Cognitive Analysis of Neural Networks Using Fractional Metric Dimension and Applications

Abstract

Fractional versions of metric related parameters have been introduced as an equivalent to solve linear optimization problems which have applications in various fields like computer science and chemistry. The understanding and analysis of various parameters in the context of networks involved in transmitting the data is referred as the cognitive analysis. These parameters analyze the abstract structures of networks which widens the scope of application in the areas such as networking and linear optimization. In particular, the metric related parameters are used in navigation of robots to their destinations by minimum utilization time and nodes. The application of neural networks can be seen in diverse areas including data flow optimization, healthcare, cognitive psychology, geographical routing, supply chain optimization problems, wireless communication networks and Internet of Things (IoT). In the current work, the cognitive analysis of certain artificial neural networks have been conducted using fractional metric dimension. The fractional metric dimension of probabilistic neural networks $P_{n,k}^{m}$ and convolutional neural networks $C_{n,k}^{m}$ have been computed. Further, an application is discussed in the context of IoT where sensor networks are deployed for the optimal installation of base stations in a fire and smoke monitoring sensor system in a 3- storey hospital building with each floor considered as layer of the artificial neural network.

Keywords

• Neural networks
• fractional metric dimension
• metric dimension
• wireless communication networks
• IoT
• sensor networking