## 1 Introduction  
Line loss rate is a vital indicator in power gird as it can reflect the operation and management levels in both economic and technical aspects [1]. It is inevitable and directly impacts the profits of power-supply corporations [2]. Commonly, line loss can be classified as technical and non-technical ones. In terms of technical line loss, it is caused by the electro-thermal effect of conductors, which is unavoidable over the transmission process. The level of technical line loss depends on the structure and operation state of the power grid, conductor type, as well as the balance condition of three-phase loads [3]. Non-technical line loss usually occurs due to electricity theft, which may lead to abnormal values in metered line loss rates. Hence, it is urgently concerned by power grid operators whether the daily line loss rate values are within a reasonable range, i.e., the pass percentages of daily line loss rates. It is sometimes difficult to distinguish normal line loss rate values and outliers from a large number of collected samples. Besides the intervals, a benchmark value of daily line loss rate is also essential for transformer regions, as it directly provides the information what a correct daily line loss rate value the region should approximately achieve, in order for operators to better know the operating condition of the region, as well to further improve the level of line loss management. In this case, an accurate calculation method is still needed nowadays to obtain the benchmark values and reasonable intervals of line loss rates, as well as to recognize outliers from those samples of line loss rates. In the field of data mining and analysis, there are usually four approaches to calculate benchmarks and detect outliers, i.e., the empirical method, statistical method, unsupervised method and supervised method [4; 5; 6; 7]. Firstly, empirical method utilizes practical experience to set an interval with fixed bounds, where a value out of the interval can be treated as an outlier. In the benchmarking of daily line loss rates, an empirical interval is customarily set to be \(-1\%\)-\(5\%\). It is noted that although line loss rate is usually non-negative, a value no less than \(-1\%\) is acceptable due to unavoidable acquisition errors. This method is simple and easy to realize, whereas a fixed interval is sometimes inaccurate and cannot reflect the influences of relevant factors. Secondly, the statistical method is aimed to research the distribution of data samples, where the outliers can be eliminated using probabilistic density functions [8] or box-plots [9; 10]. Comparing to empirical methods, the interval bounds in statistical methods is able to adapt to different testing samples, while the influencing factors of line loss rates can still hardly be involved in this kind method. Thirdly, the unsupervised method, i.e., the clustering method, is also an efficient way to detect outliers [11]. In clustering, a sample of line loss rate can be treated as a data point, where the values of line loss rate and its influencing factors are the different dimensional attributes of the point. The outliers can be identified based on the distances between the data points and clustering centers [12; 13; 14]. Unsupervised methods usually outperform empirical and statistical methods, as multi-dimensional factors can be inputted and analyzed [15]. Nevertheless, unsupervised methods still face several problems. On one hand, it is sometimes difficult to design a proper distance function as those input factors are in dissimilar dimensions and units. On the other hand, some clustering methods involve all data points to update clustering centers, e.g., \(k\)-means and fuzzy C-means (FCM), where outliers may easily affect the centers and final clustering results. Reasonable intervals cannot be calculated by unsupervised methods as well.