ECE-GY 6143 introduction to Machine Learning Problems: Convolutional Neural Networks

Introduction to Machine Learning Problems: Convolutional Neural Networks Prof. Sundeep Rangan 1. Tensors. For each of the following datasets, describe how you would represent them as tensors. Specifically, give the shape of the tensors. (a) A batch of 100 color images, each image is 256 × 256. (b) A batch of 40 EEG recordings. Each EEG records has 80 channels of output at a sample rate of 240 Hz for 10 seconds. (c) A batch of 32 videos. Each video has a frame rate of 30 frames per second and is 10 seconds long. The video is color with a resolution of 512 × 512. Solution: (a) We represent this as (sample,row,col,color) for a tensor shape of (100, 256, 256, 3). (b) There are (240)(10) = 2400 time samples in each recording. So, we represent this as (sample,time,chan) for a tensor shape of (40, 2400, 80). (c) There are (30)(10) = 300 frames in each video. So, we represent this as (sample,frame,row,col,color) for a tensor shape of (32, 300, 512, 512, 3). 2. 2D convolutions. Let X and W be arrays, X =         0 0 0 0 0 0 3 3 3 0 0 3 3 3 0 0 3 2 3 0 0 3 2 3 0 0 0 0 0 0         , W =  1 −1 1 −1  . Let Z be the 2D convolution (without reversal): Z[i, j] = X k1,k2 W[k1, k2]X[i + k1, j + k2]. (1) Assume that the arrays are indexed starting at (0, 0). (a) What are the limits of the summations over k1 and k2 in (1)? (b) What is the size of the output Z[i, j] if the convolution is computed only on the valid pixels (i.e. the pixel locations (i, j) where the summation in (1) does not exceed the boundaries of W or X). 1 This study source was downloaded by from CourseH on 11-18