Novel Kernel Least Mean Square Algorithms

This project is being proposed to explore further and deeper the recent advancements in signal processing techniques involving the Kernel Least Mean Square (KLMS) algorithm. The applications are numerous, just to name a few, like in medical, control, warfare and artificial intelligence. There has been extensive research in this area since the seminal paper on KLMS was published. The idea is motivated due to its inherent simplicity and application in problems involving machine learning. The Kernel LMS and its variant are mostly based on fixed Gaussian kernels which evaluate the distance between the two input vectors without giving weightage to the individual elements of the distance vector. This imposes certain limitations on the performance of the algorithm where individual contribution of the vector elements is not analyzed. Moreover, recently the proposed cosine kernels have shown that in certain scenarios, angular information is more significant than the distance information between vectors. In light of this, we propose the following two new variants of the KLMS algorithm based on improved kernels: 1. The weighted-Gaussian kernel, and 2. The cosine kernel. These algorithms will be benchmarked against the standard and well-established techniques in kernel adaptive filtering applied in various areas like plant identification and signal processing for wireless communication channels. A complete quantitative analysis of the algorithms will be done and tested through simulations.