solves exercise 7

Author: anishLearnsToCode

README.md

@@ -112,6 +112,14 @@ __Instructor__: Andrew Ng.
 - [Principal Component Analysis](week8/principal-component-analysis.md)
 
 ### Programming Exercises
+- [Exercise 7: Questions and Explanations](week8/ex7.pdf)
+- [K Means Clustering and PCA(Principal Component Analysis)](week8/ex7)
+    - [Perform PCA(Principal Component Analysis)](week8/ex7/pca.m)
+    - [Project a Dataset into lower dimensional space](week8/ex7/projectData.m)
+    - [Recover the Original Data from the Projection](week8/ex7/recoverData.m)
+    - [Find Closest Centroids Using K-Means](week8/ex7/findClosestCentroids.m)
+    - [Compute Centroid Means](week8/ex7/computeCentroids.m)
+    - [Initialize K means for Centroids](week8/ex7/kMeansInitCentroids.m)
 
 ## Week 9
 ### Quizzes

week8/assets/pca/question-3-2-incorrect.PNG

@@ -0,0 +1,27 @@
+function centroids = computeCentroids(X, idx, K)
+  %COMPUTECENTROIDS returns the new centroids by computing the means of the 
+  %data points assigned to each centroid.
+  %   centroids = COMPUTECENTROIDS(X, idx, K) returns the new centroids by 
+  %   computing the means of the data points assigned to each centroid. It is
+  %   given a dataset X where each row is a single data point, a vector
+  %   idx of centroid assignments (i.e. each entry in range [1..K]) for each
+  %   example, and K, the number of centroids. You should return a matrix
+  %   centroids, where each row of centroids is the mean of the data points
+  %   assigned to it.
+
+  [m n] = size(X);
+  centroids = zeros(K, n);
+  frequency = zeros(K, 1);
+  for i = 1:m
+    frequency(idx(i))++;
+    centroids(idx(i), :) += X(i, :);
+  endfor
+  mask = centroids == 0;
+  frequency = maskZeroAsOne(frequency);
+  centroids = centroids ./ frequency;
+  
+  function mat = maskZeroAsOne(mat)
+    mask = mat == 0;
+    mat += mask;
+  endfunction
+end

week8/assets/pca/question-3-incorrect.PNG

@@ -0,0 +1,59 @@
+function [h, display_array] = displayData(X, example_width)
+%DISPLAYDATA Display 2D data in a nice grid
+%   [h, display_array] = DISPLAYDATA(X, example_width) displays 2D data
+%   stored in X in a nice grid. It returns the figure handle h and the 
+%   displayed array if requested.
+
+% Set example_width automatically if not passed in
+if ~exist('example_width', 'var') || isempty(example_width) 
+	example_width = round(sqrt(size(X, 2)));
+end
+
+% Gray Image
+colormap(gray);
+
+% Compute rows, cols
+[m n] = size(X);
+example_height = (n / example_width);
+
+% Compute number of items to display
+display_rows = floor(sqrt(m));
+display_cols = ceil(m / display_rows);
+
+% Between images padding
+pad = 1;
+
+% Setup blank display
+display_array = - ones(pad + display_rows * (example_height + pad), ...
+                       pad + display_cols * (example_width + pad));
+
+% Copy each example into a patch on the display array
+curr_ex = 1;
+for j = 1:display_rows
+	for i = 1:display_cols
+		if curr_ex > m, 
+			break; 
+		end
+		% Copy the patch
+		
+		% Get the max value of the patch
+		max_val = max(abs(X(curr_ex, :)));
+		display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ...
+		              pad + (i - 1) * (example_width + pad) + (1:example_width)) = ...
+						reshape(X(curr_ex, :), example_height, example_width) / max_val;
+		curr_ex = curr_ex + 1;
+	end
+	if curr_ex > m, 
+		break; 
+	end
+end
+
+% Display Image
+h = imagesc(display_array, [-1 1]);
+
+% Do not show axis
+axis image off
+
+drawnow;
+
+end

week8/assets/pca/question-5-2-incorrect.PNG

@@ -0,0 +1,8 @@
+function drawLine(p1, p2, varargin)
+%DRAWLINE Draws a line from point p1 to point p2
+%   DRAWLINE(p1, p2) Draws a line from point p1 to point p2 and holds the
+%   current figure
+
+plot([p1(1) p2(1)], [p1(2) p2(2)], varargin{:});
+
+end