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.
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.
@cite_31 @cite_20 @cite_1 @cite_6
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Thanks to the powerful feature representations obtained through deep convolutional neural network (CNN), the performance of object detection has recently been substantially boosted. Despite the remarkable success, the problems of object rotation, within-class variability, and between-class similarity remain several major challenges. To address these problems, this paper proposes a novel and effective method to learn a rotation-invariant and Fisher discriminative CNN (RIFD-CNN) model. This is achieved by introducing and learning a rotation-invariant layer and a Fisher discriminative layer, respectively, on the basis of the existing high-capacity CNN architectures. Specifically, the rotation-invariant layer is trained by imposing an explicit regularization constraint on the objective function that enforces invariance on the CNN features before and after rotating. The Fisher discriminative layer is trained by imposing the Fisher discrimination criterion on the CNN features so that they have small within-class scatter but large between-class separation. In the experiments, we comprehensively evaluate the proposed method for object detection task on a public available aerial image dataset and the PASCAL VOC 2007 dataset. State-of-the-art results are achieved compared with the existing baseline methods. Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases. In this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations. Our scale and affine invariant detectors are based on the following recent results: (1) Interest points extracted with the Harris detector can be adapted to affine transformations and give repeatable results (geometrically stable). (2) The characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives (the Laplacian). (3) The affine shape of a point neighborhood is estimated based on the second moment matrix. Our scale invariant detector computes a multi-scale representation for the Harris interest point detector and then selects points at which a local measure (the Laplacian) is maximal over scales. This provides a set of distinctive points which are invariant to scale, rotation and translation as well as robust to illumination changes and limited changes of viewpoint. The characteristic scale determines a scale invariant region for each point. We extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood. An iterative algorithm modifies location, scale and neighborhood of each point and converges to affine invariant points. This method can deal with significant affine transformations including large scale changes. The characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point. We present a comparative evaluation of different detectors and show that our approach provides better results than existing methods. The performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points. 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.