arXiv subjects
Publications and source records attributed to Yi yang.
Let $G$ be a finite simple graph on the vertex set $V$ and let $I_G$ denote its edge ideal in the polynomial ring $S=\mathbb{K}[x_V]$. In this paper, we compute the depth and the Castelnuovo--Mumford regularity of $S/I_G$ when $G=F_{k}^{W}(K_n)$ is a $k$-fan graph, or $G=G_1\circ G_2$ or $G=G_1* G_2$ is the graph obtained from fan graphs $G_1$, $G_2$ by $\circ$ operation or $*$ operation, respectively.
This paper considers deep visual recognition on long-tailed data. To be general, we consider two applied scenarios, \ie, deep classification and deep metric learning. Under the long-tailed data distribution, the majority classes (\ie, tail classes) only occupy relatively few samples and are prone to lack of within-class diversity. A radical solution is to augment the tail classes with higher diversity. To this end, we introduce a simple and reliable method named Memory-based Jitter (MBJ). We observe that during training, the deep model constantly changes its parameters after every iteration, yielding the phenomenon of \emph{weight jitters}. Consequentially, given a same image as the input, two historical editions of the model generate two different features in the deeply-embedded space, resulting in \emph{feature jitters}. Using a memory bank, we collect these (model or feature) jitters across multiple training iterations and get the so-called Memory-based Jitter. The accumulated jitters enhance the within-class diversity for the tail classes and consequentially improves long-tailed visual recognition. With slight modifications, MBJ is applicable for two fundamental visual recognition tasks, \emph{i.e.}, deep image classification and deep metric learning (on long-tailed data). Extensive experiments on five long-tailed classification benchmarks and two deep metric learning benchmarks demonstrate significant improvement. Moreover, the achieved performance are on par with the state of the art on both tasks.