Clustering is to divide a dataset into multiple clusters based on the similarity between samples. Most existing clustering methods face two challenges. On the one hand， when defining the similarity between samples， the spatial distribution structure of the samples is often not considered， making it difficult to construct a stable similarity matrix. On the other hand， the sample graph structure constructed by graph clustering is too complex and has high computational costs. To solve these two problems， a Multi-order Nearest Neighbor Graph Clustering algorithm by fusing transition probability matrix （MNNGC） was proposed. Firstly， the nearest neighbor relationship and spatial distribution structure of samples were comprehensively considered， the similarity defined by shared nearest neighbor was weighted for densification， and the densification affinity matrix between nodes was obtained. Secondly， by utilizing multi-order probability transition between nodes， the correlation degrees of non-adjacent nodes were predicted， and a stable inter-node affinity matrix was obtained by fusing the multi-order transition probability matrix. Then， to further enhance the local structure of the graph， the multi-order nearest neighbor graph of nodes was reconstructed， and hierarchically clustered. Finally， the edge node allocation strategy was optimized. Positioning experimental results show that MNNGC achieves the highest Accuracy （Acc） among comparison clustering algorithms on all the synthetic datasets and 8 UCI datasets. The Acc， Adjusted Mutual Information （AMI）， Adjusted Rand Index （ARI） and Fowlkes and Mallows Index （FMI） of MNNGC algorithm are improved by 38.6， 27.2， 45.4 and 35.1 percentage points， respectively， compared with Local Density Peaks-based Spectral Clustering （LDP-SC） algorithm.

Aiming at the low segmentation precision caused by the lack of image feature extraction ability of the existing fractional-order nonlinear models， an instance segmentation model based on fractional-order network and Reinforcement Learning （RL） was proposed to generate high-quality contour curves of target instances in the image. The model consists of two layers of modules： 1） the first layer was a two-dimensional fractional-order nonlinear network in which the chaotic synchronization method was mainly utilized to obtain the basic characteristics of the pixels in the image， and the preliminary segmentation result of the image was acquired through the coupling and connection according to the similarity among the pixels； 2） the second layer was to establish instance segmentation as a Markov Decision Process （MDP） based on the idea of RL， and the action-state pairs， reward functions and strategies during the modeling process were designed to extract the region structure and category information of the image. Finally， the pixel features and preliminary segmentation result of the image obtained from the first layer were combined with the region structure and category information obtained from the second layer for instance segmentation. Experimental results on datasets Pascal VOC2007 and Pascal VOC2012 show that compared with the existing fractional-order nonlinear models， the proposed model has the Average Precision （AP） improved by at least 15 percentage points， verifying that the sequential decision-based instance segmentation model not only can obtain the class information of the target objects in the image， but also further enhance the ability to extract contour details and fine-grained information of the image.

The manual labeling of abundant data is laborious and the amount of Magnetic Resonance Imaging （MRI） data from a single imaging center is limited. Concerning the above problems， a Magnetic Resonance Semi-Supervised Learning （MRSSL） method utilizing multi-imaging center labeled and unlabeled MRI data was proposed and applied to knee abnormality classification. Firstly， data augmentation was used to provide the inductive bias required by the model . Next， the classification loss and the consistency loss were combined to constraint an artificial neural network to extract the discriminative features from the data. Then， the features were used for the MRI knee abnormality classification. Additionally， the corresponding Magnetic Resonance Supervised Learning （MRSL） method only using labeled samples was proposed and compared with MRSSL for the same labeled samples. The results demonstrate that MRSSL surpasses MRSL in both model classification performance and model generalization ability. Finally， MRSSL was compared with other semi-supervised learning methods. The results indicate that data augmentation plays an important role on performance improvement， and with stronger inclusiveness for MRI data， MRSSL outperforms others on the knee abnormality classification.

Concerning a kind of continuous-time capacitated network with limits on nodes process rate, a shortest dynamic time flow was proposed and its corresponding linear programming form was also given. Based on the inner relationship of the above-mentioned network and the classical continuous-time capacitated network, efficient algorithms in terms of the thought of maximal-received flow and returning flow were designed to precisely solve the shortest dynamic time flow issue in those two kinds of network respectively. Afterwards, the algorithms were proved to be correct and their complexities were also concluded to be small. Finally, an example was used to demonstrate the execution of the algorithm.