This paper addresses the problem of image set matching in kernel learning approach

and a locality geometry structure preserved discriminant analysis based on a Riemannian manifold is presented for image set matching. Riemannian manifolds have been an effective way to represent image sets

which are mapped as data points on the manifold. Then

recognition can be performed by applying the discriminant analysis on such manifolds. However

the local structure of the data points is not exposed in the discriminant analysis. In computer vision applications

the multi-view facial images are nonlinearly distributed

and features often lie on Riemannian manifolds with known geometry. Set-based matching methods utilize a set of images as input and model the probe set and gallery set individually. Hence

these methods can fully utilize the information provided by multiple images to obtain better matching and recognition accuracy. However

the popular learning algorithms such as discriminant analysis and support vector machines

etc.

are not directly applicable to such features due to the non-Euclidean nature of the underlying spaces. To overcome this limitation

each image set is mapped into a high-dimensional feature space

e.g. a high dimensional Reproducing Kernel Hilbert Space (RKHS)

using a nonlinear mapping function

to which many Euclidean algorithms can be generalized. For set based image matching techniques

as mentioned above

the key issues can be categorized based on how to represent the image sets and how to measure the similarity between two image sets. We naturally formulate the problem of the image set matching as matching points lying on the Riemannian manifold spanned by symmetric positive definite (SPD)

i.e. nonsingular covariance matrices. In general

the success of kernel-based methods is often determined by the choice of the kernel function. By exploring an efficient metric for the symmetric positive definie covariance matrices

i.e. Log-Euclidean distance

we derive a kernel function that explicitly maps the nonsingular covariance matrix from the Riemannian manifold to a Euclidean space. Different from other methods on Riemannian manifold

the local structure of data is taking into account. With the explicit mapping

a kernel version of Locality Preserving Projection (LPP) is applied to keep the local geometry structure of the image set and an image set-based matching method is proposed. The proposed method is evaluated on set-based object classification tasks and face recognition tasks. Extensive experimental results show that the proposed method outperforms other state of the art set-based object matching and face recognition methods. In this paper

according our experimental settings

it reaches 91.5% and 65.31% on recognition rate in the public ETH80 object database and YouTube Celebrities video database respectively. In this paper

we have proposed an efficient image set matching method. This method respresents each image set with its covariance matrix and models the problem as matching points on the Riemannian manifold spanned by nonsingular covariance matrix. We derived a Mercer kernel function

which successfully bridges the gap between traditional learning methods operating in vector space and the learning task on a manifold. Through comparison experiments

it is shown to be generally better than other image sets matching methods.