Many high level representations of time series have been proposed for data mining, including Fourier transforms, wavelets, eigenwaves, piecewise polynomial models, etc. Many researchers have also considered symbolic representations of time series, noting that such representations would potentiality allow researchers to avail of the wealth of data structures and algorithms from the text processing and bioinformatics communities. While many symbolic representations of time series have been introduced over the past decades, they all suffer from two fatal flaws. First, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Second, although distance measures can be defined on the symbolic approaches, these distance measures have little correlation with distance measures defined on the original time series.In this work we formulate a new symbolic representation of time series. Our representation is unique in that it allows dimensionality/numerosity reduction, and it also allows distance measures to be defined on the symbolic approach that lower bound corresponding distance measures defined on the original series. As we shall demonstrate, this latter feature is particularly exciting because it allows one to run certain data mining algorithms on the efficiently manipulated symbolic representation, while producing identical results to the algorithms that operate on the original data. In particular, we will demonstrate the utility of our representation on various data mining tasks of clustering, classification, query by content, anomaly detection, motif discovery, and visualization.

Many algorithms have been proposed for the problem of time series classification. However, it is clear that one-nearest-neighbor with Dynamic Time Warping (DTW) distance is exceptionally difficult to beat. This approach has one weakness, however; it is computationally too demanding for many realtime applications. One way to mitigate this problem is to speed up the DTW calculations. Nonetheless, there is a limit to how much this can help. In this work, we propose an additional technique, numerosity reduction, to speed up one-nearestneighbor DTW. While the idea of numerosity reduction for nearest-neighbor classifiers has a long history, we show here that we can leverage off an original observation about the relationship between dataset size and DTW constraints to produce an extremely compact dataset with little or no loss in accuracy. We test our ideas with a comprehensive set of experiments, and show that it can efficiently produce extremely fast accurate classifiers.

The problem of time series classification has attracted great interest in the last decade. However current research assumes the existence of large amounts of labeled training data. In reality, such data may be very difficult or expensive to obtain. For example, it may require the time and expertise of cardiologists, space launch technicians, or other domain specialists. As in many other domains, there are often copious amounts of unlabeled data available. For example, the PhysioBank archive contains gigabytes of ECG data. In this work we propose a semisupervised technique for building time series classifiers. While such algorithms are well known in text domains, we will show that special considerations must be made to make them both efficient and effective for the time series domain. We evaluate our work with a comprehensive set of experiments on diverse data sources including electrocardiograms, handwritten documents, manufacturing, and video datasets. The experimental results demonstrate that our approach requires only a handful of labeled examples to construct accurate classifiers.

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The vast majority of data mining algorithms require the setting of many input parameters. The dangers of working with parameter-laden algorithms are twofold. First, incorrect settings may cause an algorithm to fail in finding the true patterns. Second, a perhaps more insidious problem is that the algorithm may report spurious patterns that do not really exist, or greatly overestimate the significance of the reported patterns. This is especially likely when the user fails to understand the role of parameters in the data mining 100 E. Keogh et al.process. Data mining algorithms should have as few parameters as possible. A parameter-light algorithm would limit our ability to impose our prejudices, expectations, and presumptions on the problem at hand, and would let the data itself speak to us. In this work, we show that recent results in bioinformatics, learning, and computational theory hold great promise for a parameter-light data-mining paradigm. The results are strongly connected to Kolmogorov complexity theory. However, as a practical matter, they can be implemented using any off-the-shelf compression algorithm with the addition of just a dozen lines of code. We will show that this approach is competitive or superior to many of the state-of-the-art approaches in anomaly/interestingness detection, classification, and clustering with empirical tests on time series/DNA/text/XML/video datasets. As a further evidence of the advantages of our method, we will demonstrate its effectiveness to solve a real world classification problem in recommending printing services and products.

Shape matching and indexing is important topic in its own right, and is a fundamental subroutine in most shape data mining algorithms. Given the ubiquity of shape, shape matching is an important problem with applications in domains as diverse as biometrics, industry, medicine, zoology and anthropology. The distance/similarity measure for used for shape matching must be invariant to many distortions, including scale, offset, noise, articulation, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However, rotation invariance is noted in the literature as being an especially difficult challenge. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of discrimination ability, or in the distance measure, at the expense of efficiency. In this work, we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems our technique can take current approaches and make them four orders of magnitude faster, without false

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Sleep stage classification is a fundamental but cumbersome task in sleep analysis. To score the sleep stage automatically, this study presents a stage classification method based on a two-stage neural network. The feature learning stage as the first stage can fuse network trained features with traditional hand-crafted features. A recurrent neural network (RNN) in the second stage is fully utilized for learning temporal information between sleep epochs and obtaining classification results. To solve serious sample imbalance problem, a novel pre-training process combined with data augmentation was introduced. The proposed method was evaluated by two public databases, the Sleep-EDF and Sleep Apnea (SA). The proposed method can achieve the F1-score and Kappa coefficient of 0.806 and 0.80 for healthy subjects, respectively, and achieve 0.790 and 0.74 for the subjects with suspect sleep disorders, respectively. The results show that the method can achieve better performance compared to the state-of-the-art methods for the same databases. Model analysis displayed that the combination of the hand-crafted features and network trained features can improve the classification performance via the comparison experiments. In addition, the RNN is a good choice for learning temporal information in sleep epochs. Besides, the pre-training process with data augmentation is verified that can reduce the impact of sample imbalance. The proposed model has potential to exploit sleep information comprehensively. INDEX TERMS Sleep stage classification, feature learning, sequence learning, EEG signal. JIAHAO FAN received the B.S. degree in communication engineering in 2013, and the M.S. degree in electronic and communication engineering from Jilin University, in 2016. He is currently pursuing the Ph.D. degree with the