Fine-grained Categorization and Dataset Bootstrapping using Deep Metric Learning with Humans in the Loop

Existing fine-grained visual categorization methods often suffer from three challenges: lack of training data, large number of fine-grained categories, and high intraclass vs. low inter-class variance. In this work we propose a generic iterative framework for fine-grained categorization and dataset bootstrapping that handles these three challenges. Using deep metric learning with humans in the loop, we learn a low dimensional feature embedding with anchor points on manifolds for each category. These anchor points capture intra-class variances and remain discriminative between classes. In each round, images with high confidence scores from our model are sent to humans for labeling. By comparing with exemplar images, labelers mark each candidate image as either a "true positive" or a "false positive". True positives are added into our current dataset and false positives are regarded as "hard negatives" for our metric learning model. Then the model is retrained with an expanded dataset and hard negatives for the next round. To demonstrate the effectiveness of the proposed framework, we bootstrap a fine-grained flower dataset with 620 categories from Instagram images. The proposed deep metric learning scheme is evaluated on both our dataset and the CUB-200-2001 Birds dataset. Experimental evaluations show significant performance gain using dataset bootstrapping and demonstrate state-of-the-art results achieved by the proposed deep metric learning methods.Comment: 10 pages, 9 figures, CVPR 201

Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant

This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad \partial_t u + \partial_x p(v) =\displaystyle -\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary condition or null-Neumann boundary condition on $u$. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends time-asymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156, 439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918), we obtain a general result when the initial perturbation belongs to the same space. In addition, our main novelty lies in the facts that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave

Throughput and Delay Scaling in Supportive Two-Tier Networks

Consider a wireless network that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier consists of randomly distributed legacy nodes of density $n$, which have an absolute priority to access the spectrum. The secondary tier consists of randomly distributed cognitive nodes of density $m=n^\beta$ with $\beta\geq 2$, which can only access the spectrum opportunistically to limit the interference to the primary tier. Based on the assumption that the secondary tier is allowed to route the packets for the primary tier, we investigate the throughput and delay scaling laws of the two tiers in the following two scenarios: i) the primary and secondary nodes are all static; ii) the primary nodes are static while the secondary nodes are mobile. With the proposed protocols for the two tiers, we show that the primary tier can achieve a per-node throughput scaling of $\lambda_p(n)=\Theta(1/\log n)$ in the above two scenarios. In the associated delay analysis for the first scenario, we show that the primary tier can achieve a delay scaling of $D_p(n)=\Theta(\sqrt{n^\beta\log n}\lambda_p(n))$ with $\lambda_p(n)=O(1/\log n)$. In the second scenario, with two mobility models considered for the secondary nodes: an i.i.d. mobility model and a random walk model, we show that the primary tier can achieve delay scaling laws of $\Theta(1)$ and $\Theta(1/S)$, respectively, where $S$ is the random walk step size. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone network.Comment: 13 pages, double-column, 6 figures, accepted for publication in JSAC 201