Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing methods primarily focus on the embedding of the training data, and the generalization of the embedding to initially unseen test data is rather ignored. In this work, we build on recent theoretical results on the generalization performance of supervised manifold learning algorithms. Motivated by these performance bounds, we propose a supervised manifold learning method that computes a nonlinear embedding while constructing a smooth and regular interpolation function that extends the embedding to the whole data space in order to achieve satisfactory generalization. The embedding and the interpolator are jointly learnt such that the Lipschitz regularity of the interpolator is imposed while ensuring the separation between different classes. Experimental results on several image data sets show that the proposed method outperforms traditional classifiers and the supervised dimensionality reduction algorithms in comparison in terms of classification accuracy in most settings

Out-of-sample generalizations for supervised manifold learning for classification

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes in the learned embedding. Most nonlinear supervised manifold learning methods compute the embedding of the manifolds only at the initially available training points, while the generalization of the embedding to novel points, known as the out-of-sample extension problem in manifold learning, becomes especially important in classification applications. In this work, we propose a semi-supervised method for building an interpolation function that provides an out-of-sample extension for general supervised manifold learning algorithms studied in the context of classification. The proposed algorithm computes a radial basis function (RBF) interpolator that minimizes an objective function consisting of the total embedding error of unlabeled test samples, defined as their distance to the embeddings of the manifolds of their own class, as well as a regularization term that controls the smoothness of the interpolation function in a direction-dependent way. The class labels of test data and the interpolation function parameters are estimated jointly with a progressive procedure. Experimental results on face and object images demonstrate the potential of the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets

Advances in Character Recognition

This book presents advances in character recognition, and it consists of 12 chapters that cover wide range of topics on different aspects of character recognition. Hopefully, this book will serve as a reference source for academic research, for professionals working in the character recognition field and for all interested in the subject

Semi-supervised Learning with Deterministic Labeling and Large Margin Projection

The centrality and diversity of the labeled data are very influential to the performance of semi-supervised learning (SSL), but most SSL models select the labeled data randomly. This study first construct a leading forest that forms a partially ordered topological space in an unsupervised way, and select a group of most representative samples to label with one shot (differs from active learning essentially) using property of homeomorphism. Then a kernelized large margin metric is efficiently learned for the selected data to classify the remaining unlabeled sample. Optimal leading forest (OLF) has been observed to have the advantage of revealing the difference evolution along a path within a subtree. Therefore, we formulate an optimization problem based on OLF to select the samples. Also with OLF, the multiple local metrics learning is facilitated to address multi-modal and mix-modal problem in SSL, especially when the number of class is large. Attribute to this novel design, stableness and accuracy of the performance is significantly improved when compared with the state-of-the-art graph SSL methods. The extensive experimental studies have shown that the proposed method achieved encouraging accuracy and efficiency. Code has been made available at https://github.com/alanxuji/DeLaLA.Comment: 12 pages, ready to submit to a journa

Off-line Arabic Handwriting Recognition System Using Fast Wavelet Transform

In this research, off-line handwriting recognition system for Arabic alphabet is introduced. The system contains three main stages: preprocessing, segmentation and recognition stage. In the preprocessing stage, Radon transform was used in the design of algorithms for page, line and word skew correction as well as for word slant correction. In the segmentation stage, Hough transform approach was used for line extraction. For line to words and word to characters segmentation, a statistical method using mathematic representation of the lines and words binary image was used. Unlike most of current handwriting recognition system, our system simulates the human mechanism for image recognition, where images are encoded and saved in memory as groups according to their similarity to each other. Characters are decomposed into a coefficient vectors, using fast wavelet transform, then, vectors, that represent a character in different possible shapes, are saved as groups with one representative for each group. The recognition is achieved by comparing a vector of the character to be recognized with group representatives. Experiments showed that the proposed system is able to achieve the recognition task with 90.26% of accuracy. The system needs only 3.41 seconds a most to recognize a single character in a text of 15 lines where each line has 10 words on average