Vol.:(0123456789) 1 3 Evolutionary Intelligence https://doi.org/10.1007/s12065-019-00211-y RESEARCH PAPER Cross domain association using transfer subspace learning Rupali Sandip Kute 1,2  · Vibha Vyas 1  · Alwin Anuse 2 Received: 29 September 2018 / Revised: 14 January 2019 / Accepted: 4 February 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract Transfer learning has gained more attention recently by utilizing knowledge acquired from one domain to advance a learning performance in another domain. Existing homogeneous transfer learning methods have progressed to a point where feature spaces are common in training and testing domains. However, heterogeneous transfer learning is still in its nascent stage where features of training and testing domains are diferent. Taking this into account, Bregman Divergence Regularization is used to minimize the probability distribution diference between training and testing domains and to take them together to a shared subspace. To discriminate data within individual domains, a projection matrix is obtained using Fisher Linear Discriminant Analysis subspace learning algorithm. Experimentation is performed on two efciently used biometrics: the face and fngerprint. Two types of cross-domain settings are used: (1) Face + Finger2Finger where training samples come from face (labeled samples) and fngerprint (unlabeled samples) data sets, while testing is performed on a fngerprint dataset. (2) Finger + Face2Face where training samples come from fngerprint (labeled samples) and face (unlabeled samples) data sets while testing is performed on a face dataset. This paper proposes a cross domain association between face and fngerprint that fnds utility in forensic applications. Keywords Bregman divergence · Transfer subspace learning · Fisher linear discriminant analysis · Biometrics 1 Introduction Transfer learning conveys knowledge gained from the training domain and enhances the learning ability of the testing domain. It has gained more attention recently due to its efectiveness in a variety of applications. Auxiliary information gained is relayed from one domain to another. Auxiliary information is beyond conventional information and it improves the overall performance of the system. This information can possess common features with an ability to correlate diferent domains. Multi-task learning model [1] and Multi-domain learning model [2] are built by sharing the subset of common features which advances the performance of an individual task. In the case of instance based learn- ing, diferent weights are used to rank samples of the source domain to provide more information in the target domain [3]. Samples collected under various environmental condi- tions in diferent domains have diverse probability distribu- tion and in such cases transfer learning fails to work [4]. In transfer learning, it is important to minimize the diference between probability distribution and get the source and tar- get domains together in a joint subspace by sharing some auxiliary information. The regularization based on Bregman Divergence is proposed to minimize the probability distribu- tion diference between diferent domains [5]. Semi-supervised learning is a type of learning method which uses a small amount of labeled data and a huge amount of unlabeled data [6–8]. Similarly, transfer learn- ing also uses labeled and unlabeled data. However, semi- supervised learning considers all samples are independently and identically distributed or they are considered from the same nonlinear manifold structure [6]. This means that the probability distribution of the training samples is same as the probability distribution of the testing samples. In transfer learning, various kinds of auxiliary information from unla- beled samples is used, viz. a sample from shared features space can be used by multiple tasks [1, 9]. For example, the simulation behavior of a miniature robot can be trans- ferred to a large-scale robot [10] and, mutual-information * Rupali Sandip Kute r_patil2@redifmail.com 1 Department of E&TC, College of Engineering, Shivajinagar, Pune 411005, India 2 Department of E&TC, Maharashtra Institute of Technology, Kothrud, Pune 411038, India