As a recurrent neural network, ESN has attracted wide attention because of its simple training process and unique reservoir structure, and has been applied to time series prediction and other fields. However, ESN also has some shortcomings, such as the optimization of reservoir and collinearity. Many researchers try to optimize the structure and performance of deep ESN by constructing deep ESN. However, with the increase of the number of network layers, the problem of low computing efficiency also follows. In this paper, we combined membrane computing and neural network to build an improved deep echo state network inspired by tissue-like P system. Through analysis and comparison with other classical models, we found that the model proposed in this paper has achieved great success both in predicting accuracy and operation efficiency.

Density peaks clustering (DPC) is a simple and efficient density-based clustering algorithm without complex iterative procedures. However, DPC needs to manually choose clustering centers via a decision graph, which often can't identify real centers and breaks the continuous flow of the algorithm. In addition, DPC is highly sensitive to the cut-off distance and suffers from the domino chain reaction. To surmount the aforementioned deficiencies, an improved density peaks clustering based on potential model and diffusion strength (DPC-PMDS) is proposed in this paper. Firstly, we utilize the potential and centrality of data points to calculate the density instead of the cut-off distance. Secondly, inspired by the information diffusion in social networks, we define the influence of data points and the diffusion strength between data points, and realize the diffusion of label from each center to the core data points while selecting clustering centers. Through this process, the core structure of each clustering is obtained and the centers are accurately identified. Finally, the distances from the boundary points to each cluster computed based on centrality are applied to assign boundary points to avoid chain reaction. Extensive experiments on synthetic, UCI and Olivetti Faces datasets demonstrate that DPC-PMDS can achieve excellent clustering results over other state-of-art algorithms, especially on datasets with complex shapes and uneven density distribution.

The famous density-based clustering approach Density Peaks Clustering (DPC) is getting more and more popular recently. However, DPC algorithm is vulnerable to the parameter dc and is incapable of obtaining desired clustering results when dealing with manifold data sets. Furthermore, the allocation strategy of the remaining data points can easily lead to domino chain reaction which means that when a data point is allocated improperly, the points around it will be allocated incorrectly too. To solve these deficiencies, in this paper, we put forward an algorithm named density peaks clustering based on natural search neighbors and manifold distance metric (DPC-NSN-MDM). In the beginning, we apply natural search method (NSM) to identify the natural neighbors and further calculate the local density ρ of each data point. Secondly, when calculating distance δ of each data point, we put the manifold distance metric with a scaling factor to replace the traditional Euclidean distance metric. At last, manifold distance is also used in the allocation strategy of remaining data points to reduce the effect of the domino chain reaction. The proposed DPC-NSN-MDM algorithm succeeds in getting superb experimental performance on both synthetic data sets and real-world data sets.INDEX TERMS Density peaks clustering, manifold distance metric, natural search method, natural search neighbors.