Implicitly Constrained Semi-Supervised Linear Discriminant Analysis

Semi-supervised learning is an important and active topic of research in pattern recognition. For classification using linear discriminant analysis specifically, several semi-supervised variants have been proposed. Using any one of these methods is not guaranteed to outperform the supervised classifier which does not take the additional unlabeled data into account. In this work we compare traditional Expectation Maximization type approaches for semi-supervised linear discriminant analysis with approaches based on intrinsic constraints and propose a new principled approach for semi-supervised linear discriminant analysis, using so-called implicit constraints. We explore the relationships between these methods and consider the question if and in what sense we can expect improvement in performance over the supervised procedure. The constraint based approaches are more robust to misspecification of the model, and may outperform alternatives that make more assumptions on the data, in terms of the log-likelihood of unseen objects.Comment: 6 pages, 3 figures and 3 tables. International Conference on Pattern Recognition (ICPR) 2014, Stockholm, Swede

Semi-Supervised Discriminant Analysis Using Robust Path-Based Similarity

Linear Discriminant Analysis (LDA), which works by maximizing the within-class similarity and minimizing the between-class similarity simultaneously, is a popular dimensionality reduction technique in pattern recognition and machine learning. In real-world applications when labeled data are limited, LDA does not work well. Under many situations, however, it is easy to obtain unlabeled data in large quantities. In this paper, we propose a novel dimensionality reduction method, called Semi-Supervised Discriminant Analysis (SSDA), which can utilize both labeled and unlabeled data to perform dimensionality reduction in the semisupervised setting. Our method uses a robust path-based similarity measure to capture the manifold structure of the data and then uses the obtained similarity to maximize the separability between different classes. A kernel extension of the proposed method for nonlinear dimensionality reduction in the semi-supervised setting is also presented. Experiments on face recognition demonstrate the effectiveness of the proposed method. 1

Latent Fisher Discriminant Analysis

Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection and keyframe extraction cannot provide consistent instance-label pairs, while LDA requires labels on instance level for training. Thus it cannot be directly applied for semi-supervised classification problem. In this paper, we overcome this limitation and propose a latent variable Fisher discriminant analysis model. We relax the instance-level labeling into bag-level, is a kind of semi-supervised (video-level labels of event type are required for semantic frame extraction) and incorporates a data-driven prior over the latent variables. Hence, our method combines the latent variable inference and dimension reduction in an unified bayesian framework. We test our method on MUSK and Corel data sets and yield competitive results compared to the baseline approach. We also demonstrate its capacity on the challenging TRECVID MED11 dataset for semantic keyframe extraction and conduct a human-factors ranking-based experimental evaluation, which clearly demonstrates our proposed method consistently extracts more semantically meaningful keyframes than challenging baselines.Comment: 12 page

Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications

Food authenticity studies are concerned with determining if food samples have been correctly labelled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a model-based discriminant analysis method that includes variable selection is presented. The discriminant analysis model is fitted in a semi-supervised manner using both labeled and unlabeled data. The method is shown to give excellent classification performance on several high-dimensional multiclass food authenticity datasets with more variables than observations. The variables selected by the proposed method provide information about which variables are meaningful for classification purposes. A headlong search strategy for variable selection is shown to be efficient in terms of computation and achieves excellent classification performance. In applications to several food authenticity datasets, our proposed method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial margins

Semi-supervised Learning for Ordinal Kernel Discriminant Analysis

Ordinal classication considers those classication problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or di_cult to obtain in this type of problems because, in many cases, ordinal labels are given by an user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classi_cation where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classi_cation, which is combined with our developed classi_cation strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classication in a battery of 30 datasets, showing 1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and 2) the advantage of computing distances in the feature space induced by the kernel function

Classification via semi-Riemannian spaces

In this paper, we develop a geometric framework for linear or nonlinear discriminant subspace learning and classification. In our framework, the structures of classes are conceptualized as a semi-Riemannian manifold which is considered as a submanifold embedded in an ambient semi-Riemannian space. The class structures of original samples can be characterized and deformed by local metrics of the semi-Riemannian space. Semi-Riemannian metrics are uniquely determined by the smoothing of discrete functions and the nullity of the semi-Riemannian space. Based on the geometrization of class structures, optimizing class structures in the feature space is equivalent to maximizing the quadratic quantities of metric tensors in the semi-Riemannian space. Thus supervised discriminant subspace learning reduces to unsupervised semi-Riemannian manifold learning. Based on the proposed framework, a novel algorithm, dubbed as Semi-Riemannian Discriminant Analysis (SRDA), is presented for subspace-based classification. The performance of SRDA is tested on face recognition (singular case) and handwritten capital letter classification (nonsingular case) against existing algorithms. The experimental results show that SRDA works well on recognition and classification, implying that semi-Riemannian geometry is a promising new tool for pattern recognition and machine learning. 1