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.

Pengantar pengelompokan berbasis model

Pendekatan pengelompokan (clustering)

Jelajahi data gender

Distribusi Gaussian

Sampling a Gaussian distribution

(kurang baik) Estimasi mean dan sd

Model campuran Gaussian (GMM)

Mensimulasikan campuran dua distribusi Gaussian

Plot histogram Campuran Gaussian

Campuran tiga distribusi Gaussian

Introduction to Mixture Models

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.

Structure of mixture models

Which probability distribution?

Handwritten digits dataset

Parameters estimation

Estimation given the probabilities

Calculating the probabilities

EM algorithm

Expectation function

Maximization function

Apply the two steps

Plot the estimated clusters

Structure of Mixture Models and Parameters Estimation

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.

Univariate Gaussian Mixture Models

Number of clusters

Number of parameters

Univariate Gaussian Mixture Models with flexmix

Univariate case with flexmix

Extracting Parameters for Univariate Case

Visualizing Univariate Gaussian Mixture Model

Compare the results

Bivariate Gaussian Mixture Models

Cross-term from covariance matrix

Parameters in the bivariate case

Bivariate Gaussian Mixture Models with flexmix

Fit the model with cross-terms

Get the components

Create the ellipses

Visualize the clusters

Mixture of Gaussians with `flexmix`

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.

Bernoulli Mixture Models

Binary images

How many values?

Bernoulli Mixture Models with flexmix

Handwritten digits with `flexmix`

Poisson Mixture Models

Discover the lambda

Sample from Poisson distribution

Poisson Mixture Models with flexmix

Crimes data with `flexmix`

Mixture Models Beyond Gaussians

Chicago Crimes dataset

Digits dataset

Gender dataset

Pemodelan campuran adalah cara merepresentasikan populasi ketika kita tertarik pada heterogenitasnya. Model campuran menggunakan sebaran peluang yang sudah dikenal (misalnya Gaussian, Poisson, Binomial) untuk menyediakan kerangka statistik yang formal namun praktis bagi pengelompokan dan klasifikasi. Berbeda dari pendekatan pengelompokan standar, kita dapat mengestimasi probabilitas keanggotaan suatu klaster dan melakukan inferensi tentang subpopulasi. Sebagai contoh, dalam konteks pemasaran, Anda mungkin ingin mengelompokkan berbagai kelompok pelanggan dan menemukan probabilitas masing-masing untuk membeli produk tertentu guna menargetkan mereka dengan promosi khusus. Saat menerapkan pemrosesan bahasa alami pada sekumpulan dokumen yang besar, Anda mungkin ingin mengelompokkan dokumen ke dalam berbagai topik dan memahami seberapa penting tiap topik di setiap dokumen. Dalam kursus ini, Anda akan mempelajari apa itu Model Campuran, bagaimana cara mengestimasi model tersebut, dan kapan model ini tepat untuk digunakan!

Intermediate R

Introduction to the Tidyverse

Foundations of Probability in R

Pelajari model campuran: kerangka statistik untuk pengelompokan dan klasifikasi probabilistik.

Model Campuran di R

Pelajari model campuran: kerangka kerja statistik yang praktis dan formal untuk pengelompokan dan klasifikasi probabilistik.

Pendekatan pengelompokan (clustering)

Model Campuran di R

Latihan interaktif praktis