Optimizing Dynamic Time Warping’s Window Width for Time Series Data Mining Applications

Dynamic Time Warping (DTW) is a highly competitive distance measure for most time series data mining problems. Obtaining the best performance from DTW requires setting its only parameter, the maximum amount of warping (w). In the supervised case with ample data, w is typically set by cross-validation in the training stage. However, this method is likely to yield suboptimal results for small training sets. For the unsupervised case, learning via cross-validation is not possible because we do not have access to labeled data. Many practitioners have thus resorted to assuming that “the larger the better”, and they use the largest value of w permitted by the computational resources. However, as we will show, in most circumstances, this is a naïve approach that produces inferior clusterings. Moreover, the best warping window width is generally non-transferable between the two tasks, i.e., for a single dataset, practitioners cannot simply apply the best w learned for classification on clustering or vice versa. In addition, we will demonstrate that the appropriate amount of warping not only depends on the data structure, but also on the dataset size. Thus, even if a practitioner knows the best setting for a given dataset, they will likely be at a lost if they apply that setting on a bigger size version of that data. All these issues seem largely unknown or at least unappreciated in the community. In this work, we demonstrate the importance of setting DTW’s warping window width correctly, and we also propose novel methods to learn this parameter in both supervised and unsupervised settings. The algorithms we propose to learn w can produce significant improvements in classification accuracy and clustering quality. We demonstrate the correctness of our novel observations and the utility of our ideas by testing them with more than one hundred publicly available datasets. Our forceful results allow us to make a perhaps unexpected claim; an underappreciated “low hanging fruit” in optimizing DTW’s performance can produce improvements that make it an even stronger baseline, closing most or all the improvement gap of the more sophisticated methods proposed in recent years

DancingLines: An Analytical Scheme to Depict Cross-Platform Event Popularity

Nowadays, events usually burst and are propagated online through multiple modern media like social networks and search engines. There exists various research discussing the event dissemination trends on individual medium, while few studies focus on event popularity analysis from a cross-platform perspective. Challenges come from the vast diversity of events and media, limited access to aligned datasets across different media and a great deal of noise in the datasets. In this paper, we design DancingLines, an innovative scheme that captures and quantitatively analyzes event popularity between pairwise text media. It contains two models: TF-SW, a semantic-aware popularity quantification model, based on an integrated weight coefficient leveraging Word2Vec and TextRank; and wDTW-CD, a pairwise event popularity time series alignment model matching different event phases adapted from Dynamic Time Warping. We also propose three metrics to interpret event popularity trends between pairwise social platforms. Experimental results on eighteen real-world event datasets from an influential social network and a popular search engine validate the effectiveness and applicability of our scheme. DancingLines is demonstrated to possess broad application potentials for discovering the knowledge of various aspects related to events and different media

Matrix Profile XII: MPDist: A Novel Time Series Distance Measure to allow Data Mining in more Challenging Scenarios

At their core, many time series data mining algorithms can be reduced to reasoning about the shapes of time series subsequences. This requires a distance measure, and most algorithms use Euclidean Distance or Dynamic Time Warping (DTW) as their core subroutine. We argue that these distance measures are not as robust as the community believes. The undue faith in these measures derives from an overreliance on benchmark datasets and self-selection bias. The community is reluctant to address more difficult domains, for which current distance measures are ill-suited. In this work, we introduce a novel distance measure MPdist. We show that our proposed distance measure is much more robust than current distance measures. Furthermore, it allows us to successfully mine datasets that would defeat any Euclidean or DTW distance-based algorithm. Additionally, we show that our distance measure can be computed so efficiently, it allows analytics on fast streams

A user-friendly guide to using distance measures to compare time series in ecology

Time series are a critical component of ecological analysis, used to track changes in biotic and abiotic variables. Information can be extracted from the properties of time series for tasks such as classification (e.g., assigning species to individual bird calls); clustering (e.g., clustering similar responses in population dynamics to abrupt changes in the environment or management interventions); prediction (e.g., accuracy of model predictions to original time series data); and anomaly detection (e.g., detecting possible catastrophic events from population time series). These common tasks in ecological research all rely on the notion of (dis-) similarity, which can be determined using distance measures. A plethora of distance measures have been described, predominantly in the computer and information sciences, but many have not been introduced to ecologists. Furthermore, little is known about how to select appropriate distance measures for time-series-related tasks. Therefore, many potential applications remain unexplored. Here, we describe 16 properties of distance measures that are likely to be of importance to a variety of ecological questions involving time series. We then test 42 distance measures for each property and use the results to develop an objective method to select appropriate distance measures for any task and ecological dataset. We demonstrate our selection method by applying it to a set of real-world data on breeding bird populations in the UK and discuss other potential applications for distance measures, along with associated technical issues common in ecology. Our real-world population trends exhibit a common challenge for time series comparisons: a high level of stochasticity. We demonstrate two different ways of overcoming this challenge, first by selecting distance measures with properties that make them well suited to comparing noisy time series and second by applying a smoothing algorithm before selecting appropriate distance measures. In both cases, the distance measures chosen through our selection method are not only fit-for-purpose but are consistent in their rankings of the population trends. The results of our study should lead to an improved understanding of, and greater scope for, the use of distance measures for comparing ecological time series and help us answer new ecological questions

Outlier detection techniques for wireless sensor networks: A survey

In the field of wireless sensor networks, those measurements that significantly deviate from the normal pattern of sensed data are considered as outliers. The potential sources of outliers include noise and errors, events, and malicious attacks on the network. Traditional outlier detection techniques are not directly applicable to wireless sensor networks due to the nature of sensor data and specific requirements and limitations of the wireless sensor networks. This survey provides a comprehensive overview of existing outlier detection techniques specifically developed for the wireless sensor networks. Additionally, it presents a technique-based taxonomy and a comparative table to be used as a guideline to select a technique suitable for the application at hand based on characteristics such as data type, outlier type, outlier identity, and outlier degree

Graph Construction for Manifold Discovery

Manifold learning is a class of machine learning methods that exploits the observation that high-dimensional data tend to lie on a smooth lower-dimensional manifold. Manifold discovery is the essential first component of manifold learning methods, in which the manifold structure is inferred from available data. This task is typically posed as a graph construction problem: selecting a set of vertices and edges that most closely approximates the true underlying manifold. The quality of this learned graph is critical to the overall accuracy of the manifold learning method. Thus, it is essential to develop accurate, efficient, and reliable algorithms for constructing manifold approximation graphs. To aid in this investigation of graph construction methods, we propose new methods for evaluating graph quality. These quality measures act as a proxy for ground-truth manifold approximation error and are applicable even when prior information about the dataset is limited. We then develop an incremental update scheme for some quality measures, demonstrating their usefulness for efficient parameter tuning. We then propose two novel methods for graph construction, the Manifold Spanning Graph and the Mutual Neighbors Graph algorithms. Each method leverages assumptions about the structure of both the input data and the subsequent manifold learning task. The algorithms are experimentally validated against state of the art graph construction techniques on a multi-disciplinary set of application domains, including image classification, directional audio prediction, and spectroscopic analysis. The final contribution of the thesis is a method for aligning sequential datasets while still respecting each set’s internal manifold structure. The use of high quality manifold approximation graphs enables accurate alignments with few ground-truth correspondences

Unsupervised Joint Alignment, Clustering and Feature Learning

Joint alignment is the process of transforming instances in a data set to make them more similar based on a pre-defined measure of joint similarity. This process has great utility and applicability in many scientific disciplines including radiology, psychology, linguistics, vision, and biology. Most alignment algorithms suffer from two shortcomings. First, they typically fail when presented with complex data sets arising from multiple modalities such as a data set of normal and abnormal heart signals. Second, they require hand-picking appropriate feature representations for each data set, which may be time-consuming and ineffective, or outside the domain of expertise for practitioners. In this thesis we introduce alignment models that address both shortcomings. In the first part, we present an efficient curve alignment algorithm derived from the congealing framework that is effective on many synthetic and real data sets. We show that using the byproducts of joint alignment, the aligned data and transformation parameters, can dramatically improve classification performance. In the second part, we incorporate unsupervised feature learning based on convolutional restricted Boltzmann machines to learn a representation that is tuned to the statistics of the data set. We show how these features can be used to improve both the alignment quality and classification performance. In the third part, we present a nonparametric Bayesian joint alignment and clustering model which handles data sets arising from multiple modes. We apply this model to synthetic, curve and image data sets and show that by simultaneously aligning and clustering, it can perform significantly better than performing these operations sequentially. It also has the added advantage that it easily lends itself to semi-supervised, online, and distributed implementations. Overall this thesis takes steps towards developing an unsupervised data processing pipeline that includes alignment, clustering and feature learning. While clustering and feature learning serve as auxiliary information to improve alignment, they are important byproducts. Furthermore, we present a software implementation of all the models described in this thesis. This will enable practitioners from different scientific disciplines to utilize our work, as well as encourage contributions and extensions, and promote reproducible research

Improving Deep Reinforcement Learning Using Graph Convolution and Visual Domain Transfer

Recent developments in Deep Reinforcement Learning (DRL) have shown tremendous progress in robotics control, Atari games, board games such as Go, etc. However, model free DRL still has limited use cases due to its poor sampling efficiency and generalization on a variety of tasks. In this thesis, two particular drawbacks of DRL are investigated: 1) the poor generalization abilities of model free DRL. More specifically, how to generalize an agent\u27s policy to unseen environments and generalize to task performance on different data representations (e.g. image based or graph based) 2) The reality gap issue in DRL. That is, how to effectively transfer a policy learned in a simulator to the real world. This thesis makes several novel contributions to the field of DRL which are outlined sequentially in the following. Among these contributions is the generalized value iteration network (GVIN) algorithm, which is an end-to-end neural network planning module extending the work of Value Iteration Networks (VIN). GVIN emulates the value iteration algorithm by using a novel graph convolution operator, which enables GVIN to learn and plan on irregular spatial graphs. Additionally, this thesis proposes three novel, differentiable kernels as graph convolution operators and shows that the embedding-based kernel achieves the best performance. Furthermore, an improvement upon traditional $n$-step $Q$-learning that stabilizes training for VIN and GVIN is demonstrated. Additionally, the equivalence between GVIN and graph neural networks is outlined and shown that GVIN can be further extended to address both control and inference problems. The final subject which falls under the graph domain that is studied in this thesis is graph embeddings. Specifically, this work studies a general graph embedding framework GEM-F that unifies most of the previous graph embedding algorithms. Based on the contributions made during the analysis of GEM-F, a novel algorithm called WarpMap which outperforms DeepWalk and node2vec in the unsupervised learning settings is proposed. The aforementioned reality gap in DRL prohibits a significant portion of research from reaching the real world setting. The latter part of this work studies and analyzes domain transfer techniques in an effort to bridge this gap. Typically, domain transfer in RL consists of representation transfer and policy transfer. In this work, the focus is on representation transfer for vision based applications. More specifically, aligning the feature representation from source domain to target domain in an unsupervised fashion. In this approach, a linear mapping function is considered to fuse modules that are trained in different domains. Proposed are two improved adversarial learning methods to enhance the training quality of the mapping function. Finally, the thesis demonstrates the effectiveness of domain alignment among different weather conditions in the CARLA autonomous driving simulator