Scalable semidefinite manifold learning

Vasiloglou, Nikolaos; Gray, Alexander G.; Anderson, David V.

doi:10.1109/mlsp.2008.4685508

Cited by 10 publications

(11 citation statements)

References 7 publications

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“…In [8] a comparison of MVU with other manifold learning techniques is given, showing that MVU gives the best results. In [11], a variant of MVU, the Maximum Furthest Neighbors Unfolding (MFNU) that is scalable. MFNU tries to find new coordinates for the given dataset that preserve the original local distances between the points and at the same time it tries to maximize the distance between furthest neighbors.…”

Section: Maximum Variance Unfoldingmentioning

confidence: 99%

“…MFNU's scalability is based on the fast dual-tree algorithm [12] for computing all-nearest neighbors and on the L-BFGS optimization algorithm that has linear cost per iteration. More details can be found in [11]. Given a set of data X ∈ N ×d , where N is the number of points and d is the dimensionality.…”

Section: Maximum Variance Unfoldingmentioning

confidence: 99%

“…In [11], the authors solved a nonconvex formulation of MVU (the Maximum Furthes Neighbor Unfolding MFNU), that has the same global optimum. Experiments up to hundred thousand points were reported.…”

Section: Scaling Mvumentioning

confidence: 99%

See 2 more Smart Citations

Learning the Intrinsic Dimensions of the Timit Speech Database with Maximum Variance Unfolding

Vasiloglou

Anderson

Gray

2009

2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop

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Modern methods for nonlinear dimensionality reduction have been used extensively in the machine learning community for discovering the intrinsic dimension of several datasets. In this paper we apply one of the most successful ones Maximum Variance Unfolding on a big sample of the well known speech benchmark TIMIT. Although MVU is not generally scalable, we managed to apply to 1 million 39-dimensional points and successfully reduced the dimension down to 15. In this paper we apply some of the state-of-the-art techniques for handling big datasets. The biggest bottleneck is the local neighborhood computation. For 300K points it took 9 hours while for 1M points it took 3.5 days. We also demonstrate the weakness of MFCC representation under the k-nearest neighborhood classification since the error rate is more than 50%.

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Section: Maximum Variance Unfoldingmentioning

confidence: 99%

Section: Maximum Variance Unfoldingmentioning

confidence: 99%

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Learning the Intrinsic Dimensions of the Timit Speech Database with Maximum Variance Unfolding

Vasiloglou

Anderson

Gray

2009

2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop

Self Cite

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“…This problem has applications in recommender systems, where furthest neighbors can increase the diversity of recommendations [1,2]. Furthest neighbor search is also a component in some nonlinear dimensionality reduction algorithms [3], complete linkage clustering [4,5] and other clustering applications [6]. Thus, being able to quickly return furthest neighbors is a significant practical concern for many applications.…”

Section: Introductionmentioning

confidence: 99%

Fast Approximate Furthest Neighbors with Data-Dependent Candidate Selection

Curtin

Gardner

2016

Similarity Search and Applications

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We present a novel hashing strategy for approximate furthest neighbor search that selects projection bases using the data distribution. This strategy leads to an algorithm, which we call DrusillaHash, that is able to outperform existing approximate furthest neighbor strategies. Our strategy is motivated by an empirical study of the behavior of the furthest neighbor search problem, which lends intuition for where our algorithm is most useful. We also present a variant of the algorithm that gives an absolute approximation guarantee; to our knowledge, this is the first such approximate furthest neighbor hashing approach to give such a guarantee. Performance studies indicate that DrusillaHash can achieve comparable levels of approximation to other algorithms while giving up to an order of magnitude speedup. An implementation is available in the mlpack machine learning library (found at http://www.mlpack.org).

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“…These models have the drawback that they are often very costly (squared or cubic with respect to the number of data points). Recent approaches provide scalable alternatives, sometimes at the cost of non convexity of the problem [14,15,16]. However, the kernel has to be chosen prior to training and no metric adaptation according to the given label information takes place.…”

Section: Introductionmentioning

confidence: 99%

Adaptive local dissimilarity measures for discriminative dimension reduction of labeled data

et al. 2010

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Due to the tremendous increase of electronic information with respect to the size of data sets as well as their dimension, dimension reduction and visualization of high-dimensional data has become one of the key problems of data mining. Since embedding in lower dimensions necessarily includes a loss of information, methods to explicitly control the information kept by a specific dimension reduction technique are highly desirable. The incorporation of supervised class information constitutes an important specific case. The aim is to preserve and potentially enhance the discrimination of classes in lower dimensions. In this contribution we use an extension of prototype-based local distance learning, which results in a nonlinear discriminative dissimilarity measure for a given labeled data manifold. The learned local distance measure can be used as basis for other unsupervised dimension reduction techniques, which take into account neighborhood information. We show the combination of different dimension reduction techniques with a discriminative similarity measure learned by an extension of Learning Vector Quantization (LVQ) and their behavior with different parameter settings. The methods are introduced and discussed in terms of artificial and real world data sets.

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Scalable semidefinite manifold learning

Cited by 10 publications

References 7 publications

Learning the Intrinsic Dimensions of the Timit Speech Database with Maximum Variance Unfolding

Learning the Intrinsic Dimensions of the Timit Speech Database with Maximum Variance Unfolding

Fast Approximate Furthest Neighbors with Data-Dependent Candidate Selection

Adaptive local dissimilarity measures for discriminative dimension reduction of labeled data

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