USPS data set

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Data set
File: USPS_dataset9296.mat
This USPS data set contains all 10 digits as labels. Inputs are images as 256-length row vectors, representing 16×16 pixels each.

Instructions
Pre-processing
We will make binary classification of the digits 3 (label 0) and 8 (label 1).
Split the data set into training and validation. Training data set will have the first 80% images for each label, and the validation data set will have the last 20% of each.
Add a bias pixel to form the feature u(x)=[1,x], expanding the input into a vector of size 257.

Least Squares
For each 1<=M<=257, crop the first M features of the vector u(x). Solve the least squares theta_M for the cropped feature vector.
Produce a graph: training and validation quadratic errors of the predictor (as two curves), as validated on the entire test sets, versus number of components M.

PCA
Calculate the PCA dictionary full 256×256 matrix acquired over the training data set (without the bias pixel). You can assume the data has no bias and needs no correction.
Compress the training and validation data set independently, using the dictionary matrix for all (1<=M<=256) principled components.
Solve a Least square problem to obtain the M-length model parameters theta, using as input the M-length representation vectors z from the training set, and their true labels.
Produce a graph: training and validation quadratic errors of the PCA predictor (as two curves), versus number of components M.
Discuss, using a printout code disp(‘…’), why this graph is different from the one in Section 2.

Logistic Regression with one layer
Train using 25 iterations of stochastic gradient descent a logistic regression (with one layer) with input size of 4, being the PCA representation (M=3) and a bias input (like Section 1c). Use the following parameters: initial model parameter vector theta= 1/sqrt(M+1)*randn(M+1,1); learning rate=0.1; and minibatch size of 10 (randperm(n,k) can be helpful).
Produce a graph of training and validation logistic losses vs iteration index.

 

 

Sample Solution

 

Around quite a while back, the standardized identification was designed. Standardized tag alludes to the width of the numbers, going from dark and clear organized as per certain encoding rules used to communicate a bunch of realistic identifier data (Data ID, 2003). This unprecedented development has endured for an extremely long period. Up to this point, its effects and commitments to the trade and society have been gigantic. This report intends to present the foundation of scanner tag, look at the ideas according to a hypothetical point of view lastly, break down and assess it basically.

 

  1. Foundation

1.1 History

 

As kept in the patent documentation, Norm Woodland and Bernard Silver developed a full scope of scanner tag images in 1949 (Online Barcode Tutorial, 2005). Prior to that, no standardized identification innovation had been recorded and placed into useful application. Around then, Bernard Silver was only an alumni at Drexel Institute of Technology in Philadelphia. As per Bellis (2009), the proprietor of a nearby pecking order shop asked the Drexel Institute to explore a technique to consequently peruse data of products like cost and date during checkout. Because of this enquiry, Bernard Silver fostered an answer with Woodland utilizing bright touchy ink (Bar Code 1, 2009). The gathering laid out a model however it couldn’t be emerged because of its flimsiness and significant expense. All things considered, scanner tag has gone through a significant stretch of improvement after Woodland and Silver’s introduction.

 

1.2 Recognition and Functions

 

The standardized tag has partaken in the blast since it was tossed into market. It has been imprinted on pretty much every thing in stores (Bar Code 1, 2009). Makers use scanner tags to record the data of items. Consequently, the fundamental cycles of standardized identification acknowledgment are checking and deciphering and the principles of scanner tag encoding rely upon its quality. Most importantly, standardized tags convey one of a kind data like weight, bundling, details and shades of various merchandise. Furthermore, the long-lasting nature permits every item to have only one scanner tag which can’t be changed even the item is not generally made.

 

1.3 Forms

 

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