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23
Matrix completion for multi-label image classification
- In NIPS
"... Abstract Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this set ..."
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Cited by 22 (3 self)
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Abstract Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this setting, classification of testing data is posed as a problem of completing unknown label entries on a data matrix that concatenates training and testing features with training labels. We propose two convex algorithms for matrix completion based on a Rank Minimization criterion specifically tailored to visual data, and prove its convergence properties. A major advantage of our approach w.r.t. standard discriminative classification methods for image categorization is its robustness to outliers, background noise and partial occlusions both in the feature and label space. Experimental validation on several datasets shows how our method outperforms state-of-the-art algorithms, while effectively capturing semantic concepts of classes.
Convex Sparse Coding, Subspace Learning, and Semi-Supervised Extensions
"... Automated feature discovery is a fundamental problem in machine learning. Although classical feature discovery methods do not guarantee optimal solutions in general, it has been recently noted that certain subspace learning and sparse coding problems can be solved efficiently, provided the number of ..."
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Cited by 10 (3 self)
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Automated feature discovery is a fundamental problem in machine learning. Although classical feature discovery methods do not guarantee optimal solutions in general, it has been recently noted that certain subspace learning and sparse coding problems can be solved efficiently, provided the number of features is not restricted a priori. We provide an extended characterization of this optimality result and describe the nature of the solutions under an expanded set of practical contexts. In particular, we apply the framework to a semisupervised learning problem, and demonstrate that feature discovery can co-occur with input reconstruction and supervised training while still admitting globally optimal solutions. A comparison to existing semi-supervised feature discovery methods shows improved generalization and efficiency.
The algebraic combinatorial approach for low-rank matrix completion
, 2014
"... We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practic ..."
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Cited by 10 (2 self)
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We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More specifically, apart from introducing an algebraic combinatorial theory of low-rank matrix completion, we present probability-one algorithms to decide whether a particular entry of the matrix can be completed. We also describe methods to complete that entry from a few others, and to estimate the error which is incurred by any method completing that entry. Furthermore, we show how known results on matrix completion and their sampling assumptions can be related to our new perspective and interpreted in terms of a completability phase transition. On this revision This revision- version 4- is both abridged and extended in terms of exposition and results, as compared to version 3 Király et al. (2013). The theoretical foundations are developed in a more ad-hoc way which allow to reach the main statements and algorithmic implications more quickly. Version 3 contains a more principled derivation of the theory, more related results (e.g., estimation of missing entries and its consistency, representations for the determinantal matroid, detailed examples), but a focus which is further away from applications. A reader who is inter-ested in both is invited to read the main parts of version 4 first, then go through version 3 for a more detailed view on the theory.
Distant supervision for relation extraction with matrix completion
- In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (ACL
, 2014
"... Abstract The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification problem using matrix completion on factorized matrix of ..."
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Cited by 6 (1 self)
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Abstract The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification problem using matrix completion on factorized matrix of minimized rank. We formulate relation classification as completing the unknown labels of testing items (entity pairs) in a sparse matrix that concatenates training and testing textual features with training labels. Our algorithmic framework is based on the assumption that the rank of item-byfeature and item-by-label joint matrix is low. We apply two optimization models to recover the underlying low-rank matrix leveraging the sparsity of feature-label matrix. The matrix completion problem is then solved by the fixed point continuation (FPC) algorithm, which can find the global optimum. Experiments on two widely used datasets with different dimensions of textual features demonstrate that our low-rank matrix completion approach significantly outperforms the baseline and the state-of-the-art methods.
Article Multi-View Human Activity Recognition in Distributed Camera Sensor Networks
, 2013
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Convex Two-Layer Modeling
"... Latent variable prediction models, such as multi-layer networks, impose auxil-iary latent variables between inputs and outputs to allow automatic inference of implicit features useful for prediction. Unfortunately, such models are difficult to train because inference over latent variables must be pe ..."
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Cited by 3 (1 self)
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Latent variable prediction models, such as multi-layer networks, impose auxil-iary latent variables between inputs and outputs to allow automatic inference of implicit features useful for prediction. Unfortunately, such models are difficult to train because inference over latent variables must be performed concurrently with parameter optimization—creating a highly non-convex problem. Instead of proposing another local training method, we develop a convex relaxation of hidden-layer conditional models that admits global training. Our approach ex-tends current convex modeling approaches to handle two nested nonlinearities separated by a non-trivial adaptive latent layer. The resulting methods are able to acquire two-layer models that cannot be represented by any single-layer model over the same features, while improving training quality over local heuristics. 1
Semisupervised learning with mixed knowledge information
- In Proceedings of the Eighteenth Conference on Knowledge Discovery and Data Mining
, 2012
"... Integrating new knowledge sources into various learning tasks to improve their performance has recently become an interesting topic. In this paper we propose a novel semi-supervised learning (SSL) approach, called semi-supervised learning with Mixed Knowledge Information (SSL-MKI) which can simultan ..."
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Cited by 3 (0 self)
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Integrating new knowledge sources into various learning tasks to improve their performance has recently become an interesting topic. In this paper we propose a novel semi-supervised learning (SSL) approach, called semi-supervised learning with Mixed Knowledge Information (SSL-MKI) which can simultaneously handle both sparse labeled data and additional pairwise constraints together with unlabeled data. Specifically, we first construct a unified SSL framework to combine the manifold assumption and the pairwise constraints assumption for classification tasks. Then we present a Modified Fixed Point Continuation (MFPC) algorithm with an eigenvalue thresholding (EVT) operator to learn the enhanced kernel matrix. Finally, we develop a two-stage optimization strategy and provide an efficient SSL approach that takes advantage of Laplacian spectral regularization: semi-supervised learning with Enhanced Spectral Kernel (ESK). Experimental results on a variety of synthetic and real-world datasets demonstrate the effectiveness of the proposed ESK approach.
Dynamic Label Propagation for Semi-supervised Multi-class Multi-label Classification
"... In graph-based semi-supervised learning approaches, the classification rate is highly dependent on the size of the availabel labeled data, as well as the accuracy of the similarity measures. Here, we propose a semi-supervised multi-class/multi-label classification scheme, dynamic la-bel propagation ..."
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Cited by 2 (0 self)
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In graph-based semi-supervised learning approaches, the classification rate is highly dependent on the size of the availabel labeled data, as well as the accuracy of the similarity measures. Here, we propose a semi-supervised multi-class/multi-label classification scheme, dynamic la-bel propagation (DLP), which performs transductive learn-ing through propagation in a dynamic process. Existing semi-supervised classification methods often have difficulty in dealing with multi-class/multi-label problems due to the lack in consideration of label correlation; our algorithm in-stead emphasizes dynamic metric fusion with label infor-mation. Significant improvement over the state-of-the-art methods is observed on benchmark datasets for both multi-class and multi-label tasks. 1.
