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AMAT 592 Assignment
创建日期：2024-07-18 15:18:32
标签： AMAT 592
Assignment

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AMAT 592 Assignment 3

Assignment 3：This assignment is done by MATLAB. Compress all code fifiles into a .zip fifile and submit through Blackboard.

This assignment is done by MATLAB. Compress all code fifiles into a .zip fifile and submit through Blackboard.

1. 

The handwritten digit dataset mnist5k.mat is modifified 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 classifification using logistic regression: 

(a) Visualize the fifirst 9 training images in Xtr using MATLAB built-in function imshow. Dispaly the 9 images as a 3 × 3 tabular in the same fifigure 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 fifile is supposed to be separated from logit.m.

2.  

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 fifirst 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 effffect of PCA by comparing the original image and the recovered images side by side using subplot. Give a title to each subfifigure.

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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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