Undersampling is one of the most popular techniques for dealing with class-imbalance problems. Various undersampling methods have emerged over the past few decades. Each of them exhibits the superiority in some scenarios. However, selecting representative majority-class samples such that the structures of the selected groups are maintained according to the underlying imbalanced distribution remains a challenge. For this purpose, this paper proposes Spatial Distribution-based UnderSampling (SDUS) for imbalanced learning. SDUS uses a supervised constructive process to learn majority-class local patterns in terms of sphere neighborhoods (SPN). Two sample selection strategies, specifically, a top-down strategy and a bottom-up strategy, are proposed for maintaining the distribution pattern of original data in selecting majority-class sample subsets from different perspectives. SDUS introduces an ensemble technique that improves learning performance by utilizing the diversity caused by the randomness of the local-pattern learning process. Numerical experiments on 38 typical datasets from KEEL repository and 13 state-of-the-art comparison methods demonstrate the effectiveness of SDUS in maintaining the underlying distribution characteristics for imbalanced undersampling.

The optimal path finding problem in weighted edge networks is an old and interesting one in many fields. There were many well-known algorithms to deal with that issue. But they were confronted with the high computational complexity while the network becoming larger. We present a hierarchical quotient space model based algorithm that reduces the computational complexity. The basic idea is the following. The nodes of a given network are partitioned with respect to the weights of their adjacent edges. We construct a variety of coarser versions of the given network with new nodes corresponding to the blocks of partitions at various levels of granularity. They are called the quotient spaces (networks) of the original network. The construction of the (sub- )optimal path is then done incrementally, throughout the hierarchy of quotient networks. Since each version of the network is much simpler than the original one, especially of the coarsest spaces, the computational complexity is reduced. In this paper, we present the basic principles of the algorithm and its experimental comparison to other well-known algorithms.

In this paper, a geometrical approach for building neural networks is proposed. With the proposed approach, it is very easy to construct an efficient neural classifier to solve the handwritten Chinese character recognition problem, as well as other pattern recognition problems of large scale. Experiments are conducted to evaluate the performance of the proposed approach and results obtained are promising.

In this paper, a geometrical representation of McCulloch-Pitts neural model is presented. From the representation, a clear visual picture and interpretation of the model can be seen. Two interesting applications based on the interpretation are discussed. They are 1) a new design principle of feedforward neural networks and 2) a new proof of mapping abilities of three-layer feedforward neural networks.

We present an algorithm for generating a class of self-similar (fractal) graphs using simple probabilistic logic neuron networks and show that the graphs can be represented by a set of compressed encoding. An algorithm for quickly finding the coding, i.e., recognizing the corresponding graphs, is given and the coding are shown to be optimal (i.e., of minimal length). The same graphs can also be generated by a mathematical morphology method. These results may possibly have applications in image compression and pattern recognition.

Discusses the learning problem of neural networks with self-feedback connections and shows that when the neural network is used as associative memory, the learning problem can be transformed into some sort of programming (optimization) problem. Thus, the rather mature optimization technique in programming mathematics can be used for solving the learning problem of neural networks with self-feedback connections. Two learning algorithms based on programming technique are presented. Their complexity is just polynomial. Then, the optimization of the radius of attraction of the training samples is discussed using quadratic programming techniques and the corresponding algorithm is given. Finally, the comparison is made between the given learning algorithm and some other known algorithms.

In this paper, we present a new heuristic searching algorithm by introducing the statistical inference method on the basis of algorithm A (or A*). It is called algorithm SA. In a simplified search space, a uniform m-ary tree, we obtain the following result. Using algorithm SA, a goal node can be found with probability one, and its mean complexity is O(N·ln N) where N is the depth at which the goal is located.

A theory for planning collision-free paths of a moving object among obstacles is described. Using the concepts of state space and rotation mapping, the relationship between the positions and the corresponding collision-free orientations of a moving object among obstacles is represented as some set of a state space. This set is called the rotation mapping graph (RMG) of that object. The problem of finding collision-free paths for an object translating and rotating among obstacles is thus transformed to that of considering the connectivity of the RMG. Since the connectivity of the graph can be solved by topological methods, the problem of planning collision-free paths is easily solved in theory. Using this theory, a topological method for planning collision-free paths of a rod-object translating and rotating among obstacles is presented. If a nonrigid robotic arm is viewed as a composite rod with some degrees of freedom, the planning of collision-free paths of a robotic arm can be solved in a similar way to a rod.