Search

Linear discriminant analysis (LDA) is a popular supervised dimension reduction algorithm, which projects the data into an effective low-dimensional linear subspace while the separation between the projected data from different classes is improved. While this subspace is typically determined by solving a generalized eigenvalue decomposition problem, its high computation costs prohibit the use of LDA especially when the scale and the dimensionality of the data are large. Based on the recent success of least squares LDA (LSLDA), we propose a novel rank-one update method with a simplified class indicator matrix. Using the proposed algorithm, we are able to derive the LSLDA model efficiently. Moreover, our LSLDA model can be extended to address the learning task of concept drift, in which the recently received data exhibit with gradual or abrupt changes in distribution. In other words, our LSLDA is able to observe and model the data distribution changes, while the dependency on outdated data will be suppressed. This proposed LSLDA will benefit applications of streaming data classification or mining, and it can recognize data with newly added class labels during the learning process. Experimental results on both synthetic and real datasets (with and without concept drift) confirm the effectiveness of our propose LSLDA.

Motivated by image reconstruction, sparse representation based classification (SRC) has been shown to be an effective method for applications like face recognition. In this paper, we propose a locality-sensitive dictionary learning algorithm for SRC, in which the designed dictionary is able to preserve local data structure, resulting in improved image classification. During the dictionary update and sparse coding stages in the proposed algorithm, we provide closed-form solutions and enforce the data locality constraint throughout the learning process. In contrast to previous dictionary learning approaches utilizing sparse representation techniques, which did not (or only partially) take data locality into consideration, our algorithm is able to produce a more representative dictionary and thus achieves better performance. We conduct experiments on databases designed for face and handwritten digit recognition. For such reconstruction-based classification problems, we will confirm that our proposed method results in better or comparable performance as state-of-the-art SRC methods do, while less training time for dictionary learning can be achieved.