A New Sufficient & Necessary Condition for Testing Linear Separability Between Two Sets.

As a fundamental mathematical problem in the field of machine learning, the linear separability test still lacks a theoretically complete and computationally efficient method. This paper proposes and proves a sufficient and necessary condition for linear separability test based on a sphere model. The advantage of this test method is two-fold: (1) it provides not only a qualitative test of linear separability but also a quantitative analysis of the separability of linear separable instances; (2) it has low time cost and is more efficient than existing test methods. The proposed method is validated through a large number of experiments on benchmark datasets and artificial datasets, demonstrating both its correctness and efficiency.

A new supervised learning algorithm for spiking neurons.

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by the precise firing times of spikes. If only running time is considered, the supervised learning for a spiking neuron is equivalent to distinguishing the times of desired output spikes and the other time during the running process of the neuron through adjusting synaptic weights, which can be regarded as a classification problem. Based on this idea, this letter proposes a new supervised learning method for spiking neurons with temporal encoding; it first transforms the supervised learning into a classification problem and then solves the problem by using the perceptron learning rule. The experiment results show that the proposed method has higher learning accuracy and efficiency over the existing learning methods, so it is more powerful for solving complex and real-time problems.

An online supervised learning method based on gradient descent for spiking neurons.

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by precise firing times of spikes. The gradient-descent-based (GDB) learning methods are widely used and verified in the current research. Although the existing GDB multi-spike learning (or spike sequence learning) methods have good performance, they work in an offline manner and still have some limitations. This paper proposes an online GDB spike sequence learning method for spiking neurons that is based on the online adjustment mechanism of real biological neuron synapses. The method constructs error function and calculates the adjustment of synaptic weights as soon as the neurons emit a spike during their running process. We analyze and synthesize desired and actual output spikes to select appropriate input spikes in the calculation of weight adjustment in this paper. The experimental results show that our method obviously improves learning performance compared with the offline learning manner and has certain advantage on learning accuracy compared with other learning methods. Stronger learning ability determines that the method has large pattern storage capacity.

Effective neural network ensemble approach for improving generalization performance.

This paper, with an aim at improving neural networks' generalization performance, proposes an effective neural network ensemble approach with two novel ideas. One is to apply neural networks' output sensitivity as a measure to evaluate neural networks' output diversity at the inputs near training samples so as to be able to select diverse individuals from a pool of well-trained neural networks; the other is to employ a learning mechanism to assign complementary weights for the combination of the selected individuals. Experimental results show that the proposed approach could construct a neural network ensemble with better generalization performance than that of each individual in the ensemble combining with all the other individuals, and than that of the ensembles with simply averaged weights.

Sensitivity-based adaptive learning rules for binary feedforward neural networks.

This paper proposes a set of adaptive learning rules for binary feedforward neural networks (BFNNs) by means of the sensitivity measure that is established to investigate the effect of a BFNN's weight variation on its output. The rules are based on three basic adaptive learning principles: the benefit principle, the minimal disturbance principle, and the burden-sharing principle. In order to follow the benefit principle and the minimal disturbance principle, a neuron selection rule and a weight adaptation rule are developed. Besides, a learning control rule is developed to follow the burden-sharing principle. The advantage of the rules is that they can effectively guide the BFNN's learning to conduct constructive adaptations and avoid destructive ones. With these rules, a sensitivity-based adaptive learning (SBALR) algorithm for BFNNs is presented. Experimental results on a number of benchmark data demonstrate that the SBALR algorithm has better learning performance than the Madaline rule II and backpropagation algorithms.