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. Time series data mining has received much greater interest along with the increase in temporal data sets from different domains such as medicine, finance, multimedia, etc. Representations are important to reduce dimensionality and generate useful similarity measures. High-level representations such as Fourier transforms, wavelets, piecewise polynomial models, etc., were considered previously. Recently, autoregressive kernels were introduced to reflect the similarity of the time series. We introduce a novel approach to model the dependency structure in time series that generalizes the concept of autoregression to local autopatterns. Our approach generates a pattern-based representation along with a similarity measure called learned pattern similarity (LPS). A tree-based ensemble-learning strategy that is fast and insensitive to parameter settings is the basis for the approach. Then, a robust similarity measure based on the learned patterns is presented. This unsupervised approach to represent and measure the similarity between time series generally applies to a number of data mining tasks (e.g., clustering, anomaly detection, classification). Furthermore, an embedded learning of the representation avoids pre-defined features and an extraction step which is common in some feature-based approaches. The method generalizes in a straightforward manner to multivariate time series. The effectiveness of LPS is evaluated on time series classification problems from various domains. We compare LPS to eleven well-known similarity measures. Our experimental results show that LPS provides fast and competitive results on benchmark datasets from several domains. Furthermore, LPS provides a research direction and template approach that breaks from the linear dependency models to potentially foster other promising nonlinear approaches. Text in natural images is of arbitrary orientations, requiring detection in terms of oriented bounding boxes. Normally, a multi-oriented text detector often involves two key tasks: 1) text presence detection, which is a classification problem disregarding text orientation; 2) oriented bounding box regression, which concerns about text orientation. Previous methods rely on shared features for both tasks, resulting in degraded performance due to the incompatibility of the two tasks. To address this issue, we propose to perform classification and regression on features of different characteristics, extracted by two network branches of different designs. Concretely, the regression branch extracts rotation-sensitive features by actively rotating the convolutional filters, while the classification branch extracts rotation-invariant features by pooling the rotation-sensitive features. The proposed method named Rotation-sensitive Regression Detector (RRD) achieves state-of-the-art performance on several oriented scene text benchmark datasets, including ICDAR 2015, MSRA-TD500, RCTW-17, and COCO-Text. Furthermore, RRD achieves a significant improvement on a ship collection dataset, demonstrating its generality on oriented object detection. This paper presents a new method for detecting scale invariant interest points. The method is based on two recent results on scale space: (1) Interest points can be adapted to scale and give repeatable results (geometrically stable). (2) Local extrema over scale of normalized derivatives indicate the presence of characteristic local structures. Our method first computes a multi-scale representation for the Harris interest point detector. We then select points at which a local measure (the Laplacian) is maximal over scales. This allows a selection of distinctive points for which the characteristic scale is known. These points are invariant to scale, rotation and translation as well as robust to illumination changes and limited changes of viewpoint. For indexing, the image is characterized by a set of scale invariant points; the scale associated with each point allows the computation of a scale invariant descriptor. Our descriptors are, in addition, invariant to image rotation, of affine illumination changes and robust to small perspective deformations. Experimental results for indexing show an excellent performance up to a scale factor of 4 for a database with more than 5000 images. Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into the feature learning algorithms. For example, we present the transformation-invariant restricted Boltzmann machine that compactly represents data by its weights and their transformations, which achieves invariance of the feature representation via probabilistic max pooling. In addition, we show that our transformation-invariant feature learning framework can also be extended to other unsupervised learning methods, such as autoencoders or sparse coding. We evaluate our method on several image classification benchmark datasets, such as MNIST variations, CIFAR-10, and STL-10, and show competitive or superior classification performance when compared to the state-of-the-art. Furthermore, our method achieves state-of-the-art performance on phone classification tasks with the TIMIT dataset, which demonstrates wide applicability of our proposed algorithms to other domains. Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into the feature learning algorithms. For example, we present the transformation-invariant restricted Boltzmann machine that compactly represents data by its weights and their transformations, which achieves invariance of the feature representation via probabilistic max pooling. In addition, we show that our transformation-invariant feature learning framework can also be extended to other unsupervised learning methods, such as autoencoders or sparse coding. We evaluate our method on several image classification benchmark datasets, such as MNIST variations, CIFAR-10, and STL-10, and show competitive or superior classification performance when compared to the state-of-the-art. Furthermore, our method achieves state-of-the-art performance on phone classification tasks with the TIMIT dataset, which demonstrates wide applicability of our proposed algorithms to other domains. Time series classification is an important task with many challenging applications. A nearest neighbor (NN) classifier with dynamic time warping (DTW) distance is a strong solution in this context. On the other hand, feature-based approaches have been proposed as both classifiers and to provide insight into the series, but these approaches have problems handling translations and dilations in local patterns. Considering these shortcomings, we present a framework to classify time series based on a bag-of-features representation (TSBF). Multiple subsequences selected from random locations and of random lengths are partitioned into shorter intervals to capture the local information. Consequently, features computed from these subsequences measure properties at different locations and dilations when viewed from the original series. This provides a feature-based approach that can handle warping (although differently from DTW). Moreover, a supervised learner (that handles mixed data types, different units, etc.) integrates location information into a compact codebook through class probability estimates. Additionally, relevant global features can easily supplement the codebook. TSBF is compared to NN classifiers and other alternatives (bag-of-words strategies, sparse spatial sample kernels, shapelets). Our experimental results show that TSBF provides better results than competitive methods on benchmark datasets from the UCR time series database. In recent years, sparse signal modeling, especially using the synthesis model has been popular. Sparse coding in the synthesis model is however, NP-hard. Recently, interest has turned to the sparsifying transform model, for which sparse coding is cheap. However, natural images typically contain diverse textures that cannot be sparsified well by a single transform. Hence, in this work, we propose a union of sparsifying transforms model. Sparse coding in this model reduces to a form of clustering. The proposed model is also equivalent to a structured overcomplete sparsifying transform model with block cosparsity, dubbed OCTOBOS. The alternating algorithm introduced for learning such transforms involves simple closed-form solutions. A theoretical analysis provides a convergence guarantee for this algorithm. It is shown to be globally convergent to the set of partial minimizers of the non-convex learning problem. We also show that under certain conditions, the algorithm converges to the set of stationary points of the overall objective. When applied to images, the algorithm learns a collection of well-conditioned square transforms, and a good clustering of patches or textures. The resulting sparse representations for the images are much better than those obtained with a single learned transform, or with analytical transforms. We show the promising performance of the proposed approach in image denoising, which compares quite favorably with approaches involving a single learned square transform or an overcomplete synthesis dictionary, or gaussian mixture models. The proposed denoising method is also faster than the synthesis dictionary based approach. In sparse approximation theory, the fundamental problem is to reconstruct a signal A∈ℝn from linear measurements 〈Aψi〉 with respect to a dictionary of ψi's. Recently, there is focus on the novel direction of Compressed Sensing [9] where the reconstruction can be done with very few—O(k logn)—linear measurements over a modified dictionary if the signal is compressible, that is, its information is concentrated in k coefficients with the original dictionary. In particular, these results [9, 4, 23] prove that there exists a single O(k logn) ×n measurement matrix such that any such signal can be reconstructed from these measurements, with error at most O(1) times the worst case error for the class of such signals. Compressed sensing has generated tremendous excitement both because of the sophisticated underlying Mathematics and because of its potential applications In this paper, we address outstanding open problems in Compressed Sensing. Our main result is an explicit construction of a non-adaptive measurement matrix and the corresponding reconstruction algorithm so that with a number of measurements polynomial in k, logn, 1 e, we can reconstruct compressible signals. This is the first known polynomial time explicit construction of any such measurement matrix. In addition, our result improves the error guarantee from O(1) to 1 + e and improves the reconstruction time from poly(n) to poly(k logn) Our second result is a randomized construction of O(kpolylog (n)) measurements that work for each signal with high probability and gives per-instance approximation guarantees rather than over the class of all signals. Previous work on Compressed Sensing does not provide such per-instance approximation guarantees; our result improves the best known number of measurements known from prior work in other areas including Learning Theory [20, 21], Streaming algorithms [11, 12, 6] and Complexity Theory [1] for this case Our approach is combinatorial. In particular, we use two parallel sets of group tests, one to filter and the other to certify and estimate; the resulting algorithms are quite simple to implement Dimensionality reduction in multivariate time series analysis has broad applications, ranging from financial data analysis to biomedical research. However, high levels of ambient noise and various interferences result in nonstationary signals, which may lead to inefficient performance of conventional methods. In this paper, we propose a nonlinear dimensionality reduction framework using diffusion maps on a learned statistical manifold, which gives rise to the construction of a low-dimensional representation of the high-dimensional nonstationary time series. We show that diffusion maps, with affinity kernels based on the Kullback-Leibler divergence between the local statistics of samples, allow for efficient approximation of pairwise geodesic distances. To construct the statistical manifold, we estimate time-evolving parametric distributions by designing a family of Bayesian generative models. The proposed framework can be applied to problems in which the time-evolving distributions (of temporally localized data), rather than the samples themselves, are driven by a low-dimensional underlying process. We provide efficient parameter estimation and dimensionality reduction methodologies, and apply them to two applications: music analysis and epileptic-seizure prediction. Author-HighlightsWe build a class of Bayesian models to learn the evolving statistics of time series.We construct diffusion maps based on the time-evolving distributional information.The proposed method recovers the underlying process controlling the time series.The proposed framework is applied to the analysis of music and icEEG recordings. While approaches based on bags of features excel at low-level action classification, they are ill-suited for recognizing complex events in video, where concept-based temporal representations currently dominate. This paper proposes a novel representation that captures the temporal dynamics of windowed mid-level concept detectors in order to improve complex event recognition. We first express each video as an ordered vector time series, where each time step consists of the vector formed from the concatenated confidences of the pre-trained concept detectors. We hypothesize that the dynamics of time series for different instances from the same event class, as captured by simple linear dynamical system (LDS) models, are likely to be similar even if the instances differ in terms of low-level visual features. We propose a two-part representation composed of fusing: (1) a singular value decomposition of block Hankel matrices (SSID-S) and (2) a harmonic signature (HS) computed from the corresponding eigen-dynamics matrix. The proposed method offers several benefits over alternate approaches: our approach is straightforward to implement, directly employs existing concept detectors and can be plugged into linear classification frameworks. Results on standard datasets such as NIST's TRECVID Multimedia Event Detection task demonstrate the improved accuracy of the proposed method. Machine learning research has, to a great extent, ignored an important aspect of many real world applications: time. Existing concept learners predominantly operate on a static set of attributes; for example, classifying flowers described by leaf size, pet al colour and pet al count. However, many real datasets are not static; they cannot sensibly be represented as a fixed set of attributes. Rather, the examples are expressed as features that vary temporally, and it is the temporal variation itself that is used for classification. Consider a simple gesture recognition domain, in which the temporal features are the position of the hands, finger bends, and so on. Looking at the position of the hand at one point in time is not likely to lead to a successful classification; it is only by analysing changes in position that recognition is possible. This thesis presents a new technique for temporal classification. By extracting sub-events from the training instances and parameterising them to allow feature construction for a subsequent learning process, it is able to employ background knowledge and express learnt concepts in terms of the background knowledge. The novel results of the thesis are: a temporal learner capable of producing comprehensible and accurate classifiers for multivariate time series that can learn from a small number of instances and can integrate non-temporal features; a feature construction technique that parameterises sub-events of the training set and clusters them to construct features for a propositional learner; and a technique for post-processing classification rules produced by the learner to give a comprehensible description expressed in the same form as the original background knowledge. The thesis discusses the implementation of TClass, a temporal learner. Results show rules that are comprehensible in many cases and accuracy results close to or better than existing technique—over 98 per cent for sign language and 72 per cent for ECGs (equivalent to the accuracy of a human cardiologist). One further surprising result is that a small set of very primitive sub-events proves to be functional, avoiding the need for labour-intensive background knowledge if it is not available. Sparse coding is a common approach to learning local features for object recognition. Recently, there has been an increasing interest in learning features from spatio-temporal, binocular, or other multi-observation data, where the goal is to encode the relationship between images rather than the content of a single image. We provide an analysis of multi-view feature learning, which shows that hidden variables encode transformations by detecting rotation angles in the eigenspaces shared among multiple image warps. Our analysis helps explain recent experimental results showing that transformation-specific features emerge when training complex cell models on videos. Our analysis also shows that transformation-invariant features can emerge as a by-product of learning representations of transformations. In recent years, the rapid growth in technology has increased the opportunity for longitudinal human behavioral studies. Rich multimodal data, from wearables like Fitbit, online social networks, mobile phones etc. can be collected in natural environments. Uncovering the underlying low-dimensional structure of noisy multi-way data in an unsupervised setting is a challenging problem. Tensor factorization has been successful in extracting the interconnected low-dimensional descriptions of multi-way data. In this paper, we apply non-negative tensor factorization on a real-word wearable sensor data, StudentLife, to find latent temporal factors and group of similar individuals. Meta data is available for the semester schedule, as well as the individuals' performance and personality. We demonstrate that non-negative tensor factorization can successfully discover clusters of individuals who exhibit higher academic performance, as well as those who frequently engage in leisure activities. The recovered latent temporal patterns associated with these groups are validated against ground truth data to demonstrate the accuracy of our framework. We introduce an algorithm for a non-negative 3D tensor factorization for the purpose of establishing a local parts feature decomposition from an object class of images. In the past, such a decomposition was obtained using non-negative matrix factorization (NMF) where images were vectorized before being factored by NMF. A tensor factorization (NTF) on the other hand preserves the 2D representations of images and provides a unique factorization (unlike NMF which is not unique). The resulting "factors" from the NTF factorization are both sparse (like with NMF) but also separable allowing efficient convolution with the test image. Results show a superior decomposition to what an NMF can provide on all fronts - degree of sparsity, lack of ghost residue due to invariant parts and efficiency of coding of around an order of magnitude better. Experiments on using the local parts decomposition for face detection using SVM and Adaboost classifiers demonstrate that the recovered features are discriminatory and highly effective for classification. We propose an unsupervised method for learning multi-stage hierarchies of sparse convolutional features. While sparse coding has become an increasingly popular method for learning visual features, it is most often trained at the patch level. Applying the resulting filters convolutionally results in highly redundant codes because overlapping patches are encoded in isolation. By training convolutionally over large image windows, our method reduces the redudancy between feature vectors at neighboring locations and improves the efficiency of the overall representation. In addition to a linear decoder that reconstructs the image from sparse features, our method trains an efficient feed-forward encoder that predicts quasi-sparse features from the input. While patch-based training rarely produces anything but oriented edge detectors, we show that convolutional training produces highly diverse filters, including center-surround filters, corner detectors, cross detectors, and oriented grating detectors. We show that using these filters in multistage convolutional network architecture improves performance on a number of visual recognition and detection tasks. Recent algorithms for sparse coding and independent component analysis (ICA) have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transformations into account. We describe an unsupervised algorithm for learning both localized features and their transformations directly from images using a sparse bilinear generative model. We show that from an arbitrary set of natural images, the algorithm produces oriented basis filters that can simultaneously represent features in an image and their transformations. The learned generative model can be used to translate features to different locations, thereby reducing the need to learn the same feature at multiple locations, a limitation of previous approaches to sparse coding and ICA. Our results suggest that by explicitly modeling the interaction between local image features and their transformations, the sparse bilinear approach can provide a basis for achieving transformation-invariant vision.