Machine Learning Gaussian Mixture Models GaussianMixtureModel Classifiers GMMC

Machine Learning Gaussian Mixture Models (GMM) GMM • GMM: Gaussian mixture model • Good

Machine Learning Gaussian Mixture Models (GMM) GMM for 1 D PDF Modeling GMM: Gaussian

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling GMM: Gaussian

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling (II) GMM:

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling (III) Good

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling (IV) Bad

Machine Learning Gaussian Mixture Models (GMM) 3 Types of Cov. Matrices 1. Isotropic •

Machine Learning Gaussian Mixture Models (GMM) GMM with Isotropic Cov. Matrices • Isotropic covariance

Machine Learning Gaussian Mixture Models (GMM) GMM with Diagonal Cov. Matrices • Diagonal covariance

Machine Learning Gaussian Mixture Models (GMM) GMM with Full Cov. Matrices • Full covariance

Machine Learning Gaussian Mixture Models (GMM) GMM Growing • Growing GMM with full covariance

Machine Learning Gaussian Mixture Models (GMM) GMMC • GMMC: GMM-based Classifier • Steps 1.

Machine Learning Gaussian Mixture Models (GMM) Example of GMMC for Nonlinear Separable Dataset PDFs

Machine Learning Gaussian Mixture Models (GMM) Example of GMMC for Wine Dataset Without input

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Machine Learning Gaussian Mixture Models Gaussian-Mixture-Model Classifiers (GMMC) J. -S. Roger Jang (張智星) CSIE Dept. , National Taiwan University http: //mirlab. org/jang@mirlab. org

Machine Learning Gaussian Mixture Models (GMM) GMM • GMM: Gaussian mixture model • Good for • PDF modeling • Classification • Characteristics • Highly flexible for complicated datasets • Proven real-world applications, including speech recognition, image understanding, and many more • No guarantee for convergence to the global optimum 2 2021/6/3 2

Machine Learning Gaussian Mixture Models (GMM) GMM for 1 D PDF Modeling GMM: Gaussian Mixture Models 3 2021/6/3 3

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling GMM: Gaussian Mixture Models 4 2021/6/3 4

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling (II) GMM: Gaussian Mixture Models 5 2021/6/3 5

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling (III) Good convergence 6 2021/6/3 6

Machine Learning Gaussian Mixture Models (GMM) GMM for 2 D PDF Modeling (IV) Bad convergence 7 2021/6/3 7

Machine Learning Gaussian Mixture Models (GMM) 3 Types of Cov. Matrices 1. Isotropic • Circular contours 2. Diagonal • Ellipse contours 3. Full • 8 2021/6/3 Slanted ellipse contours 8

Machine Learning Gaussian Mixture Models (GMM) GMM with Isotropic Cov. Matrices • Isotropic covariance matrices • gmm. Train. Demo 2 d. Cov. Type 01 9 2021/6/3 9

Machine Learning Gaussian Mixture Models (GMM) GMM with Diagonal Cov. Matrices • Diagonal covariance matrices • gmm. Train. Demo 2 d. Cov. Type 02. m 10 2021/6/3 10

Machine Learning Gaussian Mixture Models (GMM) GMM with Full Cov. Matrices • Full covariance matrices • gmm. Train. Demo 2 d. Cov. Type 03. m 11 2021/6/3 11

Machine Learning Gaussian Mixture Models (GMM) GMM Growing • Growing GMM with full covariance matrices 12 2021/6/3 12

Machine Learning Gaussian Mixture Models (GMM) GMMC • GMMC: GMM-based Classifier • Steps 1. Training stage: Train a GMM for each class 2. Application stage: Assign a class of the maximum PDF to a new sample 13 2021/6/3 13

Machine Learning Gaussian Mixture Models (GMM) Example of GMMC for Nonlinear Separable Dataset PDFs and contours: 14 2021/6/3 Decision boundaries: 14

Machine Learning Gaussian Mixture Models (GMM) Example of GMMC for Wine Dataset Without input normalization: 15 2021/6/3 With input normalization: 15