We identify a fundamental issue in the popular Stochastic Neighbour Embedding (SNE and t-SNE), i.e., the "learned" similarity of any two points in high-dimensional space is not defined and cannot be computed. It underlines two previously unexplored issues in the algorithm which have undermined the quality of its final visualisation output and its ability to process large datasets. The issues are:(a) the reference probability in high-dimensional space is set based on entropy which has undefined relation with local density; and (b) the use of data independent kernel which leads to the need to determine n bandwidths for a dataset of n points. This paper establishes a principle to set the reference probability via a data-dependent kernel which has a well-defined kernel characteristic that linked directly to local density. A solution based on a recent data-dependent kernel called Isolation Kernel addresses the fundamental issue as well as its two ensuing issues. As a result, it significantly improves the quality of the final visualisation output and removes one obstacle that prevents t-SNE from processing large datasets. The solution is extremely simple, i.e., simply replacing the existing data independent kernel with Isolation Kernel, leaving the rest of the t-SNE procedure unchanged.
There are some improvements based on revised Gaussian Kernel functions in order to get better similarity measurements. @cite_8 proposes a symmetrised SNE, @cite_3 enable t-SNE to accommodate various heavy-tailed embedding similarity functions; and @cite_1 propose an algorithm based on similarity triplets of the form A is more similar to B than to C'' to model the local structure of the data more effectively.
@cite_1 @cite_3 @cite_8
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Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum, etc., in finding its optimum. In this paper, we propose the Heavy-tailed Symmetric Stochastic Neighbor Embedding (HSSNE) method, which is a generalization of the t-SNE to accommodate various heavy-tailed embedding similarity functions. With this generalization, we are presented with two difficulties. The first is how to select the best embedding similarity among all heavy-tailed functions and the second is how to optimize the objective function once the heavy-tailed function has been selected. Our contributions then are: (1) we point out that various heavy-tailed embedding similarities can be characterized by their negative score functions. Based on this finding, we present a parameterized subset of similarity functions for choosing the best tail-heaviness for HSSNE; (2) we present a fixed-point optimization algorithm that can be applied to all heavy-tailed functions and does not require the user to set any parameters; and (3) we present two empirical studies, one for unsupervised visualization showing that our optimization algorithm runs as fast and as good as the best known t-SNE implementation and the other for semi-supervised visualization showing quantitative superiority using the homogeneity measure as well as qualitative advantage in cluster separation over t-SNE. 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. Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data are popular to analyze complicated data objects and to cover domain specific data properties. Without an underlying vector space these data are given as pairwise (dis-)similarities only. The few available methods for such data focus widely on similarities and do not scale to large datasets. Kernel methods are very effective for metric similarity matrices, also at large scale, but costly transformations are necessary starting with non-metric (dis-) similarities. We propose an integrative combination of Nystrom approximation, potential double centering and eigenvalue correction to obtain valid kernel matrices at linear costs in the number of samples. By the proposed approach effective kernel approaches become accessible. Experiments with several larger (dis-)similarity datasets show that the proposed method achieves much better runtime performance than the standard strategy while keeping competitive model accuracy. The main contribution is an efficient and accurate technique, to convert (potentially non-metric) large scale dissimilarity matrices into approximated positive semi-definite kernel matrices at linear costs. HighlightsWe propose a linear time and memory efficient approach for converting low rank dissimilarity matrices to similarity matrices and vice versa.Our approach is applicable for proximities obtained from non-metric proximity measures (indefinite kernels, non-standard dissimilarity measures).The presented approach also comprises a generalization of Landmark MDS - the presented approach is in general more accurate and flexible than Landmark MDS.We provide an alternative derivation of the Nystrom approximation together with a convergence proof, also for indefinite kernels not given in the workshop paper as a core element of the approach. We introduce a novel kernel that upgrades the Weisfeiler-Lehman and other graph kernels to effectively exploit high-dimensional and continuous vertex attributes. Graphs are first decomposed into subgraphs. Vertices of the subgraphs are then compared by a kernel that combines the similarity of their labels and the similarity of their structural role, using a suitable vertex invariant. By changing this invariant we obtain a family of graph kernels which includes generalizations of Weisfeiler-Lehman, NSPDK, and propagation kernels. We demonstrate empirically that these kernels obtain state-of-the-art results on relational data sets. This paper proposes K-NRM, a kernel based neural model for document ranking. Given a query and a set of documents, K-NRM uses a translation matrix that models word-level similarities via word embeddings, a new kernel-pooling technique that uses kernels to extract multi-level soft match features, and a learning-to-rank layer that combines those features into the final ranking score. The whole model is trained end-to-end. The ranking layer learns desired feature patterns from the pairwise ranking loss. The kernels transfer the feature patterns into soft-match targets at each similarity level and enforce them on the translation matrix. The word embeddings are tuned accordingly so that they can produce the desired soft matches. Experiments on a commercial search engine's query log demonstrate the improvements of K-NRM over prior feature-based and neural-based states-of-the-art, and explain the source of K-NRM's advantage: Its kernel-guided embedding encodes a similarity metric tailored for matching query words to document words, and provides effective multi-level soft matches. We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in @math time. Our GRIEF kernel consists of @math eigenfunctions found using a Nystrom approximation from a dense Cartesian product grid of inducing points. By exploiting algebraic properties of Kronecker and Khatri-Rao tensor products, computational complexity of the training procedure can be practically independent of the number of inducing points. This allows us to use arbitrarily many inducing points to achieve a globally accurate kernel approximation, even in high-dimensional problems. The fast likelihood evaluation enables type-I or II Bayesian inference on large-scale datasets. We benchmark our algorithms on real-world problems with up to two-million training points and @math inducing points. Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an important research topic. Graph similarity search has applications in a wide range of domains including cheminformatics, bioinformatics, sensor network management, social network management, and XML documents, among others. Most of the current graph indexing methods focus on subgraph query processing, i.e. determining the set of database graphs that contains the query graph and hence do not directly support similarity search. In data mining and machine learning, various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models for supervised learning, graph kernel functions have (i) high computational complexity and (ii) non-trivial difficulty to be indexed in a graph database. Our objective is to bridge graph kernel function and similarity search in graph databases by proposing (i) a novel kernel-based similarity measurement and (ii) an efficient indexing structure for graph data management. Our method of similarity measurement builds upon local features extracted from each node and their neighboring nodes in graphs. A hash table is utilized to support efficient storage and fast search of the extracted local features. Using the hash table, a graph kernel function is defined to capture the intrinsic similarity of graphs and for fast similarity query processing. We have implemented our method, which we have named G-hash, and have demonstrated its utility on large chemical graph databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Most importantly, the new similarity measurement and the index structure is scalable to large database with smaller indexing size, faster indexing construction time, and faster query processing time as compared to state-of-the-art indexing methods such as C-tree, gIndex, and GraphGrep. 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. We present an approach for the construction of text similarity functions using a parameterized resemblance coefficient in combination with a softened cardinality function called soft cardinality. Our approach provides a consistent and recursive model, varying levels of granularity from sentences to characters. Therefore, our model was used to compare sentences divided into words, and in turn, words divided into q-grams of characters. Experimentally, we observed that a performance correlation function in a space defined by all parameters was relatively smooth and had a single maximum achievable by "hill climbing." Our approach used only surface text information, a stop-word remover, and a stemmer to tackle the semantic text similarity task 6 at SEMEVAL 2012. The proposed method ranked 3rd (average), 5th (normalized correlation), and 15th (aggregated correlation) among 89 systems submitted by 31 teams. 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. Existing billion-scale nearest neighbor search systems have mostly been compared on a single dataset of a billion of SIFT vectors, where systems based on the Inverted Multi-Index (IMI) have been performing very well, achieving state-of-the-art recall in several milliseconds. SIFT-like descriptors, however, are quickly being replaced with descriptors based on deep neural networks (DNN) that provide better performance for many computer vision tasks. In this paper, we introduce a new dataset of one billion descriptors based on DNNs and reveal the relative inefficiency of IMI-based indexing for such descriptors compared to SIFT data. We then introduce two new indexing structures, the Non-Orthogonal Inverted Multi-Index (NO-IMI) and the Generalized Non-Orthogonal Inverted Multi-Index (GNO-IMI). We show that due to additional flexibility, the new structures are able to adapt to DNN descriptor distribution in a better way. In particular, extensive experiments on the new dataset demonstrate that these data structures provide considerably better trade-off between the speed of retrieval and recall, given similar amount of memory, as compared to the standard Inverted Multi-Index. In this paper, we present a new framework for geo-locating an image utilizing a novel multiple nearest neighbor feature matching method using Generalized Minimum Clique Graphs (GMCP). First, we extract local features (e.g., SIFT) from the query image and retrieve a number of nearest neighbors for each query feature from the reference data set. Next, we apply our GMCP-based feature matching to select a single nearest neighbor for each query feature such that all matches are globally consistent. Our approach to feature matching is based on the proposition that the first nearest neighbors are not necessarily the best choices for finding correspondences in image matching. Therefore, the proposed method considers multiple reference nearest neighbors as potential matches and selects the correct ones by enforcing consistency among their global features (e.g., GIST) using GMCP. In this context, we argue that using a robust distance function for finding the similarity between the global features is essential for the cases where the query matches multiple reference images with dissimilar global features. Towards this end, we propose a robust distance function based on the Gaussian Radial Basis Function (G-RBF). We evaluated the proposed framework on a new data set of 102k street view images; the experiments show it outperforms the state of the art by 10 percent. In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions to this problem assume many comparisons are provided to learn a meaningful kernel. However, this can be considered unrealistic for many real-world tasks since a large amount of human input is often costly or difficult to obtain. Because of this, only a limited number of these comparisons may be provided. We propose a new kernel learning approach that supplements the few relative comparisons with "auxiliary" kernels built from more easily extractable features in order to learn a kernel that more completely models the notion of similarity gained from human feedback. Our proposed formulation is a convex optimization problem that adds only minor overhead to methods that use no auxiliary information. Empirical results show that in the presence of few training relative comparisons, our method can learn kernels that generalize to more out-of-sample comparisons than methods that do not utilize auxiliary information, as well as similar metric learning methods. We introduce an algorithm that, given n objects, learns a similarity matrix over all n2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form "is object a more similar to b or to c?" and is chosen to be maximally informative given the preceding responses. The output is an embedding of the objects into Euclidean space (like MDS); we refer to this as the "crowd kernel." SVMs reveal that the crowd kernel captures prominent and subtle features across a number of domains, such as "is striped" among neckties and "vowel vs. consonant" among letters. Learning hash functions codes for similarity search over multi-view data is attracting increasing attention, where similar hash codes are assigned to the data objects characterizing consistently neighborhood relationship across views. Traditional methods in this category inherently suffer three limitations: 1) they commonly adopt a two-stage scheme where similarity matrix is first constructed, followed by a subsequent hash function learning; 2) these methods are commonly developed on the assumption that data samples with multiple representations are noise-free,which is not practical in real-life applications; and 3) they often incur cumbersome training model caused by the neighborhood graph construction using all N points in the database (O(N)). In this paper, we motivate the problem of jointly and efficiently training the robust hash functions over data objects with multi-feature representations which may be noise corrupted. To achieve both the robustness and training efficiency, we propose an approach to effectively and efficiently learning low-rank kernelized11We use kernelized similarity rather than kernel, as it is not a squared symmetric matrix for data-landmark affinity matrix. hash functions shared across views. Specifically, we utilize landmark graphs to construct tractable similarity matrices in multi-views to automatically discover neighborhood structure in the data. To learn robust hash functions, a latent low-rank kernel function is used to construct hash functions in order to accommodate linearly inseparable data. In particular, a latent kernelized similarity matrix is recovered by rank minimization on multiple kernel-based similarity matrices. Extensive experiments on real-world multi-view datasets validate the efficacy of our method in the presence of error corruptions.We use kernelized similarity rather than kernel, as it is not a squared symmetric matrix for data-landmark affinity matrix. A robust hashing method for multi-view data with noise corruptions is presented.It is to jointly learn a low-rank kernelized similarity consensus and hash functions.Approximate landmark graph is employed to make training fast.Extensive experiments are conducted on benchmarks to show the efficacy of our model. Measures of genomic similarity are often the basis of flexible statistical analyses, and when based on kernel methods, they provide a powerful platform to take advantage of a broad and deep statistical theory, and a wide range of existing software; see the companion paper for a review of this material [1]. The kernel method converts information – perhaps complex or high-dimensional information – for a pair of subjects to a quantitative value representing either similarity or dissimilarity, with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This approach provides enormous opportunities to enhance genetic analyses by including a wide range of publically-available data as structured kernel ‘prior’ information. Kernel methods are appealing for their generality, yet this generality can make it challenging to formulate measures of similarity that directly address a specific scientific aim, or that are most powerful to detect a specific genetic mechanism. Although it is difficult to create a cook book of kernels for genetic studies, useful guidelines can be gleaned from a variety of novel published approaches. We review some novel developments of kernels for specific analyses and speculate on how to build kernels for complex genomic attributes based on publically available data. The creativity of analysts, with rigorous evaluations by applications to real and simulated data, will ultimately provide a much stronger array of kernel ‘tools’ for genetic analyses. In this paper, we address the person re-identification problem, discovering the correct matches for a probe person image from a set of gallery person images. We follow the learning-to-rank methodology and learn a similarity function to maximize the difference between the similarity scores of matched and unmatched images for a same person. We introduce at least three contributions to person re-identification. First, we present an explicit polynomial kernel feature map, which is capable of characterizing the similarity information of all pairs of patches between two images, called soft-patch-matching, instead of greedily keeping only the best matched patch, and thus more robust. Second, we introduce a mixture of linear similarity functions that is able to discover different soft-patch-matching patterns. Last, we introduce a negative semi-definite regularization over a subset of the weights in the similarity function, which is motivated by the connection between explicit polynomial kernel feature map and the Mahalanobis distance, as well as the sparsity constraint over the parameters to avoid over-fitting. Experimental results over three public benchmarks demonstrate the superiority of our approach. Hashing methods have been widely used for approximate nearest neighbor search in recent years due to its computational and storage effectiveness. Most existing multimodal hashing methods try to preserve the similarity relationship based on either metric distances or semantic labels in a procrustean way, while ignoring the intra-class and inter-class variations inherent in the metric space. In this paper, we propose a novel multimodal hashing method, termed as semantic neighbor graph hashing (SNGH), which aims to preserve the fine-grained similarity metric based on the semantic graph that is constructed by jointly pursuing the semantic supervision and the local neighborhood structure. Specifically, the semantic graph is constructed to capture the local similarity structure for the image modality and the text modality, respectively. Furthermore, we define a function based on the local similarity in particular to adaptively calculate multi-level similarities by encoding the intra-class and inter-class variations. After obtaining the unified hash codes, the logistic regression with kernel trick is employed to learn view-specific hash functions independently for each modality. Extensive experiments are conducted on four widely used multimodal data sets. The experimental results demonstrate the superiority of the proposed SNGH method compared with the state-of-the-art multimodal hashing methods. In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kernel methods can learn complex functions, but a kernel over unordered set inputs must somehow solve for correspondences---generally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function called the pyramid match that measures partial match similarity in time linear in the number of features. The pyramid match maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears. We show the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3-D human pose inference, and time of publication estimation for documents, and we show that the proposed method is accurate and significantly more efficient than current approaches. Abstract Similarity networks contain important topological features and patterns critical to understanding interactions among samples in a large dataset. To create a comprehensive view of the interactions within a dataset, the Similarity Network Fusion (SNF) technique has been proposed to fuse the similarity networks based on different data types into one similarity network that represents the full spectrum of underlying data. In this paper, a modified version of SNF, which is named as Contextual Information based SNF (CI-SNF), is proposed. In CI-SNF, first, modified Jaccard distance is performed on the SNF fused similarity to utilize the contextual information contained in the fused similarity network. Second, the local consistency of samples from the same category is enhanced by speculating that the samples which are located high in the Jaccard distance based ranking list of a specific query are from the same category as the query. Third, the inverted index technique is introduced to utilize the sparsity property of the locally consistent similarity network to enhance the computational efficiency. To verify the effectiveness and efficiency of CI-SNF model, it is applied in four different tasks, Cover Song Identification (CSI), image classification, cancer subtype identification, and drug taxonomy, respectively. Extensive experiments on thirteen challenging datasets demonstrate that CI-SNF scheme outperforms state-of-the-art similarity fusion algorithms including SNF in all four tasks. It is also verified that utilizing the contextual information contained in the SNF-based similarity network helps to enhance the performance of the SNF-based scheme, further.