43,040 research outputs found

    Similarity Learning for High-Dimensional Sparse Data

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    A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of the data. In this paper, we propose a method that can learn efficiently similarity measure from high-dimensional sparse data. The core idea is to parameterize the similarity measure as a convex combination of rank-one matrices with specific sparsity structures. The parameters are then optimized with an approximate Frank-Wolfe procedure to maximally satisfy relative similarity constraints on the training data. Our algorithm greedily incorporates one pair of features at a time into the similarity measure, providing an efficient way to control the number of active features and thus reduce overfitting. It enjoys very appealing convergence guarantees and its time and memory complexity depends on the sparsity of the data instead of the dimension of the feature space. Our experiments on real-world high-dimensional datasets demonstrate its potential for classification, dimensionality reduction and data exploration.Comment: 14 pages. Proceedings of the 18th International Conference on Artificial Intelligence and Statistics (AISTATS 2015). Matlab code: https://github.com/bellet/HDS

    HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

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    Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.Comment: PVLDB 11(8):906-919, 201

    Compositional Model based Fisher Vector Coding for Image Classification

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    Deriving from the gradient vector of a generative model of local features, Fisher vector coding (FVC) has been identified as an effective coding method for image classification. Most, if not all, FVC implementations employ the Gaussian mixture model (GMM) to depict the generation process of local features. However, the representative power of the GMM could be limited because it essentially assumes that local features can be characterized by a fixed number of feature prototypes and the number of prototypes is usually small in FVC. To handle this limitation, in this paper we break the convention which assumes that a local feature is drawn from one of few Gaussian distributions. Instead, we adopt a compositional mechanism which assumes that a local feature is drawn from a Gaussian distribution whose mean vector is composed as the linear combination of multiple key components and the combination weight is a latent random variable. In this way, we can greatly enhance the representative power of the generative model of FVC. To implement our idea, we designed two particular generative models with such a compositional mechanism.Comment: Fixed typos. 16 pages. Appearing in IEEE T. Pattern Analysis and Machine Intelligence (TPAMI

    Unsupervised User Stance Detection on Twitter

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    We present a highly effective unsupervised framework for detecting the stance of prolific Twitter users with respect to controversial topics. In particular, we use dimensionality reduction to project users onto a low-dimensional space, followed by clustering, which allows us to find core users that are representative of the different stances. Our framework has three major advantages over pre-existing methods, which are based on supervised or semi-supervised classification. First, we do not require any prior labeling of users: instead, we create clusters, which are much easier to label manually afterwards, e.g., in a matter of seconds or minutes instead of hours. Second, there is no need for domain- or topic-level knowledge either to specify the relevant stances (labels) or to conduct the actual labeling. Third, our framework is robust in the face of data skewness, e.g., when some users or some stances have greater representation in the data. We experiment with different combinations of user similarity features, dataset sizes, dimensionality reduction methods, and clustering algorithms to ascertain the most effective and most computationally efficient combinations across three different datasets (in English and Turkish). We further verified our results on additional tweet sets covering six different controversial topics. Our best combination in terms of effectiveness and efficiency uses retweeted accounts as features, UMAP for dimensionality reduction, and Mean Shift for clustering, and yields a small number of high-quality user clusters, typically just 2--3, with more than 98\% purity. The resulting user clusters can be used to train downstream classifiers. Moreover, our framework is robust to variations in the hyper-parameter values and also with respect to random initialization

    Taming Wild High Dimensional Text Data with a Fuzzy Lash

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    The bag of words (BOW) represents a corpus in a matrix whose elements are the frequency of words. However, each row in the matrix is a very high-dimensional sparse vector. Dimension reduction (DR) is a popular method to address sparsity and high-dimensionality issues. Among different strategies to develop DR method, Unsupervised Feature Transformation (UFT) is a popular strategy to map all words on a new basis to represent BOW. The recent increase of text data and its challenges imply that DR area still needs new perspectives. Although a wide range of methods based on the UFT strategy has been developed, the fuzzy approach has not been considered for DR based on this strategy. This research investigates the application of fuzzy clustering as a DR method based on the UFT strategy to collapse BOW matrix to provide a lower-dimensional representation of documents instead of the words in a corpus. The quantitative evaluation shows that fuzzy clustering produces superior performance and features to Principal Components Analysis (PCA) and Singular Value Decomposition (SVD), two popular DR methods based on the UFT strategy
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