{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "##
NYU CSCI-UA 9473 Introduction to ML
\n", " ###
Unsupervised Learning (Part II)
\n", "\n", "
This week we will cover the EM algorithm, spectral clustering as well as some of the linear latent variable models
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercise 1. White matter, Gray matter and cerebrospinal fluid\n", "\n", "For this exercise, you will need to install nibabel. You can do this by typing the line 'pip install nibabel' in your terminal. \n", "\n", "We consider the MR image shown below. We want to segment this image into the white matter, gray matter and cerebrospinal fluid. \n", "\n", " - Start by plotting the historgram of all pixel values (you can do this with 'numpy.histogram'). How does the distribution look like ? \n", "\n", "- Use your histogram to initialize the E-M algorithm (means and variance). The plot the resulting distributions on top ofthe histogram. Does your algorithm correctly capture the three clusters?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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