Narrow Results

This paper presents a novel classifier based on collaborative representation (CR) and multiple one-dimensional (1D) embedding with applications to face recognition. To use multiple 1D embedding (1DME) framework in semi-supervised learning is first proposed by one of the authors, J. Wang, in 2014. The main idea of the multiple 1D embedding is the following: Given a high-dimensional dataset, we first map it onto several different 1D sequences on the line while keeping the proximity of data points in the original ambient high-dimensional space. By this means, a classification problem on high dimension reduces to the one in a 1D framework, which can be efficiently solved by any classical 1D regularization method, for instance, an interpolation scheme. The dissimilarity metric plays an important role in learning a decent 1DME of the original dataset. Our another contribution is to develop a collaborative representation based dissimilarity (CRD) metric. Compared to the conventional Euclidean distance based metric, the proposed method can lead to better results. The experimental results on real-world databases verify the efficacy of the proposed method.

To efficiently improve the accuracy of hyperspectral image (HSI) classification, the spatial information is usually fused with spectral information so that the classification performance can be enhanced. In this paper, we propose a new classification method called wavelet transform-based smooth ordering (WTSO). WTSO consists of three main components: wavelet transform for feature extraction, spectral–spatial based similarity measurement, smooth ordering based 1D embedding, and construction of final classifier using interpolation scheme. Specifically, wavelet transform is first imposed to decompose the HSI signal into approximate coefficients (ACs) and details coefficients (DCs). Then, to measure the similar level of pairwise samples, a novel metric is defined on the ACs, where the spatial information serves as the prior knowledge. Next, according to the measurement results, smooth ordering is applied so that the samples are aligned in a 1D space (called 1D embedding). Finally, since the reordering samples are smooth, the labels of test samples can be recovered using the simple 1D interpolation method. In the last step, in order to reduce the bias and improve accuracy, the final classifier is constructed using multiple 1D embeddings. The use of wavelet transform in WTSO can also reduce the high dimensionality of HSI data. By converting the hight-dimensional samples into a 1D ordering sequence, WTSO can reduce the computational cost, and simultaneously perform classification for the test samples. Note that in WTSO, the smooth ordering based 1D embedding and interpolation are executed in an iterative manner. And they will be terminated after finite steps. The proposed method is experimentally demonstrated on two real HSI datasets: IndianPines and University of Pavia, achieving promising results.