International Journal of Wavelets, Multiresolution and Information Processing

The paper continues the development of the multiple 1D-embedding-based (or, 1D multi-embedding) methods for semi-supervised learning, which is preliminarily introduced by the author in [J. Wang, Semi-supervised learning using multiple one-dimensional embedding based adaptive interpolation, Int. J. Wavelets, Multiresolut. Inform Process. 14(2) (2016) 11 pp.]. This paper puts the development in a more general framework and creates a new method, which employs the ensemble technique to integrate multiple 1D embedding-based regularization and label boosting for semi-supervised learning (SSL). It combines parallel ensemble and serial ensemble. In each stage of parallel ensemble, the dataset is first smoothly mapped onto multiple 1D sequences. On each 1D embedded data, a classical regularization method is applied to construct a weak classifier. All of these weak classifiers are then integrated to an ensemble of 1D labeler (E1DL), which together with a nearest neighbor cluster (NNC) algorithm extracts a newborn labeled subset from the unlabeled set. The subset is believed to be correctly labeled with a high confidence, so that it joins with the original labeled set for the next learning stage. Repeating this process, we gradually obtain a boosted labeled set and the process will not stopped until the updated labeled set reaches a certain size. Finally, we use E1DL to build the target classifier, which labels all points of the dataset. In this paper, we also set the universal parameters for all experiments to make the algorithm as a parameter-free one. The validity of our method in the classification of the handwritten digits is confirmed by several experiments. Comparing to several other popular SSL methods, our results are very promising.

We propose a novel semi-supervised learning (SSL) scheme using adaptive interpolation on multiple one-dimensional (1D) embedded data. For a given high-dimensional dataset, we smoothly map it onto several different 1D sequences, so that the labeled subset is converted to a 1D subset for each of these sequences. Applying the cubic interpolation of the labeled subset, we obtain a subset of unlabeled points, which are assigned to the same label in all interpolations. Selecting a proportion of these points at random and adding them to the current labeled subset, we build a larger labeled subset for the next interpolation. Repeating the embedding and interpolation, we enlarge the labeled subset gradually, and finally reach a labeled set with a reasonable large size, based on which the final classifier is constructed. We explore the use of the proposed scheme in the classification of handwritten digits and show promising 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.

In this paper, we present a novel multiple 1D-embedding based clustering (M1DEBC) scheme for hyperspectral image (HSI) classification. This novel clustering scheme is an iteration algorithm of 1D-embedding based regularization, which is first proposed by J. Wang [Semi-supervised learning using ensembles of multiple 1D-embedding-based label boosting, Int. J. Wavelets$,$ Multiresolut. Inf. Process. 14(2) (2016) 33 pp.; Semi-supervised learning using multiple one-dimensional embedding-based adaptive interpolation, Int. J. Wavelets$,$ Multiresolut. Inf. Process. 14(2) (2016) 11 pp.]. In the algorithm, at each iteration, we do the following three steps. First, we construct a 1D multi-embedding, which contains $k$ different versions of 1D embedding. Each of them is realized by an isometric mapping that maps all the pixels in a HSI into a line such that the sum of the distances of adjacent pixels in the original space is minimized. Second, for each 1D embedding, we use the regularization method to find a pre-classifier to give each unlabeled sample a preliminary label. If all of the $k$ different versions of regularization vote the same preliminary label, then we call it a feasible confident sample. All the feasible confident samples and their corresponding labels constitute the auxiliary set. We randomly select a part of the elements from the auxiliary set to construct the newborn labeled set. Finally, we add the newborn labeled set into the labeled sample set. Thus, the labeled sample set is gradually enlarged in the process of the iteration. The iteration terminates until the updated labeled set reaches a certain size. Our experimental results on real hyperspectral datasets confirm the effectiveness of the proposed scheme.

In this paper, we propose a novel semi-supervised learning classification framework using box-based smooth ordering and multiple 1D-embedding-based interpolation (M1DEI) in [J. Wang, Semi-supervised learning using multiple one-dimensional embedding-based adaptive interpolation, Int. J. Wavelets Multiresolut. Inf. Process. 14(2) (2016) 11 pp.] for hyperspectral images. Due to the lack of labeled samples, conventional supervised approaches cannot generally perform efficient enough. On the other hand, obtaining labeled samples for hyperspectral image classification is difficult, expensive and time-consuming, while unlabeled samples are easily available. The proposed method can effectively overcome the lack of labeled samples by introducing new labeled samples from unlabeled samples in a label boosting framework. Furthermore, the proposed method uses spatial information from the pixels in the neighborhood of the current pixel to better catch the features of hyperspectral image. The proposed idea is that, first, we extract the box (cube data) of each pixel from its neighborhood, then apply multiple 1D interpolation to construct the classifier. Experimental results on three hyperspectral data sets demonstrate that the proposed method is efficient, and outperforms recent popular semi-supervised methods in terms of accuracies.

In this paper, we propose a novel semi-supervised multi-category classification method based on one-dimensional (1D) multi-embedding. Based on the multiple 1D embedding based interpolation technique, we embed the high-dimensional data into several different 1D manifolds and perform binary classification firstly. Then we construct the multi-category classifiers by means of one-versus-rest and one-versus-one strategies separately. A weight strategy is employed in our algorithm for improving the classification performance. The proposed method shows promising results in the classification of handwritten digits and facial images.

Small infrared (IR) target detection is an important and challenging issue in IR target tracking system. In this paper, a patch ordering-based method is proposed for small IR target detection in an image with complicated background. Inspired by the contrast mechanism of human vision system, a patch ordering-based contrast measure (POCM) is designed to deal with the input image, which cannot only suppress the background noise and clutter but also enhance the targets significantly. In this way, POCM can increase the contrast ratio between target and background. This leads to higher Signal Clutter Ratio (SCR). Then the true target can be detected by applying simple adaptive thresholding method. The experimental results on two sequences show that the proposed method can efficiently detect small IR target from heavy clutter.