Rappresenta l'istogramma di una Gaussian Mixture

Possiamo usare gli istogrammi per avere una panoramica generale della distribuzione di un mixture model. Da un istogramma possiamo intuire quante componenti potrebbe avere e se le ipotesi sulla distribuzione sono adeguate.

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Modelli di Mixture in R

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Istruzioni dell'esercizio

Usando ggplot(), crea l'istogramma per i dati simulati mixture. Per farlo, prima trasforma mixture in un data frame che abbia una variabile x.
Poi, usando la funzione geom_histogram(), specifica che l'asse y deve rappresentare la densità e che il numero di bin è 50.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# Transform into a data frame
mixture <- ___(x = ___)

# Create histogram especifiying that is a density plot
mixture %>% 
  ggplot() + geom_histogram(aes(x = x, y = ___), bins = ___)

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Questo esercizio fa parte del corso

Modelli di Mixture 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: Introduzione al clustering basato su modelli Exercise 2: Approcci al clustering Exercise 3: Esplora i dati sul genere Exercise 4: Distribuzione gaussiana Exercise 5: Campionare da una distribuzione Gaussiana Exercise 6: Stime (non proprio ottime) della media e della deviazione standard Exercise 7: Gaussian Mixture Models (GMM)Exercise 8: Simula un mix di due distribuzioni gaussiane Exercise 9: Rappresenta l'istogramma di una Gaussian Mixture

Esercizio in corso

Exercise 10: Miscela di tre distribuzioni gaussiane

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`