has been established as a model organism for investigating the fundamental principles of developmental gene interactions. The gene expression patterns of can be documented as digital images, which are annotated with anatomical ontology terms to facilitate pattern discovery and comparison. The automated annotation of gene expression pattern images has received increasing attention due to the recent expansion of the image database. The effectiveness of gene expression pattern annotation relies on the quality of feature representation. Previous studies have demonstrated that sparse coding is effective for extracting features from gene expression images. However, solving sparse coding remains a computationally challenging problem, especially when dealing with large-scale data sets and learning large size dictionaries. In this paper, we propose a novel algorithm to solve the sparse coding problem, called Stochastic Coordinate Coding (SCC). The proposed algorithm alternatively updates the sparse codes via just a few steps of coordinate descent and updates the dictionary via second order stochastic gradient descent. The computational cost is further reduced by focusing on the non-zero components of the sparse codes and the corresponding columns of the dictionary only in the updating procedure. Thus, the proposed algorithm significantly improves the efficiency and the scalability, making sparse coding applicable for large-scale data sets and large dictionary sizes. Our experiments on Drosophila gene expression data sets demonstrate the efficiency and the effectiveness of the proposed algorithm.
We summarize the optimization methods in the following. First we initialize the dictionary @math . Many dictionary initialization methods have been proposed, such as random weights @cite_1 , random patches and k-means. A detailed comparison of the performance among these initialization methods has been discussed in @cite_7 . With the initial dictionary, conventional sparse coding algorithms include the following main steps: Get an image patch @math . Calculate the sparse code @math by using LARS, FISTA or coordinate descent. Update the dictionary @math by performing stochastic gradient descent. Go to step 1 and iterate. We call each cycle, i.e. each image patch has been trained once, as an . Usually, several epochs are required to obtain a satisfactory result. When the number of image patches and the dictionary size is large, step 2 and step 3 are still very slow. We propose a novel algorithm to improve both of these parts, which is presented in the next section.
@cite_1 @cite_7
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In this paper, we propose a novel coupled dictionary training method for single-image super-resolution (SR) based on patchwise sparse recovery, where the learned couple dictionaries relate the low- and high-resolution (HR) image patch spaces via sparse representation. The learning process enforces that the sparse representation of a low-resolution (LR) image patch in terms of the LR dictionary can well reconstruct its underlying HR image patch with the dictionary in the high-resolution image patch space. We model the learning problem as a bilevel optimization problem, where the optimization includes an l1-norm minimization problem in its constraints. Implicit differentiation is employed to calculate the desired gradient for stochastic gradient descent. We demonstrate that our coupled dictionary learning method can outperform the existing joint dictionary training method both quantitatively and qualitatively. Furthermore, for real applications, we speed up the algorithm approximately 10 times by learning a neural network model for fast sparse inference and selectively processing only those visually salient regions. Extensive experimental comparisons with state-of-the-art SR algorithms validate the effectiveness of our proposed approach. We describe a novel unsupervised method for learning sparse, overcomplete features. The model uses a linear encoder, and a linear decoder preceded by a sparsifying non-linearity that turns a code vector into a quasi-binary sparse code vector. Given an input, the optimal code minimizes the distance between the output of the decoder and the input patch while being as similar as possible to the encoder output. Learning proceeds in a two-phase EM-like fashion: (1) compute the minimum-energy code vector, (2) adjust the parameters of the encoder and decoder so as to decrease the energy. The model produces "stroke detectors" when trained on handwritten numerals, and Gabor-like filters when trained on natural image patches. Inference and learning are very fast, requiring no preprocessing, and no expensive sampling. Using the proposed unsupervised method to initialize the first layer of a convolutional network, we achieved an error rate slightly lower than the best reported result on the MNIST dataset. Finally, an extension of the method is described to learn topographical filter maps. The goal of sparse recovery is to recover a k-sparse signal x e Rn from (possibly noisy) linear measurements of the form y = Ax, where A e Rmxn describes the measurement process. Standard results in compressive sensing show that it is possible to recover the signal x from m = O(k log(n k)) measurements, and that this bound is tight. The framework of model-based compressive sensing [BCDH10] overcomes the lower bound and reduces the number of measurements further to O(k) by limiting the supports of x to a subset M of the (nk) possible supports. This has led to many measurement-efficient algorithms for a wide variety of signal models, including block-sparsity and tree-sparsity. Unfortunately, extending the framework to other, more general models has been stymied by the following obstacle: for the framework to apply, one needs an algorithm that, given a signal x, solves the following optimization problem exactly: [EQUATION] (here x[n] denotes the projection of x on coordinates not in Ω). However, an approximation algorithm for this optimization task is not sufficient. Since many problems of this form are not known to have exact polynomial-time algorithms, this requirement poses an obstacle for extending the framework to a richer class of models. In this paper, we remove this obstacle and show how to extend the model-based compressive sensing framework so that it requires only approximate solutions to the aforementioned optimization problems. Interestingly, our extension requires the existence of approximation algorithms for both the maximization and the minimization variants of the optimization problem. Further, we apply our framework to the Constrained Earth Mover's Distance (CEMD) model introduced in [SHI13], obtaining a sparse recovery scheme that uses significantly less than O(k log(n k)) measurements. This is the first non-trivial theoretical bound for this model, since the validation of the approach presented in [SHI13] was purely empirical. The result is obtained by designing a novel approximation algorithm for the maximization version of the problem and proving approximation guarantees for the minimization algorithm described in [SHI13]. Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex functions, such as the Iterative Soft Thresholding Algorithm and its accelerated version (ISTA, FISTA). However, these methods don't exploit the particular structure of the problem at hand nor the input data distribution. An acceleration using neural networks was proposed in Gregor10 , coined LISTA, which showed empirically that one could achieve high quality estimates with few iterations by modifying the parameters of the proximal splitting appropriately. In this paper we study the reasons for such acceleration. Our mathematical analysis reveals that it is related to a specific matrix factorization of the Gram kernel of the dictionary, which attempts to nearly diagonalise the kernel with a basis that produces a small perturbation of the @math ball. When this factorization succeeds, we prove that the resulting splitting algorithm enjoys an improved convergence bound with respect to the non-adaptive version. Moreover, our analysis also shows that conditions for acceleration occur mostly at the beginning of the iterative process, consistent with numerical experiments. We further validate our analysis by showing that on dictionaries where this factorization does not exist, adaptive acceleration fails.