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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Recent work on mid-level visual representations aims to capture information at the level of complexity higher than typical "visual words", but lower than full-blown semantic objects. Several approaches [5,6,12,23] have been proposed to discover mid-level visual elements, that are both 1) representative, i.e., frequently occurring within a visual dataset, and 2) visually discriminative. However, the current approaches are rather ad hoc and difficult to analyze and evaluate. In this work, we pose visual element discovery as discriminative mode seeking, drawing connections to the the well-known and well-studied mean-shift algorithm [2, 1, 4, 8]. Given a weakly-labeled image collection, our method discovers visually-coherent patch clusters that are maximally discriminative with respect to the labels. One advantage of our formulation is that it requires only a single pass through the data. We also propose the Purity-Coverage plot as a principled way of experimentally analyzing and evaluating different visual discovery approaches, and compare our method against prior work on the Paris Street View dataset of [5]. We also evaluate our method on the task of scene classification, demonstrating state-of-the-art performance on the MIT Scene-67 dataset. Classification of time series has been attracting great interest over the past decade. Recent empirical evidence has strongly suggested that the simple nearest neighbor algorithm is very difficult to beat for most time series problems. While this may be considered good news, given the simplicity of implementing the nearest neighbor algorithm, there are some negative consequences of this. First, the nearest neighbor algorithm requires storing and searching the entire dataset, resulting in a time and space complexity that limits its applicability, especially on resource-limited sensors. Second, beyond mere classification accuracy, we often wish to gain some insight into the data. In this work we introduce a new time series primitive, time series shapelets, which addresses these limitations. Informally, shapelets are time series subsequences which are in some sense maximally representative of a class. As we shall show with extensive empirical evaluations in diverse domains, algorithms based on the time series shapelet primitives can be interpretable, more accurate and significantly faster than state-of-the-art classifiers. The goal of this paper is to discover a set of discriminative patches which can serve as a fully unsupervised mid-level visual representation. The desired patches need to satisfy two requirements: 1) to be representative, they need to occur frequently enough in the visual world; 2) to be discriminative, they need to be different enough from the rest of the visual world. The patches could correspond to parts, objects, "visual phrases", etc. but are not restricted to be any one of them. We pose this as an unsupervised discriminative clustering problem on a huge dataset of image patches. We use an iterative procedure which alternates between clustering and training discriminative classifiers, while applying careful cross-validation at each step to prevent overfitting. The paper experimentally demonstrates the effectiveness of discriminative patches as an unsupervised mid-level visual representation, suggesting that it could be used in place of visual words for many tasks. Furthermore, discriminative patches can also be used in a supervised regime, such as scene classification, where they demonstrate state-of-the-art performance on the MIT Indoor-67 dataset. Given a large repository of geotagged imagery, we seek to automatically find visual elements, e. g. windows, balconies, and street signs, that are most distinctive for a certain geo-spatial area, for example the city of Paris. This is a tremendously difficult task as the visual features distinguishing architectural elements of different places can be very subtle. In addition, we face a hard search problem: given all possible patches in all images, which of them are both frequently occurring and geographically informative? To address these issues, we propose to use a discriminative clustering approach able to take into account the weak geographic supervision. We show that geographically representative image elements can be discovered automatically from Google Street View imagery in a discriminative manner. We demonstrate that these elements are visually interpretable and perceptually geo-informative. The discovered visual elements can also support a variety of computational geography tasks, such as mapping architectural correspondences and influences within and across cities, finding representative elements at different geo-spatial scales, and geographically-informed image retrieval.