Shape correspondence for cel animation based on a shape association graph and spectral matching

We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes.We formulate the correspondence problem as an adapted quadratic assignment problem,which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence.To simultaneously represent the geometric and topological similarities between regions,we propose a shape association graph(SAG),whose node attributes indicate the geometric distance between regions,and whose edge attributes indicate the topological distance between combined region pairs.We convert topological distance to geometric distance between geometric objects with topological features of the pairs,and introduce Kendall shape space to calculate the intrinsic geometric distance.By utilizing the spectral properties of the affinity matrix induced by the SAG,our approach can efficiently extract globally optimal region correspondences,even if shapes have inconsistent topology and severe deformation.It is also robust to shapes undergoing similarity transformations,and compatible with parallel computing techniques.

Sample-Efficient Deep Reinforcement Learning with Directed Associative Graph

Reinforcement learning can be modeled as markov decision process mathematically.In consequence,the interaction samples as well as the connection relation between them are two main types of information for learning.However,most of recent works on deep reinforcement learning treat samples independently either in their own episode or between episodes.In this paper,in order to utilize more sample information,we propose another learning system based on directed associative graph(DAG).The DAG is built on all trajectories in real time,which includes the whole connection relation of all samples among all episodes.Through planning with directed edges on DAG,we offer another perspective to estimate stateaction pair,especially for the unknowns to deep neural network(DNN)as well as episodic memory(EM).Mixed loss function is generated by the three learning systems(DNN,EM and DAG)to improve the efficiency of the parameter update in the proposed algorithm.We show that our algorithm is significantly better than the state-of-the-art algorithm in performance and sample efficiency on testing environments.Furthermore,the convergence of our algorithm is proved in the appendix and its long-term performance as well as the effects of DAG are verified.

Discovering Association Rules with Graph Patterns in Temporal Networks

Discovering regularities between entities in temporal graphs is vital for many real-world applications(e.g.,social recommendation,emergency event detection,and cyberattack event detection).This paper proposes temporal graph association rules(TGARs)that extend traditional graph-pattern association rules in a static graph by incorporating the unique temporal information and constraints.We introduce quality measures(e.g.,support,confidence,and diversification)to characterize meaningful TGARs that are useful and diversified.In addition,the proposed support metric is an upper bound for alternative metrics,allowing us to guarantee a superset of patterns.We extend conventional confidence measures in terms of maximal occurrences of TGARs.The diversification score strikes a balance between interestingness and diversity.Although the problem is NP-hard,we develop an effective discovery algorithm for TGARs that integrates TGARs generation and TGARs selection and shows that mining TGARs is feasible over a temporal graph.We propose pruning strategies to filter TGARs that have low support or cannot make top-k as early as possible.Moreover,we design an auxiliary data structure to prune the TGARs that do not meet the constraints during the TGARs generation process to avoid conducting repeated subgraph matching for each extension in the search space.We experimentally verify the effectiveness,efficiency,and scalability of our algorithms in discovering diversified top-k TGARs from temporal graphs in real-life applications.

The κ-point Exponent Set of Central Symmetric Primitive Matrices

Let G =（Y, E） be a primitive digraph. The vertex exponent of G at a vertex v E V, denoted by expG（v）, is the least integer p such that there is a v → u walk of length p for each u E V. We choose to order the vertices of G in such a way that expG（v1） ≤ expG（v2） ≤... ≤expG（vn）. Then expG（vk） is called the k-point exponent of G and is denoted by expG（k）, 1 〈 k 〈 n. We define the k-point exponent set E（n, k） ：= {expG（k）｜G= G（A） with A E CSP（n）｜, where CSP（n） is the set of all n × n central symmetric primitive matrices and G（A） is the associated graph of the matrix A. In this paper, we describe E（n, k） for all n, k with 1 〈 k 〈 n except n ≡ l（mod 2） and 1 〈 k 〈 n - 4. We also characterize the extremal graphs when k = 1.