In power systems, load curve data is one of the most important datasets that are collected and retained by utilities. The quality of load curve data, however, is hard to guarantee since the data is subject to communication losses, meter malfunctions, and many other impacts. In this paper, a new approach to analyzing load curve data is presented. The method adopts a new view, termed , on the load curve data by analyzing the periodic patterns in the data and re-organizing the data for ease of analysis. Furthermore, we introduce algorithms to build the virtual portrait load curve data, and demonstrate its application on load curve data cleansing. Compared to existing regression-based methods, our method is much faster and more accurate for both small-scale and large-scale real-world datasets.
In addition to the above methods, data mining techniques have also been developed to detect outliers, such as @math -nearest neighbor @cite_11 @cite_24 , @math -means @cite_16 @cite_1 , @math -medoids @cite_33 , density-based clustering @cite_9 , In general, these methods classify the observations with similar features, and find the observations that do not belong strongly to any cluster or far from other clusters. Nevertheless, most data mining techniques are designed for structured relational data, which may not align well for the need of outlier detection in load curve data. In addition, these methods are normally time consuming because they need a training process on a large dataset.
@cite_33 @cite_9 @cite_1 @cite_24 @cite_16 @cite_11
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1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index. In many different application areas, e.g. sensor databases, location based services or face recognition systems, distances between odjects have to be computed based on vague and uncertain data. Commonly, the distances between these uncertain object descriptions are expressed by one numerical distance value. Based on such single-valued distance functions standard data mining algorithms can work without any changes. In this paper, we propose to express the similarity between two fuzzy objects by distance probability functions. These fuzzy distance functions assign a probability value to each possible distance value. By integrating these fuzzy distance functions directly into data mining algorithms, the full information provided by these functions is exploited. In order to demonstrate the benefits of this general approach, we enhance the density-based clustering algorithm DBSCAN so that it can work directly on these fuzzy distance functions. In a detailed experimental evaluation based on artificial and real-world data sets, we show the characteristics and benefits of our new approach. It has been almost thirty years since Shannon introduced the sampling theorem to communications theory. In this review paper we will attempt to present the various contributions made for the sampling theorems with the necessary mathematical details to make it self-contained. We will begin by a clear statement of Shannon's sampling theorem followed by its applied interpretation for time-invariant systems. Then we will review its origin as Whittaker's interpolation series. The extensions will include sampling for functions of more than one variable, random processes, nonuniform sampling, nonband-limited functions, implicit sampling, generalized functions (distributions), sampling with the function and its derivatives as suggested by Shannon in his original paper, and sampling for general integral transforms. Also the conditions on the functions to be sampled will be summarized. The error analysis of the various sampling expansions, including specific error bounds for the truncation, aliasing, jitter and parts of various other errors will be discussed and summarized. This paper will be concluded by searching the different recent applications of the sampling theorems in other fields, besides communications theory. These include optics, crystallography, time-varying systems, boundary value problems, spline approximation, special functions, and the Fourier and other discrete transforms. In this paper, we propose a novel formulation for distance-based outliers that is based on the distance of a point from its kth nearest neighbor. We rank each point on the basis of its distance to its kth nearest neighbor and declare the top n points in this ranking to be outliers. In addition to developing relatively straightforward solutions to finding such outliers based on the classical nested-loop join and index join algorithms, we develop a highly efficient partition-based algorithm for mining outliers. This algorithm first partitions the input data set into disjoint subsets, and then prunes entire partitions as soon as it is determined that they cannot contain outliers. This results in substantial savings in computation. We present the results of an extensive experimental study on real-life and synthetic data sets. The results from a real-life NBA database highlight and reveal several expected and unexpected aspects of the database. The results from a study on synthetic data sets demonstrate that the partition-based algorithm scales well with respect to both data set size and data set dimensionality.