Transductive Learning for Spatial Data Classification

Learning classifiers of spatial data presents several issues, such as the heterogeneity of spatial objects, the implicit definition of spatial relationships among objects, the spatial autocorrelation and the abundance of unlabelled data which potentially convey a large amount of information. The first three issues are due to the inherent structure of spatial units of analysis, which can be easily accommodated if a (multi-)relational data mining approach is considered. The fourth issue demands for the adoption of a transductive setting, which aims to make predictions for a given set of unlabelled data. Transduction is also motivated by the contiguity of the concept of positive autocorrelation, which typically affect spatial phenomena, with the smoothness assumption which characterize the transductive setting. In this work, we investigate a relational approach to spatial classification in a transductive setting. Computational solutions to the main difficulties met in this approach are presented. In particular, a relational upgrade of the nave Bayes classifier is proposed as discriminative model, an iterative algorithm is designed for the transductive classification of unlabelled data, and a distance measure between relational descriptions of spatial objects is defined in order to determine the k-nearest neighbors of each example in the dataset. Computational solutions have been tested on two real-world spatial datasets. The transformation of spatial data into a multi-relational representation and experimental results are reported and commented

Interactive Segmentation in Multimodal Medical Imagery Using a Bayesian Transductive Learning Approach

Labeled training data in the medical domain is rare and expensive to obtain. The lack of labeled multimodal medical image data is a major obstacle for devising learning-based interactive segmentation tools. Transductive learning (TL) or semi-supervised learning (SSL) offers a workaround by leveraging unlabeled and labeled data to infer labels for the test set given a small portion of label information. In this paper we propose a novel algorithm for interactive segmentation using transductive learning and inference in conditional mixture nave Bayes models (T-CMNB) with spatial regularization constraints. T-CMNB is an extension of the transductive nave Bayes algorithm [1, 20]. The multimodal Gaussian mixture assumption on the class-conditional likelihood and spatial regularization constraints allow us to explain more complex distributions required for spatial classification in multimodal imagery. To simplify the estimation we reduce the parameter space by assuming nave conditional independence between the feature space and the class label. The nave conditional independence assumption allows efficient inference of marginal and conditional distributions for large scale learning and inference [19]. We evaluate the proposed algorithm on multimodal MRI brain imagery using ROC statistics and provide preliminary results. The algorithm shows promising segmentation performance with a sensitivity and specificity of 90.37% and 99.74% respectively and compares competitively to alternative interactive segmentation schemes

A novel spectral-spatial co-training algorithm for the transductive classification of hyperspectral imagery data

The automatic classification of hyperspectral data is made complex by several factors, such as the high cost of true sample labeling coupled with the high number of spectral bands, as well as the spatial correlation of the spectral signature. In this paper, a transductive collective classifier is proposed for dealing with all these factors in hyperspectral image classification. The transductive inference paradigm allows us to reduce the inference error for the given set of unlabeled data, as sparsely labeled pixels are learned by accounting for both labeled and unlabeled information. The collective inference paradigm allows us to manage the spatial correlation between spectral responses of neighboring pixels, as interacting pixels are labeled simultaneously. In particular, the innovative contribution of this study includes: (1) the design of an application-specific co-training schema to use both spectral information and spatial information, iteratively extracted at the object (set of pixels) level via collective inference; (2) the formulation of a spatial-aware example selection schema that accounts for the spatial correlation of predicted labels to augment training sets during iterative learning and (3) the investigation of a diversity class criterion that allows us to speed-up co-training classification. Experimental results validate the accuracy and efficiency of the proposed spectral-spatial, collective, co-training strategy

Spectral-spatial classification of hyperspectral images: three tricks and a new supervised learning setting

Spectral-spatial classification of hyperspectral images has been the subject of many studies in recent years. In the presence of only very few labeled pixels, this task becomes challenging. In this paper we address the following two research questions: 1) Can a simple neural network with just a single hidden layer achieve state of the art performance in the presence of few labeled pixels? 2) How is the performance of hyperspectral image classification methods affected when using disjoint train and test sets? We give a positive answer to the first question by using three tricks within a very basic shallow Convolutional Neural Network (CNN) architecture: a tailored loss function, and smooth- and label-based data augmentation. The tailored loss function enforces that neighborhood wavelengths have similar contributions to the features generated during training. A new label-based technique here proposed favors selection of pixels in smaller classes, which is beneficial in the presence of very few labeled pixels and skewed class distributions. To address the second question, we introduce a new sampling procedure to generate disjoint train and test set. Then the train set is used to obtain the CNN model, which is then applied to pixels in the test set to estimate their labels. We assess the efficacy of the simple neural network method on five publicly available hyperspectral images. On these images our method significantly outperforms considered baselines. Notably, with just 1% of labeled pixels per class, on these datasets our method achieves an accuracy that goes from 86.42% (challenging dataset) to 99.52% (easy dataset). Furthermore we show that the simple neural network method improves over other baselines in the new challenging supervised setting. Our analysis substantiates the highly beneficial effect of using the entire image (so train and test data) for constructing a model.Comment: Remote Sensing 201