Parameters in het bivariate geval

De gender-gegevensset zou je ook met twee variabelen kunnen clusteren in plaats van één, maar die stap brengt extra complexiteit mee. In het univariate geval zagen we dat het aantal te schatten parameters zes is: 2 gemiddelden, 2 standaardafwijkingen en 2 proporties.

Als we een extra variabele toevoegen en de kruisterm verschillend van nul aannemen, moeten we nog steeds twee gemiddelden schatten, maar elk daarvan bestaat uit twee waarden. Bovendien bestaat de covariantiematrix uit vier waarden: de bijbehorende varianties en de kruisterm.

Hoeveel verschillende waarden moeten we schatten?

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Mixture Models in R

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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 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: Aantal clusters Exercise 3: Aantal parameters Exercise 4: Univariate Gaussiaanse mengmodellen met flexmix Exercise 5: Univariate geval met flexmix Exercise 6: Parameters extraheren voor univariate geval Exercise 7: Een univariate Gaussian Mixture Model visualiseren Exercise 8: Vergelijk de resultaten Exercise 9: Bivariate Gaussiaanse mengmodellen Exercise 10: Kruis-term uit de covariantiematrix Exercise 11: Parameters in het bivariate geval

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Exercise 12: Bivariate Gaussiaanse mengmodellen met flexmix Exercise 13: Het model met kruistermen fitten Exercise 14: Haal de componenten op Exercise 15: Maak de ellipsen Exercise 16: Visualiseer de 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`