Multi-manifold Recognition Based On Discriminative-analysis Of Canonical Correlations

In the conventional recognition, training and testing samples are usually carried out by a single sample or a handful of samples. With the rapid development of video capture device and convenient access of internet, images acquired from digital devices and net cover large variations of appearance, including pose angles, illuminations and so on, offering abundant samples for recognition. In that case, the significance and popularity of image sets recognition looms so large in real world applications. However, those images bear the shortcomings of high dimension and nonlinearity, which lead to the phenomenon of"curse of dimension", making it difficult to understand and analyze the intrinsic structure of an image set. Therefore, dimensionality reduction methods play an important role in data processing. Among all, due to its effectiveness on finding and preserving the intrinsic geometry of nonlinear data, manifold learning is the most prevalent and popular method. Typical manifold learning methods are ISOMAP, LLE, etc, which exploit a single image as an input and consider the entire training data as a manifold stemming from the idea of manifold learning.We target at the task of image sets recognition, with each set serving as an input. By means of constructing each set as a manifold, we take it for granted that the task of recognition based on sets is converted to that of multi-manifold recognition. We integrate set matching with manifold learning, and our main works are as follows:1. Based on the fundamental idea of manifold-manifold distance, we demonstrate the method of constructing local linear models in theory and practice, the measurement of pair-wise local linear subspaces, as well as multi-manifold recognition.2. We propose a method of Multi-manifold Recognition Based on Discriminative-analysis of Canonical Correlations (MRDCC), which is proved practical and effective by our experiments. As a method of set matching, it is demonstrated by our experiment results that MRDCC rank first among other contrastive recognition methods based on sets.3. We propose to match sets by pair-wise local linear subspaces, which converts the task of manifold-manifold matching to that of subspace-subspace matching.In conclusion, under the manifold-manifold distance framework, we propose an effective multi-manifold recognition algorithm, which is evaluated on Honda/UCSD face video database and ETH-80 object database, and we make further beneficial exploration of subspace-subspace matching.