Fast greedy algorithms for dictionary selection with generalized sparsity constraints

Neural Information Processing Systems

In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does our algorithm work much faster than the known methods, but it can also handle more complex sparsity constraints, such as average sparsity. Using numerical experiments, we show that our algorithm outperforms the known methods for dictionary selection, achieving competitive performances with dictionary learning algorithms in a smaller running time.


Fast greedy algorithms for dictionary selection with generalized sparsity constraints

Neural Information Processing Systems

In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does our algorithm work much faster than the known methods, but it can also handle more complex sparsity constraints, such as average sparsity. Using numerical experiments, we show that our algorithm outperforms the known methods for dictionary selection, achieving competitive performances with dictionary learning algorithms in a smaller running time.


Coupled Dictionary Learning for Unsupervised Feature Selection

AAAI Conferences

Unsupervised feature selection (UFS) aims to reduce the time complexity and storage burden, as well as improve the generalization performance. Most existing methods convert UFS to supervised learning problem by generating labels with specific techniques (e.g., spectral analysis, matrix factorization and linear predictor). Instead, we proposed a novel coupled analysis-synthesis dictionary learning method, which is free of generating labels. The representation coefficients are used to model the cluster structure and data distribution. Specifically, the synthesis dictionary is used to reconstruct samples, while the analysis dictionary analytically codes the samples and assigns probabilities to the samples. Afterwards, the analysis dictionary is used to select features that can well preserve the data distribution. The effective L2p-norm (0 < p <1) regularization is imposed on the analysis dictionary to get much sparse solution and is more effective in feature selection.We proposed an iterative reweighted least squares algorithm to solve the L2p-norm optimization problem and proved it can converge to a fixed point. Experiments on benchmark datasets validated the effectiveness of the proposed method


Neurogenesis-Inspired Dictionary Learning: Online Model Adaption in a Changing World

arXiv.org Artificial Intelligence

In this paper, we focus on online representation learning in non-stationary environments which may require continuous adaptation of model architecture. We propose a novel online dictionary-learning (sparse-coding) framework which incorporates the addition and deletion of hidden units (dictionary elements), and is inspired by the adult neurogenesis phenomenon in the dentate gyrus of the hippocampus, known to be associated with improved cognitive function and adaptation to new environments. In the online learning setting, where new input instances arrive sequentially in batches, the neuronal-birth is implemented by adding new units with random initial weights (random dictionary elements); the number of new units is determined by the current performance (representation error) of the dictionary, higher error causing an increase in the birth rate. Neuronal-death is implemented by imposing l1/l2-regularization (group sparsity) on the dictionary within the block-coordinate descent optimization at each iteration of our online alternating minimization scheme, which iterates between the code and dictionary updates. Finally, hidden unit connectivity adaptation is facilitated by introducing sparsity in dictionary elements. Our empirical evaluation on several real-life datasets (images and language) as well as on synthetic data demonstrates that the proposed approach can considerably outperform the state-of-art fixed-size (nonadaptive) online sparse coding of Mairal et al. (2009) in the presence of nonstationary data. Moreover, we identify certain properties of the data (e.g., sparse inputs with nearly non-overlapping supports) and of the model (e.g., dictionary sparsity) associated with such improvements.


Group Sparse Coding

Neural Information Processing Systems

Bag-of-words document representations are often used in text, image and video processing. While it is relatively easy to determine a suitable word dictionary for text documents, there is no simple mapping from raw images or videos to dictionary terms. The classical approach builds a dictionary using vector quantization over a large set of useful visual descriptors extracted from a training set, and uses a nearest-neighbor algorithm to count the number of occurrences of each dictionary word in documents to be encoded. More robust approaches have been proposed recently that represent each visual descriptor as a sparse weighted combination of dictionary words. While favoring a sparse representation at the level of visual descriptors, those methods however do not ensure that images have sparse representation.