The echo state network (ESN) is a powerful recurrent neural network for time series modelling. ESN inherits the simplified structure and relatively straightforward training process of conventional neural networks, and shows strong computational capabilities to solve nonlinear problems. It is able to map low-dimensional input signals to high-dimensional space for information extraction, but it is found that not every dimension of the reservoir output directly contributes to the model generalization. This work aims to improve the generalization capabilities of the ESN model by reducing the redundant reservoir output features. A novel hybrid model, namely binary grey wolf echo state network (BGWO-ESN), is proposed which optimises the ESN output connection by the feature selection scheme. Specially, the feature selection scheme of BGWO is developed to improve the ESN output connection structure. The proposed method is evaluated using synthetic and financial data sets. Experimental results demonstrate that the proposed BGWO-ESN model is more effective than other benchmarks, and obtains the lowest generalization error.
Based on matrix theory, the concept of two-dimensional matrix is extended to fit multi-dimensional matrix. In order to reduce the space redundancy, time redundancy and colour redundancy better, we propose a multi-dimensional vector matrix model. Some related properties are discussed, and Walsh orthogonal square matrix is given in multi-dimensional vector matrix space, then its application in colour image compression and coding is introduced. By means of multi-dimensional vector matrix model, colour image data can be expressed and processed in a unified mathematical model, and better compression results are obtained. On the one hand, it inherits high efficiency of classical matrix transform in the aspect of wiping off redundancy of colour space; on the other hand, it overcomes the restriction of traditional twodimensional matrix multiplication. By multi-dimensional Walsh orthogonal transform and traditional discrete cosine transform, favourable image compression effect can be obtained.
This paper extends the theory of multi-dimensional vector orthogonal transformation matrix and presents a new 4D order-4 DCT integer transform operator based on the theory of multi-dimensional vector matrix discrete cosine transform (MD-VMDCT). Meanwhile, the orthogonality of the operator and energy concentration is verified in the paper. Also the comparison between the integer and the float 4D-VMDCT is carried out. At last, the video sequence is compressed using our approach. The experimental results show that the algorithm is correct and effective. It is better than H.264/AVC under the same conditions and it is slightly lower in performance compared with float 4D-VMDCT.
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