Explore gender data

The data gender contains the Weight, the Height and the BMI indices of 10,000 people. The original data has a Gender label for 5,000 people that identify themselves as females and the other 5,000 as males. The labels will be useful later for testing how well the clustering performs against the real labels. However, in this subset of the dataset, the labels are not provided.

The data gender_with_probs also contains the probabilities of each data point belonging to a cluster. Since we are interested in two clusters, probabilities near 1 refer to one cluster and near 0 to the other.

The aim of this exercise is to have a glance at how a typical clustering dataset looks like before and after clustering.

Diese Übung ist Teil des Kurses

Mixture Models in R

Anleitung zur Übung

Use the function head to look at the first 6 observations of gender.
Use the function head to look at the first 6 observations of gender_with_probs.
Make a scatterplot with Weight in the x-axis and BMI in the y-axis. Colour the dots by their probability.

Interaktive Übung

Versuche dich an dieser Übung, indem du diesen Beispielcode vervollständigst.

# Have a look to gender (before clustering)
head(___)

# Have a look to gender_with_probs (after clustering)
head(___)

# Scatterplot with probabilities
gender_with_probs %>% 
  ggplot(aes(x = ___, y = ___, col = ___))+
  geom_point(alpha = 0.5)

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Diese Übung ist Teil des Kurses

Mixture Models in R

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In this chapter, you will be introduced to fundamental concepts in model-based clustering and how this approach differs from other clustering techniques. You will learn the generating process of Gaussian Mixture Models as well as how to visualize the clusters.

Exercise 1: Introduction to model-based clustering Exercise 2: Clustering approaches Exercise 3: Explore gender data

Aktuelle Übung

Exercise 4: Gaussian distribution Exercise 5: Sampling a Gaussian distribution Exercise 6: (not so good) Estimations of the mean and sd Exercise 7: Gaussian mixture models (GMM)Exercise 8: Simulate a mixture of two Gaussian distributions Exercise 9: Plot histogram of Gaussian Mixture Exercise 10: Mixture of three Gaussian distributions

In this chapter, you will be introduced to the main structure of Mixture Models, how to address different data with this approach and how to estimate the parameters involved. To accomplish the estimation, you will learn an iterative method called Expectation-Maximization algorithm.

Exercise 1: Structure of mixture models Exercise 2: Which probability distribution?Exercise 3: Handwritten digits dataset Exercise 4: Parameters estimation Exercise 5: Estimation given the probabilities Exercise 6: Calculating the probabilities Exercise 7: EM algorithm Exercise 8: Expectation function Exercise 9: Maximization function Exercise 10: Apply the two steps Exercise 11: Plot the estimated clusters

This chapter shows how to fit Gaussian Mixture Models in 1 and 2 dimensions with `flexmix` package. The data used is formed by 10.000 observations of people with their weight, height, body mass index and informed gender.

Exercise 1: Univariate Gaussian Mixture Models Exercise 2: Number of clusters Exercise 3: Number of parameters Exercise 4: Univariate Gaussian Mixture Models with flexmix Exercise 5: Univariate case with flexmix Exercise 6: Extracting Parameters for Univariate Case Exercise 7: Visualizing Univariate Gaussian Mixture Model Exercise 8: Compare the results Exercise 9: Bivariate Gaussian Mixture Models Exercise 10: Cross-term from covariance matrix Exercise 11: Parameters in the bivariate case Exercise 12: Bivariate Gaussian Mixture Models with flexmix Exercise 13: Fit the model with cross-terms Exercise 14: Get the components Exercise 15: Create the ellipses Exercise 16: Visualize the clusters

In this module, you will learn how Mixture Models extends to consider probability distributions different from the Gaussian and how these models are fitted with `flexmix`. The datasets used are handwritten digits images and the number of crimes in Chicago city. For the first dataset you will find clusters that summarize the handwritten digits and for the second dataset, you will find clusters of communities where is more or less dangerous to live in.

Exercise 1: Bernoulli Mixture Models Exercise 2: Binary images Exercise 3: How many values?Exercise 4: Bernoulli Mixture Models with flexmix Exercise 5: Handwritten digits with `flexmix`Exercise 6: Poisson Mixture Models Exercise 7: Discover the lambda Exercise 8: Sample from Poisson distribution Exercise 9: Poisson Mixture Models with flexmix Exercise 10: Crimes data with `flexmix`