###### Abstract
For example, several studies have transformed one-dimensional electricity consumption data into two-dimensional matrices and employed various deep neural networks (DNNs) to capture the underlying periodicity. ETD-ConvLSTM (electricity theft detector based upon convolutional long short term memory neural networks) [19] uses a ConvLSTM network to capture the periodic patterns in users' consumption. HORLN ( hybrid-order representation learning network) [10] uses the autocorrelation function to determine whether there is periodicity in different electricity consumption data. Additionally, some studies (e.g., Reference [20]) convert the electricity data into graphs and leverage graph convolutional networks (GCNs) to capture the periodicity within the graph structure. However, the aforementioned DNNs do not inherently capture temporal dependencies and fail to fully exploit the periodic features. Although HORLN uses autocorrelation to highlight the capture of periodic characteristics, it only incorporates it as a second-order feature, merging it with first-order feature information. Based on the above considerations, we propose a periodicity-enhanced deep one-class classification framework (PE-DOCC) for ETD based on a periodicity-enhanced transformer encoder named Periodicformer encoder. PE-DOCC is particularly suited for ETD due to its ability to learn from normal data without requiring labeled instances of theft. This is crucial in real-world scenarios where labeled data are sparse or unavailable. By using one-class classification, PE-DOCC builds a model that learns the characteristics of normal (non-theft) consumption patterns and can then identify any deviation from this learned pattern as potential theft. The integration of DNN (specifically the Periodicformer encoder) allows PE-DOCC to handle complex, high-dimensional data, making it more effective in capturing the intricacies of electricity usage patterns. Within the Periodicformer encoder, the paper introduces autocorrelation-based criss-cross periodic attention (CCPA). As discussed earlier,autocorrelation helps capture periodic dependencies within time series data, while CCPA simultaneously computes and combines both horizontal and vertical autocorrelations, enhancing the model's ability to extract richer, more comprehensive periodic features from the time series, thus resulting in better detection performance. The main contributions of this paper can be summarized as follows:  
1. We propose a novel PE-DOCC framework for detecting electricity theft, which incorporates unsupervised representation learning (i.e., pre-training the Periodicformer encoder by recovering partially masked input sequences) and one-class classification (anomaly detection based on local outlier factor);
2. To extract richer periodic features, within the encoder, a novel criss-cross periodic attention (CCPA) is proposed, which comprehensively considers both the horizontal and vertical periodic features;
3. Extensive experiments with ETD using the Irish dataset are conducted to compare the performance with various state-of-the-art methods. Appropriate metrics are selected for evaluation, and the effectiveness of the proposed ETD scheme is verified. The rest of the paper is organized as follows: In Section 2, typical one-class (OC) classification (including traditional machine learning-based and recent deep learning-based) ETD schemes are summarized. Section 3 presents the proposed ETD framework PE-DOCC and describes its main module in detail. Section 4 provides the comprehensive performance comparison between the proposed framework and state-of-the-art ETD methods. Finally, we briefly conclude this paper.