Graphs for the design of networks or electronic circuits are usually weighted and the spectrum of weighted graphs are often analyzed to solve problems. This paper discusses the spectrum and the spectral radii of tree...Graphs for the design of networks or electronic circuits are usually weighted and the spectrum of weighted graphs are often analyzed to solve problems. This paper discusses the spectrum and the spectral radii of trees with edge weights. We derive expressions for the spectrum and the spectral radius of a weighted star, together with the boundary limits of the spectral radii for weighted paths and weighted trees. The analysis uses the theory of nonnegative matrices and applies the 'moving edge' technique. Some simple examples of weighted paths and trees are presented to explain the results. Then, we propose some open problems in this area.展开更多
Batch processing mode is widely used in the training process of human motiun recognition. After training, the motion elassitier usually remains invariable. However, if the classifier is to be expanded, all historical ...Batch processing mode is widely used in the training process of human motiun recognition. After training, the motion elassitier usually remains invariable. However, if the classifier is to be expanded, all historical data must be gathered for retraining. This consumes a huge amount of storage space, and the new training process will be more complicated. In this paper, we use an incremental learning method to model the motion classifier. A weighted decision tree is proposed to help illustrate the process, and the probability sampling method is also used. The resuhs show that with continuous learning, the motion classifier is more precise. The average classification precision for the weighted decision tree was 88.43% in a typical test. Incremental learning consumes much less time than the batch processing mode when the input training data comes continuously.展开更多
基金Supported by the National Basic Research PrioritiesProgram(No.G19990 32 90 3
文摘Graphs for the design of networks or electronic circuits are usually weighted and the spectrum of weighted graphs are often analyzed to solve problems. This paper discusses the spectrum and the spectral radii of trees with edge weights. We derive expressions for the spectrum and the spectral radius of a weighted star, together with the boundary limits of the spectral radii for weighted paths and weighted trees. The analysis uses the theory of nonnegative matrices and applies the 'moving edge' technique. Some simple examples of weighted paths and trees are presented to explain the results. Then, we propose some open problems in this area.
基金partly supported by the National Natural Science Foundation of China under Grant 61573242the Projects from Science and Technology Commission of Shanghai Municipality under Grant No.13511501302,No.14511100300,and No.15511105100+1 种基金Shanghai Pujiang Program under Grant No.14PJ1405000ZTE Industry-Academia-Research Cooperation Funds
文摘Batch processing mode is widely used in the training process of human motiun recognition. After training, the motion elassitier usually remains invariable. However, if the classifier is to be expanded, all historical data must be gathered for retraining. This consumes a huge amount of storage space, and the new training process will be more complicated. In this paper, we use an incremental learning method to model the motion classifier. A weighted decision tree is proposed to help illustrate the process, and the probability sampling method is also used. The resuhs show that with continuous learning, the motion classifier is more precise. The average classification precision for the weighted decision tree was 88.43% in a typical test. Incremental learning consumes much less time than the batch processing mode when the input training data comes continuously.
