text: Time-series analysis is an important domain of machine learning and a plethora of methods have been developed for the task. This paper proposes a new representation of time series, which in contrast to existing approaches, decomposes a time-series dataset into latent patterns and membership weights of local segments to those patterns. The process is formalized as a constrained objective function and a tailored stochastic coordinate descent optimization is applied. The time-series are projected to a new feature representation consisting of the sums of the membership weights, which captures frequencies of local patterns. Features from various sliding window sizes are concatenated in order to encapsulate the interaction of patterns from different sizes. The derived representation offers a set of features that boosts classification accuracy. Finally, a large-scale experimental comparison against 11 baselines over 43 real life datasets, indicates that the proposed method achieves state-of-the-art prediction accuracy results.
  @cite_31: In recent years, designing the coding and pooling structures in layered networks has been shown to be a useful method for learning high-level feature representations for visual data. Yet, such learning structures have not been extensively studied for audio signals. In this paper, we investigate different pooling strategies based on the sparse coding scheme and propose a temporal pyramid pooling method to extract discriminative and shiftinvariant feature representations. We demonstrate the superiority of our new feature representation over traditional features on the acoustic event classification task.
  @cite_20: Classical dictionary learning algorithms (DLA) allow unicomponent signals to be processed. Due to our interest in two-dimensional (2D) motion signals, we wanted to mix the two components to provide rotation invariance. So, multicomponent frameworks are examined here. In contrast to the well-known multichannel framework, a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure. Within this multivariate framework, we then present sparse coding methods: multivariate orthogonal matching pursuit (M-OMP), which provides sparse approximation for multivariate signals, and multivariate DLA (M-DLA), which empirically learns the characteristic patterns (or features) that are associated to a multivariate signals set, and combines shift-invariance and online learning. Once the multivariate dictionary is learned, any signal of this considered set can be approximated sparsely. This multivariate framework is introduced to simply present the 2D rotation invariant (2DRI) case. By studying 2D motions that are acquired in bivariate real signals, we want the decompositions to be independent of the orientation of the movement execution in the 2D space. The methods are thus specified for the 2DRI case to be robust to any rotation: 2DRI-OMP and 2DRI-DLA. Shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition. As validation, our methods are applied to 2D handwritten data to extract the elementary features of this signals set, and to provide rotation invariant decomposition.
  @cite_1: Large collections of electronic clinical records today provide us with a vast source of information on medical practice. However, the utilization of those data for exploratory analysis to support clinical decisions is still limited. Extracting useful patterns from such data is particularly challenging because it is longitudinal, sparse and heterogeneous. In this paper, we propose a Nonnegative Matrix Factorization (NMF) based framework using a convolutional approach for open-ended temporal pattern discovery over large collections of clinical records. We call the method One-Sided Convolutional NMF (OSC-NMF). Our framework can mine common as well as individual shift-invariant temporal patterns from heterogeneous events over different patient groups, and handle sparsity as well as scalability problems well. Furthermore, we use an event matrix based representation that can encode quantitatively all key temporal concepts including order, concurrency and synchronicity. We derive efficient multiplicative update rules for OSC-NMF, and also prove theoretically its convergence. Finally, the experimental results on both synthetic and real world electronic patient data are presented to demonstrate the effectiveness of the proposed method.
  @cite_6: A common way to represent a time series is to divide it into short-duration blocks, each of which is then represented by a set of basis functions. A limitation of this approach, however, is that the temporal alignment of the basis functions with the underlying structure in the time series is arbitrary. We present an algorithm for encoding a time series that does not require blocking the data. The algorithm finds an efficient representation by inferring the best temporal positions for functions in a kernel basis. These can have arbitrary temporal extent and are not constrained to be orthogonal. This allows the model to capture structure in the signal that may occur at arbitrary temporal positions and preserves the relative temporal structure of underlying events. The model is shown to be equivalent to a very sparse and highly overcomplete basis. Under this model, the mapping from the data to the representation is nonlinear, but can be computed efficiently. This form also allows the use of existing methods for adapting the basis itself to data. This approach is applied to speech data and results in a shift invariant, spikelike representation that resembles coding in the cochlear nerve.
summary: There have been a few attempts in generating invariant time-series features through factorization. A shift-invariant sparse coding of signals has been proposed for reconstructing noisy or missing series segments @cite_6 . In similar domains, sparse coding factorization has been applied for deriving shift and 2D rotation invariant features of hand writing data @cite_20 , and also invariant features of audio data @cite_31 . Moreover, a temporal decomposition of multivariate streams has been used to discover patterns in patients' clinical events @cite_1 . Our method differs from distance metrics principally. Instead of measuring the similarity of series, we project the data into a new representation, where similar instances are positioned close to each other. Furthermore, the proposed method distances away from existing bag-of-patterns methods because we learn a latent decomposition of patterns, instead of counting the occurrence of segments on the original time-series. Finally, our contributions over the existing factorization methods rely on (i) a novel approach in detecting both shift and scale invariant features for time series, and (ii) building a bag-of-patterns representation of the learned invariant features for a classification scenario.