Discord Discovery Research Articles

A Parallel Discord Discovery Algorithm for a Graphics Processor

A Parallel Discord Discovery Algorithm for a Graphics Processor

A fast algorithm for complex discord searches in time series: HOT SAX Time

Time series analysis is quickly proceeding towards long and complex tasks. In recent years, fast approximate algorithms for discord search have been proposed in order to compensate for the increasing size of the time series. It is more interesting, however, to find quick exact solutions. In this research, we improved HOT SAX (Heuristically Ordered Time series using Symbolic Aggregate ApproXimation) by exploiting two main ideas: the warm-up process, and the similarity between sequences close in time. These improvements can reduce the size of the discord search space by orders of magnitude when compared with HOT SAX. The resulting algorithm, called HOT SAX Time (HST), has been validated with real and synthetic time series, and successfully compared with HOT SAX, RRA (Rare Rule Anomaly), SCAMP (SCAlable Matrix Profile), and DADD (Disk Aware Discord Discovery). The complexity of a discord search has been evaluated with a new indicator, the cost per sequence (cps), which allows one to compare searches on time series of different lengths. Numerical evidence suggests that two conditions are involved in determining the complexity of a discord search in a non-trivial way: the length of the discords, and the noise/signal ratio. This is the first exact discord search algorithm that has been demonstrated being more than 100 times faster than HOT SAX.

Model-free detection of unique events in time series

Recognition of anomalous events is a challenging but critical task in many scientific and industrial fields, especially when the properties of anomalies are unknown. In this paper, we introduce a new anomaly concept called “unicorn” or unique event and present a new, model-free, unsupervised detection algorithm to detect unicorns. The key component of the new algorithm is the Temporal Outlier Factor (TOF) to measure the uniqueness of events in continuous data sets from dynamic systems. The concept of unique events differs significantly from traditional outliers in many aspects: while repetitive outliers are no longer unique events, a unique event is not necessarily an outlier; it does not necessarily fall out from the distribution of normal activity. The performance of our algorithm was examined in recognizing unique events on different types of simulated data sets with anomalies and it was compared with the Local Outlier Factor (LOF) and discord discovery algorithms. TOF had superior performance compared to LOF and discord detection algorithms even in recognizing traditional outliers and it also detected unique events that those did not. The benefits of the unicorn concept and the new detection method were illustrated by example data sets from very different scientific fields. Our algorithm successfully retrieved unique events in those cases where they were already known such as the gravitational waves of a binary black hole merger on LIGO detector data and the signs of respiratory failure on ECG data series. Furthermore, unique events were found on the LIBOR data set of the last 30 years.

A GPU Acceleration Framework for Motif and Discord Based Pattern Mining

With the fast digitalization of our society, mining patterns from large time series data is increasingly becoming a critical problem for a wide range of big data applications. Motif and discord discovery algorithms, which offer effective solutions to identify repeatedly appearing and abnormal patterns, respectively, are fundamental building blocks for time series processing. Both approaches, however, can be time extremely consuming when handling large time series due to the subsequence-based computations of distance similarity metrics. In this article, we show that the highly involved subsequence-based computations can actually be decomposed into a few fine-grained computing patterns for efficient data parallel computing. By developing highly efficient GPU algorithms for such basic patterns and effectively composing such patterns, we are able to solve both motif and discord discovery problems under euclidean and DTW distance metrics in a unified GPU acceleration framework. Extensive experiments prove that the proposed framework outperforms pruned CPU algorithms by up to three orders of magnitude. Our work paves the foundation of building GPU acceleration frameworks for large-scale time series datasets.

Matrix profile goes MAD: variable-length motif and discord discovery in data series

In the last 15 years, data series motif and discord discovery have emerged as two useful and well-used primitives for data series mining, with applications to many domains, including robotics, entomology, seismology, medicine, and climatology. Nevertheless, the state-of-the-art motif and discord discovery tools still require the user to provide the relative length. Yet, in several cases, the choice of length is critical and unforgiving. Unfortunately, the obvious brute-force solution, which tests all lengths within a given range, is computationally untenable. In this work, we introduce a new framework, which provides an exact and scalable motif and discord discovery algorithm that efficiently finds all motifs and discords in a given range of lengths. We evaluate our approach with five diverse real datasets, and demonstrate that it is up to 20 times faster than the state-of-the-art. Our results also show that removing the unrealistic assumption that the user knows the correct length, can often produce more intuitive and actionable results, which could have otherwise been missed.

Параллельный алгоритм поиска диссонансов временного ряда для многоядерных ускорителей

Диссонанс является уточнением понятия аномальной подпоследовательности (существенно непохожей на остальные подпоследовательности) временного ряда. Задача поиска диссонанса встречается в широком спектре предметных областей, связанных с временными рядами: медицина, экономика, моделирование климата и др. В работе предложен новый параллельный алгоритм поиска диссонанса во временном ряде на платформе многоядерного ускорителя для случая, когда входные данные могут быть размещены в оперативной памяти. Алгоритм использует возможность независимого вычисления евклидовых расстояний между подпоследовательностями ряда. Алгоритм состоит из двух этапов: подготовка данных и поиск. На этапе подготовки выполняется построение вспомогательных матричных структур данных, обеспечивающих распараллеливание и векторизацию вычислений. На стадии поиска осуществляется нахождение диссонанса с помощью построенных структур данных. Выполнена реализация алгоритма для ускорителей архитектур Intel MIC (Many Integrated Core) и NVIDIA GPU, распараллеливание выполнено с помощью технологий программирования OpenMP и OpenAcc соответственно. Представлены результаты вычислительных экспериментов, подтверждающих масштабируемость разработанного алгоритма. Discord is a refinement of the concept of anomalous subsequence of a time series. The discord discovery problem frequently occurs in a wide range of application areas related to time series: medicine, economics, climate modeling, etc. In this paper we propose a new parallel discord discovery algorithm for many-core systems in the case when the input data fit in the main memory. The algorithm exploits the ability to independently calculate the Euclidean distances between the subsequences of the time series. Computations are paralleled using OpenMP and OpenAcc for the Intel MIC (Many Integrated Core) and NVIDIA GPU platforms, respectively. The algorithm consists of two stages, namely precomputations and discovery. At the precomputation stage, we construct the auxiliary matrix data structures to ensure the efficient vectorization of computations on an accelerator. At the discovery stage, the algorithm searches for a discord based on the constructed structures. A number of numerical experiments confirm a high scalability of the proposed algorithm.

A Multi-resolution Approximation for Time Series

Time series is a common and well-known way for describing temporal data. However, most of the state-of-the-art techniques for analysing time series have focused on generating a representation for a single level of resolution. For analysing of a time series at several levels of resolutions, one would require to compute different representations, one for each resolution level. We introduce a multi-resolution representation for time series based on local trends and mean values. We require the level of resolution as parameter, but it can be automatically computed if we consider the maximum resolution of the time series. Our technique represents a time series using trend-value pairs on each segment belonging to a resolution level. To provide a useful representation for data mining tasks, we also propose dissimilarity measures and a symbolic representation based on the SAX technique for efficient similarity search using a multi-resolution indexing scheme. We evaluate our method for classification and discord discovery tasks over a diversity of data domains, achieving a better performance in terms of efficiency and effectiveness compared with some of the best-known classic techniques. Indeed, for some of the experiments, the time series mining algorithms using our multi-resolution representation were an order of magnitude faster, in terms of distance computations, than the state of the art.

ESPSA: A prediction-based algorithm for streaming time series segmentation

Streaming time series segmentation is one of the major problems in streaming time series mining, which can create the high-level representation of streaming time series, and thus can provide important supports for many time series mining tasks, such as indexing, clustering, classification, and discord discovery. However, the data elements in streaming time series, which usually arrive online, are fast-changing and unbounded in size, consequently, leading to a higher requirement for the computing efficiency of time series segmentation. Thus, it is a challenging task how to segment streaming time series accurately under the constraint of computing efficiency. In this paper, we propose exponential smoothing prediction-based segmentation algorithm (ESPSA). The proposed algorithm is developed based on a sliding window model, and uses the typical exponential smoothing method to calculate the smoothing value of arrived data element of streaming time series as the prediction value of the future data. Besides, to determine whether a data element is a segmenting key point, we study the statistical characteristics of the prediction error and then deduce the relationship between the prediction error and the compression rate. The extensive experiments on both synthetic and real datasets demonstrate that the proposed algorithm can segment streaming time series effectively and efficiently. More importantly, compared with candidate algorithms, the proposed algorithm can reduce the computing time by orders of magnitude.

Finding time series discord based on bit representation clustering

The problem of finding time series discord has attracted much attention recently due to its numerous applications and several algorithms have been suggested. However, most of them suffer from high computation cost and cannot satisfy the requirement of real applications. In this paper, we propose a novel discord discovery algorithm BitClusterDiscord which is based on bit representation clustering. Firstly, we use PAA (Piecewise Aggregate Approximation) bit serialization to segment time series, so as to capture the main variation characteristic of time series and avoid the influence of noise. Secondly, we present an improved K-Medoids clustering algorithm to merge several patterns with similar variation behaviors into a common cluster. Finally, based on bit representation clustering, we design two pruning strategies and propose an effective algorithm for time series discord discovery. Extensive experiments have demonstrated that the proposed approach can not only effectively find discord of time series, but also greatly improve the computational efficiency.

Disk aware discord discovery: finding unusual time series in terabyte sized datasets

The problem of finding unusual time series has recently attracted much attention, and several promising methods are now in the literature. However, virtually all proposed methods assume that the da...

Disk aware discord discovery: finding unusual time series in terabyte sized datasets

The problem of finding unusual time series has recently attracted much attention, and several promising methods are now in the literature. However, virtually all proposed methods assume that the data reside in main memory. For many real-world problems this is not be the case. For example, in astronomy, multi-terabyte time series datasets are the norm. Most current algorithms faced with data which cannot fit in main memory resort to multiple scans of the disk /tape and are thus intractable. In this work we show how one particular definition of unusual time series, the time series discord, can be discovered with a disk aware algorithm. The proposed algorithm is exact and requires only two linear scans of the disk with a tiny buffer of main memory. Furthermore, it is very simple to implement. We use the algorithm to provide further evidence of the effectiveness of the discord definition in areas as diverse as astronomy, web query mining, video surveillance, etc., and show the efficiency of our method on datasets which are many orders of magnitude larger than anything else attempted in the literature.