In the last few years, there have been many works in the area of hybrid neural learning algorithms combining a global and local based method for training artificial neural networks. In this paper, we discuss various connection strategies that can be applied to a special kind of a hybrid neural learning algorithm group, one that combines a genetic algorithm-based method with various least square-based methods like QR factorization. The relative advantages and disadvantages of the different connection types are studied to find a suitable connection topology for combining the two different learning methods. The methodology also finds the optimum number of hidden neurons using a hierarchical combination methodology structure for weights and architecture. We have tested our proposed approach on XOR, 10 bit odd parity, and some other real-world benchmark data sets, such as the hand-writing character dataset from CEDAR, Breast cancer, and Heart Disease from the UCI machine learning repository.
Density estimation is the ubiquitous base modelling mechanism employed for many tasks such as clustering, classification, anomaly detection and information retrieval. Commonly used density estimation methods such as kernel density estimator and k-nearest neighbour density estimator have high time and space complexities which render them inapplicable in problems with large data size and even a moderate number of dimensions. This weakness sets the fundamental limit in existing algorithms for all these tasks. We propose the first density estimation method which stretches this fundamental limit to an extent that dealing with millions of data can now be done easily and quickly. We analyze the error of the new estimation (from the true density) using a bias-variance analysis. We then perform an empirical evaluation of the proposed method by replacing existing density estimators with the new one in two current density-based algorithms, namely, DBSCAN and LOF. The results show that the new density estimation method significantly improves the runtime of DBSCAN and LOF, while maintaining or improving their task-specific performances in clustering and anomaly detection, respectively. The new method empowers these algorithms, currently limited to small data size only, to process very large databases - setting a new benchmark for what density-based algorithms can achieve.