Geodesic Distance Function Learning via Heat Flow on Vector Fields

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. Note that the distance function on a manifold can always be well-defined. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm

Adaptive Tag Selection for Image Annotation

Not all tags are relevant to an image, and the number of relevant tags is image-dependent. Although many methods have been proposed for image auto-annotation, the question of how to determine the number of tags to be selected per image remains open. The main challenge is that for a large tag vocabulary, there is often a lack of ground truth data for acquiring optimal cutoff thresholds per tag. In contrast to previous works that pre-specify the number of tags to be selected, we propose in this paper adaptive tag selection. The key insight is to divide the vocabulary into two disjoint subsets, namely a seen set consisting of tags having ground truth available for optimizing their thresholds and a novel set consisting of tags without any ground truth. Such a division allows us to estimate how many tags shall be selected from the novel set according to the tags that have been selected from the seen set. The effectiveness of the proposed method is justified by our participation in the ImageCLEF 2014 image annotation task. On a set of 2,065 test images with ground truth available for 207 tags, the benchmark evaluation shows that compared to the popular top-$k$ strategy which obtains an F-score of 0.122, adaptive tag selection achieves a higher F-score of 0.223. Moreover, by treating the underlying image annotation system as a black box, the new method can be used as an easy plug-in to boost the performance of existing systems

How machine learning informs ride-hailing services: A survey

In recent years, online ride-hailing services have emerged as an important component of urban transportation system, which not only provide significant ease for residents’ travel activities, but also shape new travel behavior and diversify urban mobility patterns. This study provides a thorough review of machine-learning-based methodologies for on-demand ride-hailing services. The importance of on-demand ride-hailing services in the spatio-temporal dynamics of urban traffic is first highlighted, with machine-learning-based macro-level ride-hailing research demonstrating its value in guiding the design, planning, operation, and control of urban intelligent transportation systems. Then, the research on travel behavior from the perspective of individual mobility patterns, including carpooling behavior and modal choice behavior, is summarized. In addition, existing studies on order matching and vehicle dispatching strategies, which are among the most important components of on-line ride-hailing systems, are collected and summarized. Finally, some of the critical challenges and opportunities in ride-hailing services are discussed