Research And Application Of Unsupervised Grey Incidence Clustering Based On Multi-dimensional DTW Distance

Grey incidence clustering is an important tool in grey system research and an effective tool for dealing with uncertain information systems.Existing grey incidence analysis and grey incidence clustering models are confined to one-dimensional sequences.Although there are some models for multi-dimensional sequences,they can only deal with complete sequences.For incomplete sequences,it is often necessary to preprocess by means of padding or deletion,thus introducing new uncertainties.In addition,the clustering threshold of existing grey incidence clustering methods need to be specified manually,and there exists a large difficulty and error in manually specifying threshold because of the limitation of domain knowledge and data characteristics,thus affecting the quality of clustering.In view of the above problems,this paper carried out the following research:1.Grey incidence analysis model for dealing with multi-dimensional incomplete sequences.Aiming at the problem that the existing multi-dimensional grey incidence analysis model can not deal with the incomplete sequences,a grey incidence analysis model using multi-dimensional DTW distance is proposed based on the three-dimensional grey incidence analysis model and the multi-dimensional dynamic time bending distance.The grey incidence analysis method can be used to deal with multi-dimensional incomplete sequences by constructing an alignment matrix between the comparison sequence and the reference sequence and finding a shortest curvature path to match the multi-dimensional sequences of different lengths.Finally,the correctness and validity of the method are verified by experiments.2.Efficient grey incidence clustering method for dealing with multi-dimensional incomplete sequences.The existing grey incidence clustering methods not only cannot deal with multi-dimensional incomplete sequence,but also need to construct the association matrix by calculating the degree of incidence between each two sequences.The calculation process is complicated and easy to be influenced by the transitivity of degree of incidence.Based on the new grey incidence analysis model,this paper proposes a grey incidence clustering method using multi-dimensional DTW distance by introducing the construction of reference sequence.Firstly,the reference sequence is obtained according to the data feature of each dimension of the sequence,and then the degree of incidence between the observation sequence and the reference sequence is calculated.The experimental results show that the method is simpler and the clustering accuracy is higher when dealing with multi-dimensional incomplete sequences.3.Unsupervised grey incidence clustering method for dealing with multi-dimensional incomplete sequences.In order to solve the problem of manually assigning thresholds for the existing grey incidence clustering method,an unsupervised clustering method is proposed based on k-Means combining the strategy of stepwise approximation,thus the optimal clustering effect is obtained.When introduce it into the grey incidence clustering method based on the multi-dimensional DTW distance,an incidence clustering method is achieving without human intervention.The experimental results show that the method has better quality and better adaptability.Finally,by applying this method to regional economic evaluation,the application field of this method is extended.