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        CEG5301代做、MATLAB編程語言代寫

        時間:2024-03-15  來源:合肥網hfw.cc  作者:hfw.cc 我要糾錯



        CEG5301 Machine Learning with Applications:
        Part I: Homework #3
        Important note: the due date is 17/03/2024. Please submit the softcopy of your report
        to the submission folder in CANVAS. Late submission is not allowed unless it is well
        justified. Please supply the MATLAB code or Python Code in your answer if computer
        experiment is involved.
        Please note that the MATLAB toolboxes for RBFN and SOM are not well developed.
        Please write your own codes to implement RBFN and SOM instead of using the
        MATLAB toolbox.
        Q1. Function Approximation with RBFN (10 Marks)
        Consider using RBFN to approximate the following function:
        𝑦𝑦 = 1.2 sin(𝜋𝜋𝜋𝜋) − cos(2.4𝜋𝜋𝜋𝜋) , 𝑓𝑓𝑓𝑓𝑓𝑓 w**9;w**9; ∈ [−1.6, 1.6]
        The training set is constructed by dividing the range [−1.6, 1.6] using a uniform step
        length 0.08, while the test set is constructed by dividing the range [−1.6, 1.6] using
        a uniform step length 0.01. Assume that the observed outputs in the training set are
        corrupted by random noise as follows.
        𝑦𝑦(𝑖𝑖) = 1.2 sin 𝜋𝜋𝜋𝜋(𝑖𝑖)  − cos 2.4𝜋𝜋𝜋𝜋(𝑖𝑖)  + 0.3𝑛𝑛(𝑖𝑖)
        where the random noise 𝑛𝑛(𝑖𝑖) is Gaussian noise with zero mean and stand deviation of
        one, which can be generated by MATLAB command randn. Note that the test set is not
        corrupted by noises. Perform the following computer experiments:
        a) Use the exact interpolation method (as described on pages 17-26 in the slides of
        lecture five) and determine the weights of the RBFN. Assume the RBF is Gaussian
        function with standard deviation of 0.1. Evaluate the approximation performance of
        the resulting RBFN using the test set.
         (3 Marks)
        b) Follow the strategy of “Fixed Centers Selected at Random” (as described on page 38
        in the slides of lecture five), randomly select 20 centers among the sampling points.
        Determine the weights of the RBFN. Evaluate the approximation performance of the
        resulting RBFN using test set. Compare it to the result of part a).
        (4 Marks)
        c) Use the same centers and widths as those determined in part a) and apply the
        regularization method as described on pages 43-46 in the slides for lecture five. Vary
        the value of the regularization factor and study its effect on the performance of RBFN.
        (3 Marks)
        2
        Q2. Handwritten Digits Classification using RBFN (20 Marks)
        In this task, you will build a handwritten digits classifier using RBFN. The training data
        is provided in MNIST_M.mat. Each binary image is of size 28*28. There are 10
        classes in MNIST_M.mat; please select two classes according to the last two different
        digits of your matric number (e.g. A0642311, choose classes 3 and 1; A1234567,
        choose classes 6 and 7). The images in the selected two classes should be assigned the
        label “1” for this question’s binary classification task, while images in all the remaining
        eight classes should be assigned the label “0”. Make sure you have selected the correct
        2 classes for both training and testing. There will be some mark deduction for wrong
        classesselected. Please state your handwritten digit classes for both training and testing.
        In MATLAB, the following code can be used to load the training and testing data:
        -------------------------------------------------------------------------------------------------------
        load mnist_m.mat;
        % train_data  training data, 784x1000 matrix
        % train_classlabel  the labels of the training data, 1x1000 vector
        % test_data  test data, 784x250 matrix
        % train_classlabel  the labels of the test data, 1x250 vector
        -------------------------------------------------------------------------------------------------------
        After loading the data, you may view them using the code below:
        -------------------------------------------------------------------------------------------------------
        tmp=reshape(train_data(:,column_no),28,28);
        imshow(tmp);
        -------------------------------------------------------------------------------------------------------
        To select a few classes for training, you may refer to the following code:
        -------------------------------------------------------------------------------------------------------
        trainIdx = find(train_classlabel==0 | train_classlabel==1 | train_classlabel==2); % find the
        location of classes 0, 1, 2
        Train_ClassLabel = train_classlabel(trainIdx);
        Train_Data = train_data(:,trainIdx);
        -------------------------------------------------------------------------------------------------------
        Please use the following code to evaluate:
        -------------------------------------------------------------------------------------------------------
        TrAcc = zeros(1,1000);
        TeAcc = zeros(1,1000);
        thr = zeros(1,1000);
        TrN = length(TrLabel);
        TeN = length(TeLabel);
        for i = 1:1000
         t = (max(TrPred)-min(TrPred)) * (i-1)/1000 + min(TrPred);
         thr(i) = t;

        TrAcc(i) = (sum(TrLabel(TrPred<t)==0) + sum(TrLabel(TrPred>=t)==1)) / TrN;
        TeAcc(i) = (sum(TeLabel(TePred<t)==0) + sum(TeLabel(TePred>=t)==1)) / TeN;
        end
        3
        plot(thr,TrAcc,'.- ',thr,TeAcc,'^-');legend('tr','te');
        -------------------------------------------------------------------------------------------------------
        TrPred and TePred are determined by TrPred(j) = ∑ w**8;w**8;𝑖𝑖𝜑𝜑𝑖𝑖(TrData(: , j)) Ү**;Ү**;
        𝑖𝑖=0 and
        TePred(j) = ∑ w**8;w**8;𝑖𝑖𝜑𝜑𝑖𝑖(TeData(: , j)) Ү**;Ү**;
        𝑖𝑖=0 where Ү**;Ү**; is the number of hidden neurons.
        TrData and TeData are the training and testing data selected based on your matric
        number. TrLabel and TeLabel are the ground-truth label information (Convert to {0,1}
        before use!).
        You are required to complete the following tasks:
        a) Use Exact Interpolation Method and apply regularization. Assume the RBF is
        Gaussian function with standard deviation of 100. Firstly, determine the weights of
        RBFN without regularization and evaluate its performance; then vary the value of
        regularization factor and study its effect on the resulting RBFNs’ performance.
        (6 Marks)

        b) Follow the strategy of “Fixed Centers Selected at Random” (as described in page 38
        of lecture five). Randomly select 100 centers among the training samples. Firstly,
        determine the weights of RBFN with widths fixed at an appropriate size and compare
        its performance to the result of a); then vary the value of width from 0.1 to 10000 and
        study its effect on the resulting RBFNs’ performance.
        (8 Marks)

        c) Try classical “K-Mean Clustering” (as described in pages 39-40 of lecture five) with
        2 centers. Firstly, determine the weights of RBFN and evaluate its performance; then
        visualize the obtained centers and compare them to the mean of training images of each
        class. State your findings.
        (6 Marks)
        4
        Q3. Self-Organizing Map (SOM) (20 Marks)
        a) Write your own code to implement a SOM that maps a **dimensional output layer
        of 40 neurons to a “hat” (sinc function). Display the trained weights of each output
        neuron as points in a 2D plane, and plot lines to connect every topological adjacent
        neurons (e.g. the 2nd neuron is connected to the 1st and 3rd neuron by lines). The training
        points sampled from the “hat” can be obtained by the following code:
        -------------------------------------------------------------------------------------------------------
        x = linspace(-pi,pi,400);
        trainX = [x; sinc(x)];  2x400 matrix
        plot(trainX(1,:),trainX(2,:),'+r'); axis equal
        -------------------------------------------------------------------------------------------------------
        (3 Marks)
        b) Write your own code to implement a SOM that maps a 2-dimensional output layer
        of 64 (i.e. 8×8) neurons to a “circle”. Display the trained weights of each output neuron
        as a point in the 2D plane, and plot lines to connect every topological adjacent neurons
        (e.g. neuron (2,2) is connected to neuron (1,2) (2,3) (3,2) (2,1) by lines). The training
        points sampled from the “circle” can be obtained by the following code:
        -------------------------------------------------------------------------------------------------------
        X = randn(800,2);
        s2 = sum(X.^2,2);
        trainX = (X.*repmat(1*(gammainc(s2/2,1).^(1/2))./sqrt(s2),1,2))';  2x800 matrix
        plot(trainX(1,:),trainX(2,:),'+r'); axis equal
        -------------------------------------------------------------------------------------------------------
        (4 Marks)
        c) Write your own code to implement a SOM that clusters and classifies handwritten
        digits. The training data is provided in Digits.mat. The dataset consists of images in 5
        classes, namely 0 to 4. Each image with the size of 28*28 is reshaped into a vector and
        stored in the Digits.mat file. After loading the mat file, you may find the 4 matrix/arrays,
        which respectively are train_data, train_classlabel, test_data and test_classlabel. There
        are totally 1000 images in the training set and 100 images in the test set. Please omit 2
        classes according to the last digit of your matric number with the following rule:
        omitted class1 = mod(the last digit, 5), omitted_class2 = mod(the last digit+1, 5). For
        example, if your matric number is A06423**, ignore classes mod(7,5)=2 and
        mod(8,5)=3; A1234569, ignore classes 4 and 0.
        Thus, you need to train a model for a 3-classes classification task. Make sure you have
        selected the correct 3 classes for both training and testing. There will be some mark
        deduction for wrong classes selected. Please state your handwritten digit classes for
        both training and testing.
        After loading the data, complete the following tasks:
        c-1) Print out corresponding conceptual/semantic map of the trained SOM (as
        described in page 24 of lecture six) and visualize the trained weights of each output
        neuron on a 10×10 map (a simple way could be to reshape the weights of a neuron
        5
        into a 28×28 matrix, i.e. dimension of the inputs, and display it as an image). Make
        comments on them, if any.
        (8 Marks)
        c-2) Apply the trained SOM to classify the test images (in test_data). The
        classification can be done in the following fashion: input a test image to SOM, and
        find out the winner neuron; then label the test image with the winner neuron’s label
        (note: labels of all the output neurons have already been determined in c-1).
        Calculate the classification accuracy on the whole test set and discuss your
        findings.
        (5 Marks)
        The recommended values of design parameters are:
        1. The size of the SOM is 1×40 for a), 8×8 for b), 10×10 for c).
        2. The total iteration number N is set to be 500 for a) & b), 1000 for c). Only the
        first (self-organizing) phase of learning is used in this experiment.
        3. The learning rate 𝜂𝜂(𝑛𝑛) is set as:
        𝜂𝜂(𝑛𝑛) = 𝜂𝜂0 exp  − 𝑛𝑛
        𝜏𝜏2
          , 𝑛𝑛 = 0,1,2, …
        where 𝜂𝜂0 is the initial learning rate and is set to be 0.1, 𝜏𝜏2 is the time constant
        and is set to be N.
        4. The time-varying neighborhood function is:
        ℎ𝑗𝑗,𝑖𝑖(w**9;w**9;)(𝑛𝑛) = exp  − 𝑑𝑑𝑗𝑗,𝑖𝑖
        2
        2ҵ**;ҵ**;(𝑛𝑛)2  , 𝑛𝑛 = 0,1,2, …
        where 𝑑𝑑𝑗𝑗,𝑖𝑖 is the distance between neuron j and winner i, ҵ**;ҵ**;(𝑛𝑛) is the effective
        width and satisfies:
        ҵ**;ҵ**;(𝑛𝑛) = ҵ**;ҵ**;0 exp  − 𝑛𝑛
        𝜏𝜏1
          , 𝑛𝑛 = 0,1,2, …
        where ҵ**;ҵ**;0 is the initial effective width and is set according to the size of output
        layer’s lattice, 𝜏𝜏1 is the time constant and is chosen as 𝜏𝜏𝑖𝑖 = Ү**;Ү**;
        log(ҵ**;ҵ**;0)
        .
        Again, please feel free to experiment with other design parameters which may be
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