FINGERPRINT MATCHING BASED ON DISTANCE METRIC LEARNING Dalwon Jang and Chang D. Yoo Div. of EE, School of EECS, KAIST, Yuseong Gu, Daejeon 305-701, Korea dal1@kaist.ac.kr and cdyoo@ee.kaist.ac.kr ABSTRACT This paper considers a method for learning a distance metric in a ﬁngerprinting system which identiﬁes a query content by measuring the distance between its ﬁngerprint and a ﬁnger- print stored in a database. A metric having a general form of the Mahalanobis distance is learned with the goal that the dis- tance between ﬁngerprints extracted from perceptually simi- lar contents should be smaller than the distance between ﬁn- gerprints extracted from perceptually dissimilar contents. The metric is learned by minimizing a cost function designed to achieve the goal. The cost function is convex, and the global minimum can be obtained using convex optimization. In our experiment, the distance metric learning is applied in an au- dio ﬁngerprinting system, and it is experimentally shown that the learned distance metric improves the identiﬁcation perfor- mance. Index Terms— Fingerprinting, Identiﬁcation, Distance measurement 1. INTRODUCTION There is a growing demand for protecting, managing, and in- dexing digital content, and as a viable solution, ﬁngerprinting is receiving increased attention. Fingerprinting is a technique that identiﬁes an unknown content using a short feature vector called ﬁngerprint. In recent years, various audio/video/image ﬁngerprinting systems have been proposed [1]-[7]. A ﬁngerprinting system for content identiﬁcation gener- ally consists of three essential components: ﬁngerprint ex- traction, database (DB) search, and ﬁngerprint matching [4]. In the ﬁngerprint extraction process, a query ﬁngerprint is ex- tracted from a query content. In the DB search process, a set of candidate ﬁngerprints from a DB close to the query ﬁngerprint are obtained. In the ﬁngerprint matching process, the distances between the candidate ﬁngerprints and the query ﬁngerprint are computed based on a distance metric. The ﬁn- gerprinting system provides the meta-data associated with the closest candidate ﬁngerprint. This work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD, Basic Research Promotion Fund)(KRF-2008-314- D00309) The ﬁngerprint extraction and matching processes inﬂu- ence the identiﬁcation performance more than the DB search process which determines the computational efﬁciency of the system. The identiﬁcation performance depends highly on the distance metric used in ﬁngerprint matching process. In this paper, a method for learning a distance metric in ﬁngerprint matching is considered [8, 9, 10, 11]. In recent years, various literatures have shown that distance metric learn- ing can improve classiﬁcation and clustering performances [11]. The distance metric used in previous ﬁngerprinting sys- tems, which is not determined by learning, may not be suit- able to the ﬁngerprint used in the ﬁngerprinting system and the distortions, thus the identiﬁcation performance can be im- proved by metric learning. By learning a distance metric from training data consist- ing of original and distorted contents, the identiﬁcation per- formance can be improved. Fingerprints of original contents are assumed to be ﬁngerprints stored in a DB, and ﬁnger- prints of distorted contents are assumed to be the query ﬁn- gerprints. For correct identiﬁcation, the distance of the ﬁn- gerprint of a distorted content to the ﬁngerprint of the orig- inal content from which the distorted content was obtained - called hereafter corresponding content - should be smaller than the distance to ﬁngerprints of other original contents - called hereafter non-corresponding contents. A large distance margin should be established between ﬁngerprints of the dis- torted and non-corresponding contents [10]. This is the goal of the distance metric learning considered in this paper, and speciﬁcally a distance metric having a general form of the Mahalanobis distance is considered. A cost function to be minimized is designed so that the cost increases when the ﬁn- gerprint of the distorted content is further away from the ﬁn- gerprint of the corresponding content than from ﬁngerprints of non-corresponding contents. The parameter of the distance metric is determined by minimizing the cost function by con- vex optimization. We assume that the ﬁngerprint is real val- ued, thus the distance metric learning considered in this paper is effective only for the real-valued ﬁngerprint. The remainder of this paper is organized as follows. Sec- tion 2 explains the distance metric, and Section 3 explains the cost function used to learn the distance metric. Section 4 presents the experimental results, and Section 5 concludes the paper.