Classical fuzzy rough set often uses fuzzy rough dependency as an evaluation function of feature selection. However, this function only retains the maximum membership degree of a sample to one decision class, it cannot describe the classification error. Therefore, in this article, a novel criterion function for feature selection is proposed to overcome this weakness. To characterize the classification error rate, we first introduce a class of irreflexive and symmetric fuzzy binary relations to redefine the concepts of fuzzy rough approximations. Then, we propose a novel concept of dependency: inner product dependency to describe the classification error and construct a criterion function to evaluate the importance of candidate features. The proposed criterion function not only can maintain a maximum dependency function, but also guarantees the minimum classification error. The experimental analysis shows that the proposed criterion function is effective for datasets with a large overlap between different categories.

Yaobo Liang, Nan Duan, Yeyun Gong, Ning Wu, Fenfei Guo, Weizhen Qi, Ming Gong, Linjun Shou, Daxin Jiang, Guihong Cao, Xiaodong Fan, Ruofei Zhang, Rahul Agrawal, Edward Cui, Sining Wei, Taroon Bharti, Ying Qiao, Jiun-Hung Chen, Winnie Wu, Shuguang Liu, Fan Yang, Daniel Campos, Rangan Majumder, Ming Zhou. Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP). 2020.

Duplicate URLs have brought serious troubles to the whole pipeline of a search engine, from crawling, indexing, to result serving. URL normalization is to transform duplicate URLs to a canonical form using a set of rewrite rules. Nowadays URL normalization has attracted significant attention as it is lightweight and can be flexibly integrated into both the online (e.g. crawling) and the offline (e.g. index compression) parts of a search engine. To deal with a large scale of websites, automatic approaches are highly desired to learn rewrite rules for various kinds of duplicate URLs. In this paper, we rethink the problem of URL normalization from a global perspective and propose a pattern tree-based approach, which is remarkably different from existing approaches. Most current approaches learn rewrite rules by iteratively inducing local duplicate pairs to more general forms, and inevitably suffer from noisy training data and are practically inefficient. Given a training set of URLs partitioned into duplicate clusters for a targeted website, we develop a simple yet efficient algorithm to automatically construct a URL pattern tree. With the pattern tree, the statistical information from all the training samples is leveraged to make the learning process more robust and reliable. The learning process is also accelerated as rules are directly summarized based on pattern tree nodes. In addition, from an engineering perspective, the pattern tree helps select deployable rules by removing conflicts and redundancies. An evaluation on more than 70 million duplicate URLs from 200 websites showed that the proposed approach achieves very promising performance, in terms of both de-duping effectiveness and computational efficiency.

We consider detecting object instances from multiple classes on grayscale images. Traditional approaches learn a classifier for each class separately and apply each of them in an exhaustive search over positions and scales. We achieve an efficient detection by organizing the search coarse-to-fine based on a hierarchical partitioning of the entire hypothesis space, the set of all possible object instances, so that groups of hypotheses can be pruned simultaneously without evaluating each one individually. In this paper, we develop an algorithm to jointly learn the hierarchy along with a classifier at each node by exploring the common parts shared among a group of object instances at all levels in the hierarchy. We also show how the confusions of the initial coarse-to-fine search can be resolved by comparing pairs of conflicting detections using cheap binary classifiers. The whole process is illustrated by detecting and recognizing handwritten digits.

We consider the problem of detecting and localizing instances from multiple object classes. Suppose an overcomplete index - an initial list with extra detections but none missed - is provided. We and others have previously shown how this can be done efficiently with coarse-to-fine search. How would one prune such a list to a final interpretation? We propose a method based on contextual disambiguation: first, a Viterbi algorithm is utilized to extract N candidate interpretations by using the global context to provide constraints among object classes or poses. Then, the extracted candidates are compared in a pairwise fashion to resolve remaining ambiguities, and the final interpretation is constructed. The whole procedure is illustrated by experiments in reading license plates.

Multiclass shape detection, in the sense of recognizing and localizing instances from multiple shape classes, is formulated as a two-step process in which local indexing primes global interpretation. During indexing a list of instantiations (shape identities and poses) is compiled, constrained only by no missed detections at the expense of false positives. Global information, such as expected relationships among poses, is incorporated afterward to remove ambiguities. This division is motivated by computational efficiency. In addition, indexing itself is organized as a coarse-to-fine search simultaneously in class and pose. This search can be interpreted as successive approximations to likelihood ratio tests arising from a simple ("naive Bayes") statistical model for the edge maps extracted from the original images. The key to constructing efficient "hypothesis tests" for multiple classes and poses is local ORing; in particular, spread edges provide imprecise but common and locally invariant features. Natural tradeoffs then emerge between discrimination and the pattern of spreading. These are analyzed mathematically within the model-based framework and the whole procedure is illustrated by experiments in reading license plates.