In open set learning, a model must be able to generalize to novel classes when it encounters a sample that does not belong to any of the classes it has seen before. Open set learning poses a realistic learning scenario that is receiving growing attention. Existing studies on open set learning mainly focused on detecting novel classes, but few studies tried to model them for differentiating novel classes. In this paper, we recognize that novel classes should be different from each other, and propose distribution networks for open set learning that can model different novel classes based on probability distributions. We hypothesize that, through a certain mapping, samples from different classes with the same classification criterion should follow different probability distributions from the same distribution family. A deep neural network is learned to map the samples in the original feature space to a latent space where the distributions of known classes can be jointly learned with the network. We additionally propose a distribution parameter transfer and updating strategy for novel class modeling when a novel class is detected in the latent space. By novel class modeling, the detected novel classes can serve as known classes to the subsequent classification. Our experimental results on image datasets MNIST and CIFAR10 show that the distribution networks can detect novel classes accurately, and model them well for the subsequent classification tasks.
For a training dataset with a nonexhaustive list of classes, i.e. some classes are not yet known and hence are not represented, the resulting learning problem is ill-defined. In this case a sample from a missing class is incorrectly classified to one of the existing classes. For some applications the cost of misclassifying a sample could be negligible. However, the significance of this problem can better be acknowledged when the potentially undesirable consequences of incorrectly classifying a food pathogen as a nonpathogen are considered. Our research is directed towards the real-time detection of food pathogens using optical-scattering technology. Bacterial colonies consisting of the progeny of a single parent cell scatter light at 635 nm to produce unique forward-scatter signatures. These spectral signatures contain descriptive characteristics of bacterial colonies, which can be used to identify bacteria cultures in real time. One bottleneck that remains to be addressed is the nonexhaustive nature of the training library. It is very difficult if not impractical to collect samples from all possible bacteria colonies and construct a digital library with an exhaustive set of scatter signatures. This study deals with the real-time detection of samples from a missing class and the associated problem of learning with a nonexhaustive training dataset. Our proposed method assumes a common prior for the set of all classes, known and missing. The parameters of the prior are estimated from the samples of the known classes. This prior is then used to generate a large number of samples to simulate the space of missing classes. Finally a Bayesian maximum likelihood classifier is implemented using samples from real as well as simulated classes. Experiments performed with samples collected for 28 bacteria subclasses favor the proposed approach over the state of the art. We present a framework for online inference in the presence of a nonexhaustively defined set of classes that incorporates supervised classification with class discovery and modeling. A Dirichlet process prior (DPP) model defined over class distributions ensures that both known and unknown class distributions originate according to a common base distribution. In an attempt to automatically discover potentially interesting class formations, the prior model is coupled with a suitably chosen data model, and sequential Monte Carlo sampling is used to perform online inference. Our research is driven by a biodetection application, where a new class of pathogen may suddenly appear, and the rapid increase in the number of samples originating from this class indicates the onset of an outbreak. Technologies for rapid detection of bacterial pathogens are crucial for securing the food supply. A light-scattering sensor recently developed for real-time identification of multiple colonies has shown great promise for distinguishing bacteria cultures. The classification approach currently used with this system relies on supervised learning. For accurate classification of bacterial pathogens, the training library should be exhaustive, i.e., should consist of samples of all possible pathogens. Yet, the sheer number of existing bacterial serovars and more importantly the effect of their high mutation rate would not allow for a practical and manageable training. In this study, we propose a Bayesian approach to learning with a nonexhaustive training dataset for automated detection of unknown bacterial serovars, i.e., serovars for which no samples exist in the training library. The main contribution of our work is the Wishart conjugate priors defined over class distributions. This allows us to employ the prior information obtained from known classes to make inferences about unknown classes as well. By this means, we identify new classes of informational value and dynamically update the training dataset with these classes to make it increasingly more representative of the sample population. This results in a classifier with improved predictive performance for future samples. We evaluated our approach on a 28-class bacteria dataset and also on the benchmark 26-class letter recognition dataset for further validation. The proposed approach is compared against state-of-the-art involving density-based approaches and support vector domain description, as well as a recently introduced Bayesian approach based on simulated classes. Copyright © 2010 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 3: 289-301, 2010