MT4514 Graph Theory Assignment 1 图论代写 This assignment forms 5% of the assessment for this module. The assignment will be marked out of 20 marks. Please answer all questions, This assi...View details
AMAT 592 Assignment 2
MATLAB作业代写 This assignment is done by MATLAB. Put all your code together in one executable .m file and submit on Blackboard.
• This assignment is done by MATLAB. Put all your code together in one executable .m file and submit on Blackboard.
1. Linear regression with least squares
2. Robust linear regression MATLAB作业代写
The data set linreg+outlier.mat contains the feature vector x and label vector y, but one of the point is an outlier. In this case, we consider the robust linear regression or the so-called least absolute deviation (LAD) problem
(b) Solve the corresponding least squares (LS) problem:
Plot the obtained LS regression line (in different style and color) in the same figure from part (a).
The handwritten digit dataset mnist5k.mat is modified from the original MNIST gray-scale image dataset, where samples of digit 9 belong to class 1 and otherwise class −1. It contains a training set Xtr with labels Ytr and a testing set Xte with labels Yte. There are 5000 sample images in both training and testing sets and each sample is stored a vector of 784 gray-scale pixel values between 0 and 255. We do binary classification using logistic regression:
(a) Visualize the first 9 training images in Xtr using MATLAB built-in function imshow. Dispaly the 9 images as a 3 × 3 tabular in the same figure using subplot. Note that you need to reshape each sample into a 28 × 28 matrix before visualization.
(b) Write a function named as logit.m to implement gradient decent algorithm for the logistic regression problem (1) using a constant step size η. The input arguments of logit include Xtr, Ytr, Xte, Yte, the constant step size η, and the regularization parameter λ. The output of logit should be the training accuracy, test accuracy, and the objective value at each iteration (stored as a vector). You should adopt a proper stopping criterion for gradient decent implementation. Call your function logit.m by choosing proper values of η and λ. Note that your main file is supposed to be separated from logit.m.
For this part, you need to:
i. Print out the final training accuracy and test accuracy (A reasonable test accuracy should be > 94%)
In this problem, we use PCA to reduce the dimension of raw face images. Load the data face.mat, and we will have the variable X which is the data matrix of size 400 × 10304, where each row vector represents a gray-scale image originally of 112 × 92 pixels.
First of all, center the data points (i.e., row vectors) in X by subtracting their mean mu from each row. Denote the preprocessed data matrix by variable X_0. Apply PCA to X_0 and reduce data’ s dimension to k = 350. You can use the following command (taking the i-th image as an example) to recover the image:
Recon = X_0(i,:)∗V_k∗V_k’ + mu,
where V_k= V(:,1:k) contains the first k principal components. Recall the set of principal components can be computed via built-in function svd for SVD. Remember to reshape the vector Recon into a 112 × 92 matrix to show the image.
Pick any image from X, and show the effect of PCA by comparing the original image and the recovered images side by side using subplot. Give a title to each subfigure.