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Calculate the (1) feature map, (2) reduced feature map,

Calculate the (1) feature map, (2) reduced feature map,

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Exercise: Convolutional Neural Network Calculation** **Problem Statement:** Consider the following process involving a 6x6 input matrix, a 3x3 convolutional filter, 2x2 max pooling, and the ReLU (Rectified Linear Unit) activation function. **Objective:** Calculate the following: 1. **Feature Map** 2. **Reduced Feature Map** (after max pooling) 3. **Final Feature Map** (after applying ReLU) **Given:** - **6x6 Input Matrix:** \[ \begin{bmatrix} 8 & 2 & 0 & 0 & 1 & 2 \\ 0 & 7 & 3 & 0 & 1 & 3 \\ 0 & 0 & 6 & 4 & 1 & 1 \\ 1 & 3 & 1 & 8 & 0 & 0 \\ 0 & 0 & 1 & 2 & 5 & 4 \\ 1 & 1 & 0 & 4 & 0 & 2 \\ \end{bmatrix} \] - **3x3 Filter:** \[ \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \\ \end{bmatrix} \] **Steps for Calculation:** 1. **Compute the Feature Map:** - Perform convolution of the 6x6 input matrix with the 3x3 filter. 2. **Apply 2x2 Max Pooling:** - Reduce the feature map by taking the maximum value in each 2x2 section. 3. **Apply ReLU Activation:** - Apply the ReLU function, which outputs the input directly if it is positive; otherwise, it outputs zero. **Note:** The specific numerical calculations are not included here. Refer to convolution and pooling techniques and apply them to the matrices provided for detailed results. This exercise demonstrates an essential process in Convolutional Neural Networks (CNNs), enhancing understanding of image processing and feature extraction.
Transcribed Image Text:**Exercise: Convolutional Neural Network Calculation** **Problem Statement:** Consider the following process involving a 6x6 input matrix, a 3x3 convolutional filter, 2x2 max pooling, and the ReLU (Rectified Linear Unit) activation function. **Objective:** Calculate the following: 1. **Feature Map** 2. **Reduced Feature Map** (after max pooling) 3. **Final Feature Map** (after applying ReLU) **Given:** - **6x6 Input Matrix:** \[ \begin{bmatrix} 8 & 2 & 0 & 0 & 1 & 2 \\ 0 & 7 & 3 & 0 & 1 & 3 \\ 0 & 0 & 6 & 4 & 1 & 1 \\ 1 & 3 & 1 & 8 & 0 & 0 \\ 0 & 0 & 1 & 2 & 5 & 4 \\ 1 & 1 & 0 & 4 & 0 & 2 \\ \end{bmatrix} \] - **3x3 Filter:** \[ \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \\ \end{bmatrix} \] **Steps for Calculation:** 1. **Compute the Feature Map:** - Perform convolution of the 6x6 input matrix with the 3x3 filter. 2. **Apply 2x2 Max Pooling:** - Reduce the feature map by taking the maximum value in each 2x2 section. 3. **Apply ReLU Activation:** - Apply the ReLU function, which outputs the input directly if it is positive; otherwise, it outputs zero. **Note:** The specific numerical calculations are not included here. Refer to convolution and pooling techniques and apply them to the matrices provided for detailed results. This exercise demonstrates an essential process in Convolutional Neural Networks (CNNs), enhancing understanding of image processing and feature extraction.
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