Crea le ellissi

L'area racchiusa dall'ellisse rappresenta il 95% delle osservazioni del cluster, quindi questa curva è utile per visualizzare dove si trova il cluster. Poiché abbiamo già estratto le medie (mean_comp_number) e le matrici di covarianza (covariance_comp_number), possiamo creare facilmente le ellissi per i due cluster.

Tieni però presente che le ellissi non considerano le proporzioni e mostrano solo dove sono i cluster, ma non la loro importanza.

Questo esercizio fa parte del corso

Modelli di Mixture in R

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Istruzioni dell'esercizio

Usa la funzione ellipse() per creare queste curve. La funzione prende la matrice di covarianza come argomento x e la media come argomento centre.
Usa il numero di righe nel dataset gender come npoints.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

# Create ellipse curve 1
ellipse_comp_1 <- ___(x = ___, 
                          centre = ___,
                          npoints = nrow(___))
head(ellipse_comp_1)

# Create ellipse curve 2
ellipse_comp_2 <- ___(x = ___, 
                          centre = ___,
                          npoints = ___(gender))
head(ellipse_comp_2)

Modifica ed esegui il codice

Questo esercizio fa parte del corso

Modelli di Mixture in R

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4.8+

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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: Modelli di Mixture Gaussiana univariati Exercise 2: Numero di cluster Exercise 3: Numero di parametri Exercise 4: Modelli di Mixture Gaussiana univariata con flexmix Exercise 5: Caso univariato con flexmix Exercise 6: Estrazione dei parametri per il caso univariato Exercise 7: Visualizzare un Mixture Model gaussiano univariato Exercise 8: Confronta i risultati Exercise 9: Modelli di Mixture Gaussiana bivariata Exercise 10: Termine incrociato della matrice di covarianza Exercise 11: Parametri nel caso bivariato Exercise 12: Modelli di mixture gaussiana bivariata con flexmix Exercise 13: Stima il modello con termini incrociati Exercise 14: Ottieni le componenti Exercise 15: Crea le ellissi

Esercizio in corso

Exercise 16: Visualizza i cluster

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`