real datasets demonstrate the efficacy of clustering using the proposed penalized likelihood approach.

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