Understanding Dilated Mathematical Relationship between Image Features and the Convolutional Neural Network’s Learnt Parameters

Abstract

Deep learning, in general, was built on input data transformation and presentation, model training with parameter tuning, and recognition of new observations using the trained model. However, this came with a high computation cost due to the extensive input database and the length of time required in training. Despite the model learning its parameters from the transformed input data, no direct research has been conducted to investigate the mathematical relationship between the transformed information (i.e., features, excitation) and the model’s learnt parameters (i.e., weights). This research aims to explore a mathematical relationship between the input excitations and the weights of a trained convolutional neural network. The objective is to investigate three aspects of this assumed feature-weight relationship: (1) the mathematical relationship between the training input images’ features and the model’s learnt parameters, (2) the mathematical relationship between the images’ features of a separate test dataset and a trained model’s learnt parameters, and (3) the mathematical relationship between the difference of training and testing images’ features and the model’s learnt parameters with a separate test dataset. The paper empirically demonstrated the existence of this mathematical relationship between the test image features and the model’s learnt weights by the ANOVA analysis.

A Model Selection Algorithm for Complex Multi-Domain Cnn Systems Based on Feature-Weights Relation in Deep Learning

“…Finally, the proof of the existence of a linkage between the features extracted from a training image and the trained model's structure and excitation weights was explored by the mathematical relationship between the resulting model's parameters and the model's featured input, Alsaghir et al [26]. In their work, A feature-weight (FW) linkage was built to calculate the primary model-related FW array for comparing the extracted features of a test image to allocate the related model correctly in a multi-model system.…”