In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
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Question: Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them. Given multiple objects and matches computed between a few object pairs in isolation, the goal is to recover an entire collection of maps that are (1) globally consistent, and (2) close to the provided maps and under certain conditions provably the ground-truth maps. Despite recent advances on this problem, the best-known recovery guarantees are limited to a small constant barrier none of the existing methods find theoretical support when more than 50% of input correspondences are corrupted. Moreover, prior approaches focus mostly on fully similar objects, while it is practically more demanding to match instances that are only partially similar to each other (e.g., different views of a single physical object). In this paper, we propose an algorithm to jointly match multiple objects that exhibit only partial similarities, given a few (possibly highly incomplete) pairwise matches that are densely corrupted. By encoding a consistent partial map collection into a 0-1 semidefinite matrix, we propose to recover the ground-truth maps via a parameter-free convex program called MatchLift, following a spectral method that pre-estimates the total number of distinct elements to be matched. Numerically, this program can be efficiently solved via alternating direction methods of multipliers (ADMM) along with a greedy rounding strategy. Theoretically, MatchLift exhibits near-optimal error-correction ability, i.e. in the asymptotic regime it is guaranteed to work even when a dominant fraction 1 ( log n n ) of the input maps behave like random outliers. Furthermore, MatchLift succeeds with minimal input complexity, namely, perfect matching can be achieved as soon as the provided maps form a connected map graph. We evaluate the proposed algorithm on various benchmark data sets including synthetic examples and real-world examples, all of which confirm the practical applicability and usefulness of MatchLift.

Answer: Near-Optimal Joint Object Matching via Convex Relaxation

Question: Knowledge graph embedding aims to embed entities and relations of knowledge graphs into low-dimensional vector spaces. Translating embedding methods regard relations as the translation from head entities to tail entities, which achieve the state-of-the-art results among knowledge graph embedding methods. However, a major limitation of these methods is the time consuming training process, which may take several days or even weeks for large knowledge graphs, and result in great diculty in practical applications. In this paper, we propose an ecient parallel framework for translating embedding methods, called ParTrans-X, which enables the methods to be paralleled without locks by utilizing the distinguished structures of knowledge graphs. Experiments on two datasets with three typical translating embedding methods, i.e., TransE [3], TransH [19], and a more ecient variant TransEAdaGrad [11] validate that ParTrans-X can speed up the training process by more than an order of magnitude.

Answer: Eicient Parallel Translating Embedding For Knowledge Graphs

Question: Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous, non-anonymous, or organized in groups. Although powerful solvers for this abstract problem exist, they make simplifying assumptions by ignoring kinematic constraints, making it difficult to use the resulting plans on actual robots. In this paper, we present a solution which takes kinematic constraints, such as maximum velocities, into account, while guaranteeing a user-specified minimum safety distance between robots. We demonstrate our approach in simulation and on real robots in 2D and 3D environments.

Answer:
Path Planning With Kinematic Constraints For Robot Groups