The explosion of streaming data poses challenges to feature learning methods including linear discriminant analysis (LDA). Many existing LDA algorithms are not efficient enough to incrementally update with samples that sequentially arrive in various manners. First, we propose a new fast batch LDA (FLDA/QR) learning algorithm that uses the cluster centers to solve a lower triangular system that is optimized by the Cholesky-factorization. To take advantage of the intrinsically incremental mechanism of the matrix, we further develop an exact incremental algorithm (IFLDA/QR). The Gram-Schmidt process with reorthogonalization in IFLDA/QR significantly saves the space and time expenses compared with the rank-one QR-updating of most existing methods. IFLDA/QR is able to handle streaming data containing 1) new labeled samples in the existing classes, 2) samples of an entirely new (novel) class, and more significantly, 3) a chunk of examples mixed with those in 1) and 2). Both theoretical analysis and numerical experiments have demonstrated much lower space and time costs (2~10 times faster) than the state of the art, with comparable classification accuracy.

Instead of assuming a closed-world environment comprising a fixed number of objects, modern pattern recognition systems need to recognize outliers, identify anomalies, or discover entirely new objects, which is known as zero-shot object recognition. However, many existing zero-shot learning methods are not efficient enough to incrementally update themselves with new samples mixed with known or novel class labels. In this paper, we propose an incremental zero-shot learning framework (IIAP/QR) based on indirect-attribute-prediction (IAP) model. Firstly, a fast incremental classifier based on null space based linear discriminant analysis with QR-updating (NLDA/QR) is put forward, which can solve small-sample-size (SSS) problem and unequal-sample-size (USS) problem that usually occur in incremental learning using the centroid of each class as input. Then with the probabilistic inference of Class-Attribute layer and Attribute-Zero shot classification layer, IIAP/QR model can efficiently update itself for the insertion of both new samples to the existing class and totally novel classes with comparable recognition accuracy for zero-shot object recognition.