The Dynamic Time Warping （DTW） algorithm measures the similarity between two time series by finding the best match between two time series. Aiming at the problem of excessive stretching and compression during time series matching due to noise existing in the sequence， a Noise robust Dynamic Time Warping （NoiseDTW） algorithm was proposed. Firstly， after introducing extra noise into the original signal， and the problem of one point aligning multiple points in sequence alignment was solved. Secondly， by finding an optimal matching path between two time series with multiple possible matching paths， the influence of randomness of noise on the time series similarity measure was reduced. Finally， the matching paths were mapped to the original sequence. Experimental results show that compared to Euclidean Distance （ED）， DTW， Sakoe-Chiba window DTW （Sakoe-Chiba DTW） and Weighted DTW （WDTW） algorithms， combined with K-Nearest Neighbors （KNN）， the proposed algorithm has the classification accuracy improved by 1 to 15 percentage points compared to the suboptimal algorithm on eight time series datasets， respectively， indicating that the proposed algorithm has good classification performance and is robust to noise.

Exposure bias seriously affects the recommendation accuracy of collaborative filtering model， resulting in the prediction results deviating from the real interests of users. However， the modeling ability of the existing models for exposure bias is limited， and these models even magnify the bias. Therefore， a recommendation model that integrates Multimodal DeepWalk and Bias Calibration factor （MmDW-BC） was proposed. Firstly， the multimodal attribute features of items were introduced as the connected edges in item graph to alleviate the problem of interactive data sparsity of low-exposure items. On this basis， the graph embedding module， Multimodal DeepWalk （MmDW）， was constructed to obtain rich node representation by integrating item multimodal information into the embedding vectors. Finally， a new bias calibration algorithm was designed based on the calibration strategy to predict user preferences. Experimental results on Amazon and ML-1M datasets show that definitely considering exposure bias to improve the recommendation accuracy in MmDW-BC recommendation model is necessary and effective.