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cs229_code.zip （172个子文件）

findClosestCentroids 0B

ex7faces.mat 10.52MB

ex3data1.mat 7.16MB

ex4data1.mat 7.16MB

spamTrain.mat 419KB

ex8_movies.mat 218KB

ex8_movieParams.mat 196KB

spamTest.mat 110KB

ex8data2.mat 91KB

ex3weights.mat 78KB

ex4weights.mat 78KB

bird_small.mat 45KB

ex8data1.mat 9KB

ex6data2.mat 7KB

ex6data3.mat 6KB

ex7data2.mat 5KB

ex5data1.mat 1KB

ex7data1.mat 995B

ex6data1.mat 981B

ex7.pdf 699KB

ex6.pdf 571KB

ex1.pdf 478KB

ex2.pdf 421KB

ex8.pdf 415KB

ex4.pdf 348KB

ex3.pdf 287KB

ex5.pdf 183KB

bird_small.png 32KB

ex8_cofi.py 7KB

ex4.py 7KB

ex7_pca.py 7KB

ex5.py 6KB

ex7.py 5KB

ex1_multi.py 4KB

nncostfunction.py 4KB

ex2.py 4KB

ex6.py 4KB

ex8.py 4KB

ex2_reg.py 4KB

ex6_spam.py 3KB

processEmail.py 3KB

ex3_nn.py 3KB

ex1.py 3KB

ex3.py 2KB

emailFeatures.py 2KB

cofiCostFunction.py 2KB

checkCostFunction.py 2KB

gradientDescent.py 2KB

oneVsAll.py 2KB

learningCurve.py 2KB

runkMeans.py 2KB

displayData.py 1KB

validationCurve.py 1KB

selectThreshold.py 1KB

featureNormalize.py 1KB

linearRegCostFunction.py 1KB

plotDecisionBoundary.py 1KB

costFunctionReg.py 1KB

lrCostFunction.py 1KB

findClosestCentroids.py 1KB

predictOneVsAll.py 1KB

checkNNGradients.py 979B

predict.py 967B

costFunction.py 967B

plotData.py 919B

pca.py 891B

computeCentroids.py 851B

recoverData.py 837B

projectData.py 779B

estimateGaussian.py 735B

computeCost.py 662B

predict.py 648B

visualizeFit.py 637B

randInitializeWeights.py 623B

plotData.py 620B

plotData.py 614B

polyFeatures.py 613B

computeNumericalGradient.py 595B

normalEqn.py 590B

trainLinearReg.py 546B

gaussianKernel.py 521B

kMeansInitCentroids.py 507B

sigmoidgradient.py 459B

computeNumericalGradient.py 419B

multivariateGaussian.py 387B

visualizeBoundary.py 383B

sigmoid.py 357B

plotFit.py 350B

mapFeature.py 329B

predict.py 308B

normalizeRatings.py 301B

loadMovieList.py 295B

featureNormalize.py 194B

debugInitializeWeights.py 188B

featureNormalize.py 172B

sigmoid.py 74B

sigmoid.py 72B

runkMeans.cpython-36.pyc 2KB

共 172 条

Programming Exercise 7:

K-means Clustering and Principal Component

Analysis

Machine Learning

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 use 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/MATLAB to change to

this directory before starting this exercise.

You can also ﬁnd instructions for installing Octave/MATLAB in the “En-

vironment Setup Instructions” of the course website.

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-means

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

submit.m - Submission script that sends your solutions to our servers

[?] 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-means)

[?] 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

The exercises in this course use Octave

or MATLAB, a high-level program-

ming language well-suited for numerical computations. If you do not have

Octave or MATLAB installed, please refer to the installation instructions in

the “Environment Setup Instructions” of the course website.

At the Octave/MATLAB command line, typing help followed by a func-

tion name displays documentation for a built-in function. For example, help

plot will bring up help information for plotting. Further documentation for

Octave functions can be found at the Octave documentation pages. MAT-

LAB documentation can be found at the MATLAB documentation pages.

We also strongly encourage using the online Discussions to discuss ex-

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

by others or share your source code with others.

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

Octave is a free alternative to MATLAB. For the programming exercises, you are free

to use either Octave or MATLAB.

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 procedure 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 repeatedly carries out two steps: (i) As-

signing each training example x

(i)

to its closest centroid, 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 solutions.

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 solutions.

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 1.

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