A kernel-based framework for learning graded relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Empirical White Noise Processes and the Subjective Probabilistic Approaches

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis

Uncertainty-Aware Principal Component Analysis

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach

Separating a Real-Life Nonlinear Image Mixture

When acquiring an image of a paper document, the image printed on the back page sometimes shows through. The mixture of the front- and back-page images thus obtained is markedly nonlinear, and thus constitutes a good real-life test case for nonlinear blind source separation. This paper addresses a difficult version of this problem, corresponding to the use of "onion skin" paper, which results in a relatively strong nonlinearity of the mixture, which becomes close to singular in the lighter regions of the images. The separation is achieved through the MISEP technique, which is an extension of the well known INFOMAX method. The separation results are assessed with objective quality measures. They show an improvement over the results obtained with linear separation, but have room for further improvement

Semantic Information G Theory and Logical Bayesian Inference for Machine Learning

An important problem with machine learning is that when label number n\u3e2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic