Similarity between objects is multi-faceted and it can be easier for human annotators to measure it when the focus is on a specific aspect. We consider the problem of mapping objects into view-specific embeddings where the distance between them is consistent with the similarity comparisons of the form "from the t-th view, object A is more similar to B than to C". Our framework jointly learns view-specific embeddings exploiting correlations between views. Experiments on a number of datasets, including one of multi-view crowdsourced comparison on bird images, show the proposed method achieves lower triplet generalization error when compared to both learning embeddings independently for each view and all views pooled into one view. Our method can also be used to learn multiple measures of similarity over input features taking class labels into account and compares favorably to existing approaches for multi-task metric learning on the ISOLET dataset.
Embedding of objects from triplet or paired distance comparisons goes back to the work of Shepard and Kruskal and studied extensively @cite_13 @cite_10 @cite_7 @cite_9 @cite_2 recently.
@cite_13 @cite_7 @cite_9 @cite_2 @cite_10
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For humans, it is usually easier to make statements about the similarity of objects in relative, rather than absolute terms. Moreover, subjective comparisons of objects can be based on a number of different and independent attributes. For example, objects can be compared based on their shape, color, etc. In this paper, we consider the problem of uncovering these hidden attributes given a set of relative distance judgments in the form of triplets. The attribute that was used to generate a particular triplet in this set is unknown. Such data occurs, e.g., in crowdsourcing applications where the triplets are collected from a large group of workers. We propose the Multiview Triplet Embedding (MVTE) algorithm that produces a number of low-dimensional maps, each corresponding to one of the hidden attributes. The method can be used to assess how many different attributes were used to create the triplets, as well as to assess the difficulty of a distance comparison task, and find objects that have multiple interpretations in relation to the other objects. Low-dimensional embedding based on non-metric data (e.g., non-metric multidimensional scaling) is a problem that arises in many applications, especially those involving human subjects. This paper investigates the problem of learning an embedding of n objects into d-dimensional Euclidean space that is consistent with pairwise comparisons of the type “object a is closer to object b than c.” While there are O(n3) such comparisons, experimental studies suggest that relatively few are necessary to uniquely determine the embedding up to the constraints imposed by all possible pairwise comparisons (i.e., the problem is typically over-constrained). This paper is concerned with quantifying the minimum number of pairwise comparisons necessary to uniquely determine an embedding up to all possible comparisons. The comparison constraints stipulate that, with respect to each object, the other objects are ranked relative to their proximity. We prove that at least Q(dn log n) pairwise comparisons are needed to determine the embedding of all n objects. The lower bounds cannot be achieved by using randomly chosen pairwise comparisons. We propose an algorithm that exploits the low-dimensional geometry in order to accurately embed objects based on relatively small number of sequentially selected pairwise comparisons and demonstrate its performance with experiments. This paper considers the problem of learning an embedding of data based on similarity triplets of the form “A is more similar to B than to C”. This learning setting is of relevance to scenarios in which we wish to model human judgements on the similarity of objects. We argue that in order to obtain a truthful embedding of the underlying data, it is insufficient for the embedding to satisfy the constraints encoded by the similarity triplets. In particular, we introduce a new technique called t-Distributed Stochastic Triplet Embedding (t-STE) that collapses similar points and repels dissimilar points in the embedding — even when all triplet constraints are satisfied. Our experimental evaluation on three data sets shows that as a result, t-STE is much better than existing techniques at revealing the underlying data structure. Similarity comparisons of the form "Is object a more similar to b than to c?" are useful for computer vision and machine learning applications. Unfortunately, an embedding of @math points is specified by @math triplets, making collecting every triplet an expensive task. In noticing this difficulty, other researchers have investigated more intelligent triplet sampling techniques, but they do not study their effectiveness or their potential drawbacks. Although it is important to reduce the number of collected triplets, it is also important to understand how best to display a triplet collection task to a user. In this work we explore an alternative display for collecting triplets and analyze the monetary cost and speed of the display. We propose best practices for creating cost effective human intelligence tasks for collecting triplets. We show that rather than changing the sampling algorithm, simple changes to the crowdsourcing UI can lead to much higher quality embeddings. We also provide a dataset as well as the labels collected from crowd workers. We present a method for learning an embedding that places images of humans in similar poses nearby. This embedding can be used as a direct method of comparing images based on human pose, avoiding potential challenges of estimating body joint positions. Pose embedding learning is formulated under a triplet-based distance criterion. A deep architecture is used to allow learning of a representation capable of making distinctions between different poses. Experiments on human pose matching and retrieval from video data demonstrate the potential of the method. We seek to detect visual relations in images of the form of triplets t = (subject, predicate, object), such as "person riding dog", where training examples of the individual entities are available but their combinations are rare or unseen at training. This is an important set-up due to the combinatorial nature of visual relations : collecting sufficient training data for all possible triplets would be very hard. The contributions of this work are three-fold. First, we learn a representation of visual relations that combines (i) individual embeddings for subject, object and predicate together with (ii) a visual phrase embedding that represents the relation triplet. Second, we learn how to transfer visual phrase embeddings from existing training triplets to unseen test triplets using analogies between relations that involve similar objects. Third, we demonstrate the benefits of our approach on two challenging datasets involving rare and unseen relations : on HICO-DET, our model achieves significant improvement over a strong baseline, and we confirm this improvement on retrieval of unseen triplets on the UnRel rare relation dataset. Embedding algorithms search for a low dimensional continuous representation of data, but most algorithms only handle objects of a single type for which pairwise distances are specified. This paper describes a method for embedding objects of different types, such as images and text, into a single common Euclidean space, based on their co-occurrence statistics. The joint distributions are modeled as exponentials of Euclidean distances in the low-dimensional embedding space, which links the problem to convex optimization over positive semidefinite matrices. The local structure of the embedding corresponds to the statistical correlations via random walks in the Euclidean space. We quantify the performance of our method on two text data sets, and show that it consistently and significantly outperforms standard methods of statistical correspondence modeling, such as multidimensional scaling, IsoMap and correspondence analysis. We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. Consider two sets of spatial objects R and S, where each object is assigned a score (e.g., ranking). Given a spatial distance threshold e and an integer k, the top-k spatial distance join (k- SDJ) returns the k pairs of objects, which have the highest combined score (based on an aggregate function γ) among all object pairs in R×S which have spatial distance at most e. Despite the practical application value of this query, it has not received adequate attention in the past. In this paper, we fill this gap by proposing methods that utilize both location and score information from the objects, enabling top-k join computation by accessing a limited number of objects. Extensive experiments demonstrate that a technique which accesses blocks of data from R and S ordered by the object scores and then joins them using an aR-tree based module performs best in practice and outperforms alternative solutions by a wide margin. This paper contributes a joint embedding model for predicting relations between a pair of entities in the scenario of relation inference. It differs from most stand-alone approaches which separately operate on either knowledge bases or free texts. The proposed model simultaneously learns low-dimensional vector representations for both triplets in knowledge repositories and the mentions of relations in free texts, so that we can leverage the evidence both resources to make more accurate predictions. We use NELL to evaluate the performance of our approach, compared with cutting-edge methods. Results of extensive experiments show that our model achieves significant improvement on relation extraction. In the past several years studies have started to appear comparing the accuracies of various science mapping approaches. These studies primarily compare the cluster solutions resulting from different similarity approaches, and give varying results. In this study we compare the accuracies of cluster solutions of a large corpus of 2,153,769 recent articles from the biomedical literature (2004–2008) using four similarity approaches: co-citation analysis, bibliographic coupling, direct citation, and a bibliographic coupling-based citation-text hybrid approach. Each of the four approaches can be considered a way to represent the research front in biomedicine, and each is able to successfully cluster over 92p of the corpus. Accuracies are compared using two metrics—within-cluster textual coherence as defined by the Jensen-Shannon divergence, and a concentration measure based on the grant-to-article linkages indexed in MEDLINE. Of the three pure citation-based approaches, bibliographic coupling slightly outperforms co-citation analysis using both accuracy measures; direct citation is the least accurate mapping approach by far. The hybrid approach improves upon the bibliographic coupling results in all respects. We consider the results of this study to be robust given the very large size of the corpus, and the specificity of the accuracy measures used. © 2010 Wiley Periodicals, Inc. Many binary code embedding techniques have been proposed for large-scale approximate nearest neighbor search in computer vision. Recently, product quantization that encodes the cluster index in each subspace has been shown to provide impressive accuracy for nearest neighbor search. In this paper, we explore a simple question: is it best to use all the bit budget for encoding a cluster index in each subspace? We have found that as data points are located farther away from the centers of their clusters, the error of estimated distances among those points becomes larger. To address this issue, we propose a novel encoding scheme that distributes the available bit budget to encoding both the cluster index and the quantized distance between a point and its cluster center. We also propose two different distance metrics tailored to our encoding scheme. We have tested our method against the-state-of-the-art techniques on several well-known benchmarks, and found that our method consistently improves the accuracy over other tested methods. This result is achieved mainly because our method accurately estimates distances between two data points with the new binary codes and distance metric. The modern image search system requires semantic understanding of image, and a key yet under-addressed problem is to learn a good metric for measuring the similarity between images. While deep metric learning has yielded impressive performance gains by extracting high level abstractions from image data, a proper objective loss function becomes the central issue to boost the performance. In this paper, we propose a novel angular loss, which takes angle relationship into account, for learning better similarity metric. Whereas previous metric learning methods focus on optimizing the similarity (contrastive loss) or relative similarity (triplet loss) of image pairs, our proposed method aims at constraining the angle at the negative point of triplet triangles. Several favorable properties are observed when compared with conventional methods. First, scale invariance is introduced, improving the robustness of objective against feature variance. Second, a third-order geometric constraint is inherently imposed, capturing additional local structure of triplet triangles than contrastive loss or triplet loss. Third, better convergence has been demonstrated by experiments on three publicly available datasets. This paper proposes a novel translation-based knowledge graph embedding that preserves the logical properties of relations such as transitivity and symmetricity. The embedding space generated by existing translation-based embeddings do not represent transitive and symmetric relations precisely, because they ignore the role of entities in triples. Thus, we introduce a role-specific projection which maps an entity to distinct vectors according to its role in a triple. That is, a head entity is projected onto an embedding space by a head projection operator, and a tail entity is projected by a tail projection operator. This idea is applied to TransE, TransR, and TransD to produce lppTransE, lppTransR, and lppTransD, respectively. According to the experimental results on link prediction and triple classification, the proposed logical property preserving embeddings show the state-of-the-art performance at both tasks. These results prove that it is critical to preserve logical properties of relations while embedding knowledge graphs, and the proposed method does it effectively. The purpose of object matching is to decide the similarity between two objects. This paper introduces 24 possible distance measures based on the Hausdorff distance between two point sets. These measures can be used to match two sets of edge points extracted from any two objects. Based on experiments on synthetic images containing various levels of noise, the authors determined that one of these distance measures, called the modified Hausdorff distance (MHD) has the best performance for object matching. The advantages of MHD ever other distances are also demonstrated on several edge snaps of objects extracted from real images. We address the problem of metric learning for multi-view data, namely the construction of embedding projections from data in different representations into a shared feature space, such that the Euclidean distance in this space provides a meaningful within-view as well as between-view similarity. Our motivation stems from the problem of cross-media retrieval tasks, where the availability of a joint Euclidean distance function is a prerequisite to allow fast, in particular hashing-based, nearest neighbor queries. We formulate an objective function that expresses the intuitive concept that matching samples are mapped closely together in the output space, whereas non-matching samples are pushed apart, no matter in which view they are available. The resulting optimization problem is not convex, but it can be decomposed explicitly into a convex and a concave part, thereby allowing efficient optimization using the convex-concave procedure. Experiments on an image retrieval task show that nearest-neighbor based cross-view retrieval is indeed possible, and the proposed technique improves the retrieval accuracy over baseline techniques. We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the two primary methods of constructing Frechet embeddings for finite metrics, due to Bourgain (1985) and Rao (1999). We prove that any n-point metric space (X, d) embeds in Hilbert space with distortion (O ( _ X n ) , ) where α X is a geometric estimate on the decomposability of X. As an immediate corollary, we obtain an (O ( ( _ X ) n ) ) distortion embedding, where λ X is the doubling constant of X. Since λ X ≤ n, this result recovers Bourgain’s theorem, but when the metric X is, in a sense, “low-dimensional,” improved bounds are achieved. We examine the embedding approach to reason new relational facts from a largescale knowledge graph and a text corpus. We propose a novel method of jointly embedding entities and words into the same continuous vector space. The embedding process attempts to preserve the relations between entities in the knowledge graph and the concurrences of words in the text corpus. Entity names and Wikipedia anchors are utilized to align the embeddings of entities and words in the same space. Large scale experiments on Freebase and a Wikipedia NY Times corpus show that jointly embedding brings promising improvement in the accuracy of predicting facts, compared to separately embedding knowledge graphs and text. Particularly, jointly embedding enables the prediction of facts containing entities out of the knowledge graph, which cannot be handled by previous embedding methods. At the same time, concerning the quality of the word embeddings, experiments on the analogical reasoning task show that jointly embedding is comparable to or slightly better than word2vec (Skip-Gram). Estimating distances in the Internet has been studied in the recent years due to its ability to improve the performance of many applications, e.g., in the peer-to-peer realm. One scalable approach to estimate distances between nodes is to embed the nodes in some d dimensional geometric space and to use the pair distances in this space as the estimate for the real distances. Several algorithms were suggested in the past to do this in low dimensional Euclidean spaces. It was noted in recent years that the Internet structure has a highly connected core and long stretched tendrils, and that most of the routing paths between nodes in the tendrils pass through the core. Therefore, we suggest in this work, to embed the Internet distance metric in a hyperbolic space where routes are bent toward the center. We found that if the curvature, that defines the extend of the bending, is selected in the adequate range, the accuracy of Internet distance embedding can be improved. We demonstrate the strength of our hyperbolic embedding with two applications: selecting the closest server and building an application level multicast tree. For the latter, we present a distributed algorithm for building geometric multicast trees that achieve good trade-offs between delay (stretch) and load (stress). We also present a new efficient centralized embedding algorithm that enables the accurate embedding of short distances, something that have never been done before. We investigate techniques for analysis and retrieval of object trajectories in two or three dimensional space. Such data usually contain a large amount of noise, that has made previously used metrics fail. Therefore, we formalize non-metric similarity functions based on the longest common subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translation of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and time warping distance functions (for real and synthetic data) and show the superiority of our approach, especially in the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach.