Dynamic topic discovery through sequential projections

Ding, Weicong; Ishwar, Prakash; Saligrama, Venkatesh

doi:10.1109/acssc.2013.6810463

Cited by 20 publications

(43 citation statements)

References 18 publications

(27 reference statements)

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“…It would therefore be an interesting direction of further research to analyze and apply this model in other contexts. Further it would be of interest to study the robustness of Algorithm 1 if combined with random projections (see [10,4]), and to consider non-additive noise models, e.g., spectral variability in the context of HSI [33].…”

Section: Conclusion and Further Workmentioning

confidence: 99%

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Gillis

Luce

2018

IEEE Trans. on Image Process.

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A nonnegative matrix factorization (NMF) can be computed efficiently under the , which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these are based on nonnegative sparse regression and self-dictionaries, and require the solution of large-scale convex optimization problems. In this paper, we study a particular nonnegative sparse regression model with self-dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem, where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.A nonnegative matrix factorization (NMF) can be computed efficiently under the , which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these are based on nonnegative sparse regression and self-dictionaries, and require the solution of large-scale convex optimization problems. In this paper, we study a particular nonnegative sparse regression model with self-dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem, where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.

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Section: Conclusion and Further Workmentioning

confidence: 99%

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Gillis

Luce

2018

IEEE Trans. on Image Process.

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“…As can be seen, the estimated topics do form recognizable themes that can be assigned meaningful labels. The full list of all K = 100 topics estimated on the NYT dataset can be found in [3]. 3 The zzz prefix in the NYT vocabulary is used to annotate certain special named entities.…”

Section: B Real-world Datamentioning

confidence: 99%

“…The full list of all K = 100 topics estimated on the NYT dataset can be found in [3]. 3 The zzz prefix in the NYT vocabulary is used to annotate certain special named entities. For example, zzz nfl annotates NFL.…”

Section: B Real-world Datamentioning

confidence: 99%

A Provably Efficient Algorithm for Separable Topic Discovery

Ding

Ishwar

Saligrama

2016

IEEE J. Sel. Top. Signal Process.

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We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent factors that have certain properties. Our focus is on the class of topic models in which each shared latent factor contains a novel word that is unique to that factor, a property that has come to be known as separability. Our algorithm is based on the key insight that the novel words correspond to the extreme points of the convex hull formed by the row-vectors of a suitably normalized word co-occurrence matrix. We leverage this geometric insight to establish polynomial computation and sample complexity bounds based on a few isotropic random projections of the rows of the normalized word co-occurrence matrix. Our proposed randomprojections-based algorithm is naturally amenable to an efficient distributed implementation and is attractive for modern webscale distributed data mining applications.

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“…One of the proposal is in [5], where the incremental primal dual gradient update is proposed. Another proposal is shown in [14], in which the random projection scenario is employed to randomly select a small set of the constraints in solving the optimization problem in (15).…”

Section: Future Workmentioning

confidence: 99%

First Order Methods for Robust non-negative matrix factorization for large scale noisy data

Liu

Aeron

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or rows) [1]. In real applications, however, such separability assumption is hard to satisfy. Following [4] and [5], in this paper, we look at the Linear Programming (LP) based reformulation to locate the extreme rays of the convex cone but in a noisy setting. Furthermore, in order to deal with the large scale data, we employ First-Order Methods (FOM) to mitigate the computational complexity of LP, which primarily results from a large number of constraints. We show the performance of the algorithm on real and synthetic data sets.

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Dynamic topic discovery through sequential projections

Cited by 20 publications

References 18 publications

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

A Provably Efficient Algorithm for Separable Topic Discovery

First Order Methods for Robust non-negative matrix factorization for large scale noisy data

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