Sunday, September 30, 2012

Full-class set classification using the Hungarian algorithm

ORIGINAL ARTICLE Full-class set classification using the Hungarian algorithm Ludmila I. Kuncheva Received: 23 March 2010 / Accepted: 23 June 2010 / Published online: 16 September 2010 C211 Springer-Verlag 2010 Abstract Consider a set-classification task where c objects must be labelled simultaneously in c classes, knowing that there is only one object coming from each class (full-class set). Such problems may occur in auto- matic attendance registration systems, simultaneous tracking of fast moving objects and more. A Bayes-optimal solution

to the full-class set classification problem is pro- posed using a single classifier and the Hungarian assign- ment algorithm. The advantage of set classification over individually based classification is demonstrated both the- oretically and experimentally, using simulated, benchmark and real data. Keywords Full-class set classification C1 Bayes-optimal classifier C1 Label assignment problem 1 Introduction For many years now, pattern recognition and machine learning have devoted major efforts to improving classifi- cation accuracy, and have allegedly cast aside a number of challenges arising from real-life problems [7]. One of the standard assumptions in classical pattern recognition is that the data comes as an independent identically distributed (i.i.d) sequence of instances. Here we abandon this assumption and consider dependent data where a set of instances has to be classified together, knowing that the set contains at most one instance from each class (or exactly one instance from each class, if the cardinality of the set equals the number of classes). Consider an automatic sys- tem that uses face recognition to record students’ atten- dance of a lesson against a predefined list of identities. Without enforcing the one-to-one correspondence, one identity may be assigned to two or more students. If the individual face classifier is reasonably correct, then some mistakes can be remedied. In this context, a classifier is informally described as ‘‘reasonably correct’’ if the true class is ranked high among all classes, even when the top ranked class is incorrect. An example of non-i.i.d classification, called the multi- ple-instance problem, arises in complex machine learning applications where the information about the instances is incomplete or ambiguous [4, 11, 17], e.g., in drug activity prediction [4]. The training examples come in ‘‘bags’’ labelled either positive or negative. For a positive bag, it is known that at least one instance in the bag has true positive label. For a bag labelled negative, all instances are known to be negative. The problem is to design a classifier that can label as accurately as possible an unseen bag of instances. Set classification is considered by Ning and Karypis [13], where all the instances in the set to be classified are known to have come from the same class. This problem may arise in face recognition where multiple images of the same person’s face are submitted as a set. Collective rec- ognition is another scenario where a set of instances are labelled together [12, 16]. The...

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