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Gaussian Mixture Model

Dr. Dinesh Kumar Vishwakarma

Professor,

Department of Information Technology,

Delhi Technological University, Delhi-110042

dinesh@dtu.ac.in

http://www.dtu.ac.in/Web/Departments/InformationTechnology/faculty/dkvishwakarma.php

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Introduction

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A Gaussian Mixture Model (GMM) is a probabilistic model that assumes all data points are generated from a mixture of a finite number of Gaussian distributions with unknown parameters.

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Applications of GMM

3

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K-Means vs GMM

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Hard vs Soft Clustering

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Definition

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Definition…

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Example

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Example…

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Example…

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Marks

Avg Cluster

Top Cluster

45

0.95

0.05

60

0.60

0.40

80

0.10

0.90

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Calculations

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10

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Calculations…

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x

40

45

50

55

60

70

75

80

85

90

γ₁ (Cluster 1)

0.99

0.99

0.99

0.95

0.82

0.18

0.05

0.01

0.01

0.01

γ₂ (Cluster 2)

0.01

0.01

0.01

0.05

0.18

0.82

0.95

0.99

0.99

0.99

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Calculations…

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Calculations…

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Calculations…

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Calculations…

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🧠 Final Insight

👉 Repeat EM steps until:

  • Means stabilize
  • Likelihood converges

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References

  • Jolliffe, I. T. (2002). Principal Component Analysis. Springer.
  • Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.

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