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.

Input: Consider Input: CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the full matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only O(nr ln r) observed entries are needed by the proposed algorithm to perfectly recover a rank r matrix of size n × n, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm.

Output: CUR Algorithm for Partially Observed Matrices


Input: Consider Input: Warehouse is one of the important aspects of a company. Therefore, it is necessary to improve Warehouse Management System (WMS) to have a simple function that can determine the layout of the storage goods. In this paper we propose an improved warehouse layout method based on ant colony algorithm and backtracking algorithm. The method works on two steps. First, it generates a solutions parameter tree from backtracking algorithm. Then second, it deducts the solutions parameter by using a combination of ant colony algorithm and backtracking algorithm. This method was tested by measuring the time needed to build the tree and to fill up the space using two scenarios. The method needs 0.294 to 33.15 seconds to construct the tree and 3.23 seconds (best case) to61.41 minutes (worst case) to fill up the warehouse. This method is proved to be an attractive alternative solution for warehouse layout system. Keywords—warehouse layout; block stacking method; ant colony algorithm; backtracking algorithm.

Output: Warehouse Layout Method Based on Ant Colony and Backtracking Algorithm


Input: Consider Input: The goal of argumentation mining, an evolving research field in computational linguistics, is to design methods capable of analyzing people’s argumentation. In this article, we go beyond the state of the art in several ways. (i) We deal with actual Web data and take up the challenges given by the variety of registers, multiple domains, and unrestricted noisy user-generated Web discourse. (ii) We bridge the gap between normative argumentation theories and argumentation phenomena encountered in actual data by adapting an argumentation model tested in an extensive annotation study. (iii) We create a new gold standard corpus (90k tokens in 340 documents) and experiment with several machine learning methods to identify argument components. We offer the data, source codes, and annotation guidelines to the community under free licenses. Our findings show that argumentation mining in user-generated Web discourse is a feasible but challenging task.


Output: Argumentation Mining in User-Generated Web Discourse