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K-means算法和PCA Matlab实现.rar （21个子文件）

K-means算法和PCA Matlab实现

mlclass-ex7

pca.m 889B

plotProgresskMeans.m 840B

displayData.m 1KB

featureNormalize.m 510B

ex7data1.mat 995B

submit.m 9KB

submitWeb.m 10KB

kMeansInitCentroids.m 659B

ex7_pca.m 7KB

ex7faces.mat 10.52MB

ex7data2.mat 5KB

plotDataPoints.m 433B

computeCentroids.m 1KB

runkMeans.m 2KB

drawLine.m 232B

recoverData.m 1013B

bird_small.png 32KB

projectData.m 961B

findClosestCentroids.m 1KB

ex7.m 5KB

ex7.pdf 668KB

Programming Exercise 7:

K-means Clustering and Principal Component

Analysis

Machine Learning

November 29, 2011

Introduction

In this exercise, you will implement the K-means clustering algorithm and

apply it to compress an image. In the second part, you will us e principal

component analysis to ﬁnd a low-dimensional representation of face images.

Before starting on the programming exercise, we strongly recommend watch-

ing the video lectures and completing the review questions for the associated

topics.

To get started with the exercise, you will need to download the starter

code and unzip its contents to the directory where you wish to complete

the exercise. If needed, use the cd command in Octave to change to this

directory before starting this exercise.

Files included in this exercise

ex7.m - Octave/Matlab script for the ﬁrst exercise on K-means

ex7 pca.m - Octave/Matlab script for the second exercise on PCA

ex7data1.mat - Example Dataset for PCA

ex7data2.mat - Example Dataset for K-me ans

ex7faces.mat - Faces Dataset

bird small.png - Example Image

displayData.m - Displays 2D data stored in a matrix

drawLine.m - Draws a line over an exsiting ﬁgure

plotDataPoints.m - Initialization for K-means centroids

plotProgresskMeans.m - Plots each step of K-means as it proceeds

runkMeans.m - Runs the K-means algorithm

[?] pca.m - Perform principal component analysis

[?] projectData.m - Projects a data set into a lower dimensional space

[?] recoverData.m - Recovers the original data from the projection

[?] findClosestCentroids.m - Find closest centroids (used in K-me ans)

[?] computeCentroids.m - Compute centroid means (used in K-means)

[?] kMeansInitCentroids.m - Initialization for K-means centroids

? indicates ﬁles you will need to complete

Throughout the ﬁrst part of the exercise, you will be using the script

ex7.m, for the second part you will use ex7 pca.m. These scripts set up the

dataset for the problems and make calls to functions that you will write.

You are only required to modify functions in other ﬁles, by following the

instructions in this assignment.

Where to get help

We also strongly encourage using the online Q&A Forum to discuss exer-

cises with other students. However, do not look at any source code written

by others or share your source code with others.

If you run into network errors using the submit script, you can also use

an online form for submitting your solutions. To use this alternative submis-

sion interface, run the submitWeb script to generate a submission ﬁle (e.g.,

submit

ex7 part2.txt). You can then submit this ﬁle through the web

submission form in the programming exercises page (go to the programming

exercises page, then select the exercise you are submitting for). If you are

having no problems submitting through the standard submission system us-

ing the submit script, you do not need to use this alternative submission

interface.

1 K-means Clustering

In this this exercise, you will implement the K-means algorithm and use it

for image compression. You will ﬁrst start on an example 2D dataset that

will help you gain an intuition of how the K-means algorithm works. After

that, you wil use the K-means algorithm for image compression by reducing

the number of colors that occur in an image to only those that are most

common in that image. You will be using ex7.m for this part of the exercise.

1.1 Implementing K-means

The K-means algorithm is a method to automatically cluster similar data

examples together. Concretely, you are given a training set {x

(1)

, ..., x

(m)

}

(where x

(i)

∈ R

), and want to group the data into a few cohesive “clusters”.

The intuition behind K-means is an iterative proc edure that starts by guess-

ing the initial centroids, and then reﬁnes this guess by repeatedly assigning

examples to their closest centroids and then recomputing the centroids based

on the assignments.

The K-means algorithm is as follows:

% Initialize centroids

centroids = kMeansInitCentroids(X, K);

for iter = 1:iterations

% Cluster assignment step: Assign each data point to the

% closest centroid. idx(i) corresponds to cˆ(i), the index

% of the centroid assigned to example i

idx = findClosestCentroids(X, centroids);

% Move centroid step: Compute means based on centroid

% assignments

centroids = computeMeans(X, idx, K);

end

The inner-loop of the algorithm rep e atedly carries out two steps: (i) As-

signing each training example x

(i)

to its closest c entroid, and (ii) Recomput-

ing the mean of each centroid using the points assigned to it. The K-means

algorithm will always converge to some ﬁnal set of means for the centroids.

Note that the converged solution may not always be ideal and depends on the

initial setting of the centroids. Therefore, in practice the K-means algorithm

is usually run a few times with diﬀerent random initializations. One way to

choose between these diﬀerent solutions from diﬀerent random initializations

is to choose the one with the lowest cost function value (distortion).

You will implement the two phases of the K-means algorithm separately

in the next sections.

1.1.1 Finding closest centroids

In the “cluster assignment” phase of the K-means algorithm, the algorithm

assigns every training example x

(i)

to its closest centroid, given the current

positions of centroids. Speciﬁcally, for every example i we set

(i)

:= j that minimizes ||x

(i)

− µ

where c

(i)

is the index of the centroid that is closest to x

(i)

, and µ

is the

position (value) of the j’th centroid. Note that c

(i)

corresponds to idx(i) in

the starter code.

Your task is to complete the code in findClosestCentroids.m. This

function takes the data matrix X and the locations of all centroids inside

centroids and should output a one-dimensional array idx that holds the

index (a value in {1, ..., K}, where K is total number of centroids) of the

closest centroid to every training example.

You can implement this using a loop over every training example and

every centroid.

Once you have completed the code in findClosestCentroids.m, the

script ex7.m will run your code and you should see the output [1 3 2]

corresponding to the centroid assignments for the ﬁrst 3 examples.

You should now submit your “ﬁnding closest centroids” function.

1.1.2 Computing centroid means

Given assignments of every point to a centroid, the second phase of the

algorithm recomputes, for each centroid, the mean of the points that were

assigned to it. Speciﬁcally, for every centroid k we set

i∈C

(i)

where C

is the set of examples that are assigned to centroid k. Concretely,

if two examples say x

(3)

and x

(5)

are assigned to centroid k = 2, then you

should update µ

(3)

+ x

(5)

You should now complete the code in computeCentroids.m. You can

implement this function using a loop over the centroids. You can also use a

loop over the examples; but if you can use a vectorized implementation that

does not use such a loop, your code may run faster.

Once you have completed the code in computeCentroids.m, the script

ex7.m will run your code and output the centroids after the ﬁrst step of K-

means.

You should now submit your compute centroids function.

1.2 K-means on example dataset

−1 0 1 2 3 4 5 6 7 8 9

Iteration number 10

Figure 1: The expected output.

After you have completed the two functions (findClosestCentroids and

computeCentroids), the next step in ex7.m will run the K-means algorithm

on a toy 2D dataset to help you understand how K-means works. Your

functions are called from inside the runKmeans.m script. We encourage you

to take a look at the function to understand how it works. Notice that the

code calls the two functions you implemented in a loop.

When you run the next step, the K-means code will produce a visualiza-

tion that steps you through the progress of the algorithm at each iteration.

Press enter multiple times to see how each step of the K-means algorithm

changes the centroids and cluster assignments. At the end, your ﬁgure should

look as the one displayed in Figure

评论收藏

内容反馈

zxt6405

2013-08-22

还行，英文文档
wtt_0322

2013-05-19

还可以，对新手还是有用的
shenxiu2014

2014-06-10

还行，但有的在我这上面有错误啊
lflying2005

2014-06-03

对初学者都是好东西
fhwll

2015-06-14

还可以的，写的不错

XQing_90

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