Implications of ZNormalization in the Matrix Profile Companies are increasingly measuring their products and services, resulting in a rising amount of available time series data, making techniques to extract usable information needed. One stateoftheart technique for time series is the Matrix Profile, which has been used for various applications including motifdiscord discovery, visualizations and semantic segmentation. Internally, the Matrix Profile utilizes the znormalized Euclidean distance to compare the shape of subsequences between two series. However, when comparing subsequences that are relatively flat and contain noise, the resulting distance is high despite the visual similarity of these subsequences. This property violates some of the assumptions made by Matrix Profile based techniques, resulting in worse performance when series contain flat and noisy subsequences. By studying the properties of the znormalized Euclidean distance, we derived a method to eliminate this effect requiring only an estimate of the standard deviation of the noise. In this paper we describe various practical properties of the znormalized Euclidean distance and show how these can be used to correct the performance of Matrix Profile related techniques. We demonstrate our techniques using anomaly detection using a Yahoo! Webscope anomaly dataset, semantic segmentation on the PAMAP2 activity dataset and for data visualization on a UCI activity dataset, all containing realworld data, and obtain overall better results after applying our technique. Our technique is a straightforward extension of the distance calculation in the Matrix Profile and will benefit any derived technique dealing with time series containing flat and noisy subsequences.

Matrix Profile XVIII: Time Series Mining in the Face of Fast Moving Streams using a Learned Approximate Matrix Profile In recent years, the Matrix Profile has emerged as a promising approach to allow data mining on large time series archives. By efficiently computing all of the essential distance information between subsequences in a time series, the Matrix Profile makes many analytic problems, including classification and anomaly detection, easy or even trivial. However, for many tasks, in addition to archives of data, we may face neverending streams of newly arriving data. While there is an algorithm to maintain a Matrix Profile in the face of newly arriving data, it is limited to streams arriving on the order of one Hz and with small archives of historical data. However, in domains as diverse as seismology, neuroscience and entomology, we may encounter datasets that stream at rates that are orders of magnitude faster. In this work we introduce LAMP, a model that predicts, in constant time, the Matrix Profile value that would have been assigned to an incoming subsequence. This allows us to exploit the utility of the Matrix Profile in settings that would otherwise be untenable. While learning LAMP models is computationally expensive, this stage is done offline with an arbitrary computational paradigm. The models can then be deployed on resourceconstrained devices including wearable sensors. We demonstrate the utility of LAMP with experiments on diverse and challenging datasets with billions of datapoints on a simple desktop machine. We achieve more than 10000x speedup over exact methods on the same data.