Scalable Linear Visual Feature Learning via Online Parallel Nonnegative Matrix Factorization

Neural System Identification With Spike-Triggered Non-Negative Matrix Factorization

Neuronal circuits formed in the brain are complex with intricate connection patterns. Such complexity is also observed in the retina with a relatively simple neuronal circuit. A retinal ganglion cell (GC) receives excitatory inputs from neurons in previous layers as driving forces to fire spikes. Analytical methods are required to decipher these components in a systematic manner. Recently a method called spike-triggered non-negative matrix factorization (STNMF) has been proposed for this purpose. In this study, we extend the scope of the STNMF method. By using retinal GCs as a model system, we show that STNMF can detect various computational properties of upstream bipolar cells (BCs), including spatial receptive field, temporal filter, and transfer nonlinearity. In addition, we recover synaptic connection strengths from the weight matrix of STNMF. Furthermore, we show that STNMF can separate spikes of a GC into a few subsets of spikes, where each subset is contributed by one presynaptic BC. Taken together, these results corroborate that STNMF is a useful method for deciphering the structure of neuronal circuits.

Fine-Grained Image Classification Using Modified DCNNs Trained by Cascaded Softmax and Generalized Large-Margin Losses

We develop a fine-grained image classifier using a general deep convolutional neural network (DCNN). We improve the fine-grained image classification accuracy of a DCNN model from the following two aspects. First, to better model the h -level hierarchical label structure of the fine-grained image classes contained in the given training data set, we introduce h fully connected (fc) layers to replace the top fc layer of a given DCNN model and train them with the cascaded softmax loss. Second, we propose a novel loss function, namely, generalized large-margin (GLM) loss, to make the given DCNN model explicitly explore the hierarchical label structure and the similarity regularities of the fine-grained image classes. The GLM loss explicitly not only reduces between-class similarity and within-class variance of the learned features by DCNN models but also makes the subclasses belonging to the same coarse class be more similar to each other than those belonging to different coarse classes in the feature space. Moreover, the proposed fine-grained image classification framework is independent and can be applied to any DCNN structures. Comprehensive experimental evaluations of several general DCNN models (AlexNet, GoogLeNet, and VGG) using three benchmark data sets (Stanford car, fine-grained visual classification-aircraft, and CUB-200-2011) for the fine-grained image classification task demonstrate the effectiveness of our method.

Discriminative and Orthogonal Subspace Constraints-Based Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is one widely used feature extraction technology in the tasks of image clustering and image classification. For the former task, various unsupervised NMF methods based on the data distribution structure information have been proposed. While for the latter task, the label information of the dataset is one very important guiding. However, most previous proposed supervised NMF methods emphasis on imposing the discriminant constraints on the coefficient matrix. When dealing with new coming samples, the transpose or the pseudoinverse of the basis matrix is used to project these samples to the low dimension space. In this way, the label influence to the basis matrix is indirect. Although, there are also some methods trying to constrain the basis matrix in NMF framework, either they only restrict within-class samples or impose improper constraint on the basis matrix. To address these problems, in this article a novel NMF framework named discriminative and orthogonal subspace constraints-based nonnegative matrix factorization (DOSNMF) is proposed. In DOSNMF, the discriminative constraints are imposed on the projected subspace instead of the directly learned representation. In this manner, the discriminative information is directly connected with the projected subspace. At the same time, an orthogonal term is incorporated in DOSNMF to adjust the orthogonality of the learned basis matrix, which can ensure the orthogonality of the learned subspace and improve the sparseness of the basis matrix at the same time. This framework can be implemented in two ways. The first way is based on the manifold learning theory. In this way, two graphs, i.e., the intrinsic graph and the penalty graph, are constructed to capture the intra-class structure and the inter-class distinctness. With this design, both the manifold structure information and the discriminative information of the dataset are utilized. For convenience, we name this method as the name of the framework, i.e., DOSNMF. The second way is based on the Fisher’s criterion, we name it Fisher’s criterion-based DOSNMF (FDOSNMF). The objective functions of DOSNMF and FDOSNMF can be easily optimized using multiplicative update (MU) rules. The new methods are tested on five datasets and compared with several supervised and unsupervised variants of NMF. The experimental results reveal the effectiveness of the proposed methods.

Merging weighted SVMs for parallel incremental learning

Parallel incremental learning is an effective approach for rapidly processing large scale data streams, where parallel and incremental learning are often treated as two separate problems and solved one after another. Incremental learning can be implemented by merging knowledge from incoming data and parallel learning can be performed by merging knowledge from simultaneous learners. We propose to simultaneously solve the two learning problems with a single process of knowledge merging, and we propose parallel incremental wESVM (weighted Extreme Support Vector Machine) to do so. Here, wESVM is reformulated such that knowledge from subsets of training data can be merged via simple matrix addition. As such, the proposed algorithm is able to conduct parallel incremental learning by merging knowledge over data slices arriving at each incremental stage. Both theoretical and experimental studies show the equivalence of the proposed algorithm to batch wESVM in terms of learning effectiveness. In particular, the algorithm demonstrates desired scalability and clear speed advantages to batch retraining.