textit{Drosophila melanogaster} has been established as a model organism for investigating the fundamental principles of developmental gene interactions. The gene expression patterns of textit{Drosophila melanogaster} can be documented as digital ima
ges, 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.
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However,
such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. Note that the distance function on a manifold can always be well-defined. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm.
