We propose to learn multiple local Mahalanobis distance metrics to perform k-nearest neighbor (kNN) classification of temporal sequences. Temporal sequences are first aligned by dynamic time warping (DTW); given the alignment path, similarity between two sequences is measured by the DTW distance, which is computed as the accumulated distance between matched temporal point pairs along the alignment path. Traditionally, Euclidean metric is used for distance computation between matched pairs, which ignores the data regularities and might not be optimal for applications at hand. Here we propose to learn multiple Mahalanobis metrics, such that DTW distance becomes the sum of Mahalanobis distances. We adapt the large margin nearest neighbor (LMNN) framework to our case, and formulate multiple metric learning as a linear programming problem. Extensive sequence classification results show that our proposed multiple metrics learning approach is effective, insensitive to the preceding alignment qualities, and reaches the state-of-the-art performances on UCR time series datasets.
Time series shapelet is introduced in @cite_16 , and it is a time series subsequence (patterns) which is discriminative of class-membership. The authors propose to enumerate all possible candidate subsequences, evaluate their qualities using information gain, and build a decision tree classifier out of the top ranked shapelets. Mining shapelets in their case is to search for more important subsequences, while disregarding less important subsequences. In the vision community, there are several related works @cite_13 @cite_6 @cite_20 , all of which are devoted to discovering mid-level visual patches from images. Mid-level visual patch is conceptually similar to shapelet in time series, and it a image patch which is both representative and discriminative for scene categories. They @cite_13 @cite_6 pose the discriminative patch search procedure as a discriminative clustering process, in which they selectively choose important patches but discarding other common patches. We are different from above work in that, we never have to greedily select important subsequences, instead, we take all subsequences into account and automatically learn their importance through metric learning.
@cite_20 @cite_16 @cite_13 @cite_6
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Time series shapelets are discriminative subsequences and their similarity to a time series can be used for time series classification. Since the discovery of time series shapelets is costly in terms of time, the applicability on long or multivariate time series is difficult. In this work we propose Ultra-Fast Shapelets that uses a number of random shapelets. It is shown that Ultra-Fast Shapelets yield the same prediction quality as current state-of-the-art shapelet-based time series classifiers that carefully select the shapelets by being by up to three orders of magnitudes. Since this method allows a ultra-fast shapelet discovery, using shapelets for long multivariate time series classification becomes feasible. A method for using shapelets for multivariate time series is proposed and Ultra-Fast Shapelets is proven to be successful in comparison to state-of-the-art multivariate time series classifiers on 15 multivariate time series datasets from various domains. Finally, time series derivatives that have proven to be useful for other time series classifiers are investigated for the shapelet-based classifiers. It is shown that they have a positive impact and that they are easy to integrate with a simple preprocessing step, without the need of adapting the shapelet discovery algorithm. Shapelets are discriminative subsequences of time series, usually embedded in shapelet-based decision trees. The enumeration of time series shapelets is, however, computationally costly, which in addition to the inherent difficulty of the decision tree learning algorithm to effectively handle high-dimensional data, severely limits the applicability of shapelet-based decision tree learning from large (multivariate) time series databases. This paper introduces a novel tree-based ensemble method for univariate and multivariate time series classification using shapelets, called the generalized random shapelet forest algorithm. The algorithm generates a set of shapelet-based decision trees, where both the choice of instances used for building a tree and the choice of shapelets are randomized. For univariate time series, it is demonstrated through an extensive empirical investigation that the proposed algorithm yields predictive performance comparable to the current state-of-the-art and significantly outperforms several alternative algorithms, while being at least an order of magnitude faster. Similarly for multivariate time series, it is shown that the algorithm is significantly less computationally costly and more accurate than the current state-of-the-art. Shapelets are discriminative patterns in time series, that best predict the target variable when their distances to the respective time series are used as features for a classifier. Since the shapelet is simply any time series of some length less than or equal to the length of the shortest time series in our data set, there is an enormous amount of possible shapelets present in the data. Initially, shapelets were found by extracting numerous candidates and evaluating them for their prediction quality. Then, [2] proposed a novel approach of learning time series shapelets called LTS. A new mathematical formalization of the task via a classification objective function was proposed and a tailored stochastic gradient learning was applied. It enabled learning near-to-optimal shapelets without the overhead of trying out lots of candidates. The Euclidean distance measure was used as distance metric in the proposed approach. As a limitation, it is not able to learn a single shapelet, that can be representative of different subsequences of time series, which are just warped along time axis. To consider these cases, we propose to use Dynamic Time Warping (DTW) as a distance measure in the framework of LTS. The proposed approach was evaluated on 11 real world data sets from the UCR repository and a synthetic data set created by ourselves. The experimental results show that the proposed approach outperforms the existing methods on these data sets. The purpose of mid-level visual element discovery is to find clusters of image patches that are both representative and discriminative. Here we study this problem from the prospective of pattern mining while relying on the recently popularized Convolutional Neural Networks (CNNs). We observe that a fully-connected CNN activation extracted from an image patch typically possesses two appealing properties that enable its seamless integration with pattern mining techniques. The marriage between CNN activations and association rule mining, a well-known pattern mining technique in the literature, leads to fast and effective discovery of representative and discriminative patterns from a huge number of image patches. When we retrieve and visualize image patches with the same pattern, surprisingly, they are not only visually similar but also semantically consistent, and thus give rise to a mid-level visual element in our work. Given the patterns and retrieved mid-level visual elements, we propose two methods to generate image feature representations for each. The first method is to use the patterns as codewords in a dictionary, similar to the Bag-of-Visual-Words model, we compute a Bag-of-Patterns representation. The second one relies on the retrieved mid-level visual elements to construct a Bag-of-Elements representation. We evaluate the two encoding methods on scene and object classification tasks, and demonstrate that our approach outperforms or matches recent works using CNN activations for these tasks.