Bivariate Gaussian Mixture Models

Mixture Models in R

Victor Medina

Researcher at The University of Edinburgh

Gender data

One variable

gender %>% 
    select(Weight) %>% 
    head()

    Weight
1 241.8936
2 162.3105
3 212.7409
4 220.0425
5 206.3498
6 152.2122

Two variables

gender %>% 
    select(Weight, BMI) %>% 
    head()

    Weight        BMI
1 241.8936 31.18576
2 162.3105 24.12104
3 212.7409 27.23291
4 220.0425 30.06706
5 206.3498 29.70803
6 152.2122 23.66049
Mixture Models in R

One variable

Two variables

Mixture Models in R

Modeling with mixture models

  1. Which is the suitable probability distribution?
    • Bivariate Gaussian distribution
  2. How many sub-populations should we consider?
    • Two clusters
  3. Which are the parameters and their estimations?
    • The means (now in 2 dimension), the "standard deviation" (now a matrix) and the proportions
    • flexmix for the estimations
Mixture Models in R

Bivariate Gaussian distribution

mean

10  5

covariance_matrix

     [,1] [,2]
[1,]   25    0
[2,]    0   25
Mixture Models in R

Bivariate Gaussian distribution

mean

10  5

covariance_matrix

     [,1] [,2]
[1,]   25   20
[2,]   20   25

Mixture Models in R

Coming back to the Gender data

  1. Which distribution?
    • Bivariate Gaussian distribution
  2. How many clusters?
    • Two
  3. Which parameters?
    • The proportions
    • The means
    • The covariance matrices
Mixture Models in R

Let's practice!

Mixture Models in R

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