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Building energy consumption (BEC) prediction often requires constructing a corresponding model for each building based historical data. However, the constructed model for one building is difficult to be reused in other buildings. Recent approaches have shown that cloud-edge collaboration architecture is promising in realizing model reuse. How to complete the reuse of cloud energy consumption prediction models at the edge and reduce the computational cost of the model training is one of the key issues that need to be solved. To handle the above problems, a cloud-edge collaboration based transferring prediction method for BEC is proposed in this paper. Specifically, a model library stored prediction models for different types of buildings is constructed based the historical energy consumption data and the long short-term memory (LSTM) network in the cloud firstly; then, the similarity measurement strategies of time series with different granularity are given, and the model to be transferred from the model library is matched by analyzing the similarity between observation data uploaded to the cloud and the historical data collected in the cloud; finally, the fine-tuning strategy of the matching prediction model is given, and this model is fine-tuned at the edge to achieve its reuse in concrete application scenarios. Experiments on practical datasets reveal that compared with the prediction model which doesn't utilize the transfer strategy, the proposed prediction model has better performance according to MAE and RMSE. Experimental results also confirm that the proposed method effectively reduces the computational cost of the network training at the edge. [ABSTRACT FROM AUTHOR]