In this paper, we first introduce the concept of an adaptive MRA (AMRA) structure which is a variant of the classical MRA structure suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology for the general case of affine-like systems, and derive a Unitary Extension Principle (UEP) for filter design. Finally, we apply our results to the directional representation system of shearlets. This leads to a comprehensive theory for fast decomposition algorithms associated with shearlet systems which encompasses tight shearlet frames with spatially compactly supported generators within such an AMRA structure. Also shearlet-like systems associated with parabolic scaling and unimodular matrices optimally close to rotation as well as 3D shearlet systems are studied within this framework.
A particular credit deserves the work in @cite_26 , in which the adaptivity ideas were already lurking. The main difference to this paper is the additional freedom provided by the AMRA structure.
@cite_26
2164259805 2094595236 2949889664 2296308987
Citation recommendation is an interesting but challenging research problem. Most existing studies assume that all papers adopt the same criterion and follow the same behavioral pattern in deciding relevance and authority of a paper. However, in reality, papers have distinct citation behavioral patterns when looking for different references, depending on paper content, authors and target venues. In this study, we investigate the problem in the context of heterogeneous bibliographic networks and propose a novel cluster-based citation recommendation framework, called ClusCite, which explores the principle that citations tend to be softly clustered into interest groups based on multiple types of relationships in the network. Therefore, we predict each query's citations based on related interest groups, each having its own model for paper authority and relevance. Specifically, we learn group memberships for objects and the significance of relevance features for each interest group, while also propagating relative authority between objects, by solving a joint optimization problem. Experiments on both DBLP and PubMed datasets demonstrate the power of the proposed approach, with 17.68 improvement in Recall@50 and 9.57 growth in MRR over the best performing baseline. A model is presented of the manifestation of the birth and development of a scientific specialty in a collection of journal papers. The proposed model, Cumulative Advantage by Paper with Exemplars (CAPE) is an adaptation of Price's cumulative advantage model (D. Price, [1976]. Two modifications are made: (a) references are cited in groups by paper, and (b) the model accounts for the generation of highly cited exemplar references immediately after the birth of the specialty. This simple growth process mimics many characteristic features of real collections of papers, including the structure of the paper-to-reference matrix, the reference-per-paper distribution, the paper-per-reference distribution, the bibliographic coupling distribution, the cocitation distribution, the bibliographic coupling clustering coefficient distribution, and the temporal distribution of exemplar references. The model yields a great deal of insight into the process that produces the connectedness and clustering of a collection of articles and references. Two examples are presented and successfully modeled: a collection of 131 articles on MEMS RF (microelectromechnical systems radio frequency) switches, and a collection of 901 articles on the subject of complex networks. © 2005 Wiley Periodicals, Inc. We present a novel abstractive summarization framework that draws on the recent development of a treebank for the Abstract Meaning Representation (AMR). In this framework, the source text is parsed to a set of AMR graphs, the graphs are transformed into a summary graph, and then text is generated from the summary graph. We focus on the graph-to-graph transformation that reduces the source semantic graph into a summary graph, making use of an existing AMR parser and assuming the eventual availability of an AMR-to-text generator. The framework is data-driven, trainable, and not specifically designed for a particular domain. Experiments on gold-standard AMR annotations and system parses show promising results. Code is available at: this https URL We present a two-stage framework to parse a sentence into its Abstract Meaning Representation (AMR). We first use a dependency parser to generate a dependency tree for the sentence. In the second stage, we design a novel transition-based algorithm that transforms the dependency tree to an AMR graph. There are several advantages with this approach. First, the dependency parser can be trained on a training set much larger than the training set for the tree-to-graph algorithm, resulting in a more accurate AMR parser overall. Our parser yields an improvement of 5 absolute in F-measure over the best previous result. Second, the actions that we design are linguistically intuitive and capture the regularities in the mapping between the dependency structure and the AMR of a sentence. Third, our parser runs in nearly linear time in practice in spite of a worst-case complexity ofO(n 2 ).