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Register a new userEnhanced Ensemble Clustering via Fast Propagation of Cluster-wise Similarities
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Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of the existing algorithms tend to investigate the ensemble information at the object-level, yet often lack the ability to explore the rich information at higher levels of granularity. Second, they mostly focus on the direct connections (e.g., direct intersection or pair-wise co-occurrence) in the multiple base clusterings, but generally neglect the multi-scale indirect relationship hidden in them. To address these two issues, this paper presents a novel ensemble clustering approach based on fast propagation of cluster-wise similarities via random walks. We first construct a cluster similarity graph with the base clusters treated as graph nodes and the cluster-wise Jaccard coefficient exploited to compute the initial edge weights. Upon the constructed graph, a transition probability matrix is defined, based on which the random walk process is conducted to propagate the graph structural information. Specifically, by investigating the propagating trajectories starting from different nodes, a new cluster-wise similarity matrix can be derived by considering the trajectory relationship. Then, the newly obtained cluster-wise similarity matrix is mapped from the cluster-level to the object-level to achieve an enhanced co-association (ECA) matrix, which is able to simultaneously capture the object-wise co-occurrence relationship as well as the multi-scale cluster-wise relationship in ensembles. Finally, two novel consensus functions are proposed to obtain the consensus clustering result. Extensive experiments on a variety of real-world datasets have demonstrated the effectiveness and efficiency of our approach.
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Pairwise similarities and dissimilarities between data points might be easier to obtain than fully labeled data in real-world classification problems, e.g., in privacy-aware situations. To handle such pairwise information, an empirical risk minimization approach has been proposed, giving an unbiased estimator of the classification risk that can be computed only from pairwise similarities and unlabeled data. However, this direction cannot handle pairwise dissimilarities so far. On the other hand, semi-supervised clustering is one of the methods which can use both similarities and dissimilarities. Nevertheless, they typically require strong geometrical assumptions on the data distribution such as the manifold assumption, which may deteriorate the performance. In this paper, we derive an unbiased risk estimator which can handle all of similarities/dissimilarities and unlabeled data. We theoretically establish estimation error bounds and experimentally demonstrate the practical usefulness of our empirical risk minimization method.
Though deep neural networks have achieved significant progress on various tasks, often enhanced by model ensemble, existing high-performance models can be vulnerable to adversarial attacks. Many efforts have been devoted to enhancing the robustness of individual networks and then constructing a straightforward ensemble, e.g., by directly averaging the outputs, which ignores the interaction among networks. This paper presents a new method that explores the interaction among individual networks to improve robustness for ensemble models. Technically, we define a new notion of ensemble diversity in the adversarial setting as the diversity among non-maximal predictions of individual members, and present an adaptive diversity promoting (ADP) regularizer to encourage the diversity, which leads to globally better robustness for the ensemble by making adversarial examples difficult to transfer among individual members. Our method is computationally efficient and compatible with the defense methods acting on individual networks. Empirical results on various datasets verify that our method can improve adversarial robustness while maintaining state-of-the-art accuracy on normal examples.
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on $L_1$ norm or even sub-linear potentials corresponding to quasinorms $L_p$ ($0<p<1$). The back side of these approaches is increase in computational cost for optimization. Till so far, no approaches have been suggested to deal with {it arbitrary} error functionals, in a flexible and computationally efficient framework. In this paper, we develop a theory and basic universal data approximation algorithms ($k$-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize {it arbitrary sub-quadratic error potentials} using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods.
Clustering ensemble has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering ensemble. One of the arguments for weighted clustering ensemble is that elements (clusterings or clusters) in a clustering ensemble are of different quality, or that objects or features are of varying significance. However, it is not possible to directly apply the weighting mechanisms from classification (supervised) domain to clustering (unsupervised) domain, also because clustering is inherently an ill-posed problem. This paper provides an overview of weighted clustering ensemble by discussing different types of weights, major approaches to determining weight values, and applications of weighted clustering ensemble to complex data. The unifying framework presented in this paper will help clustering practitioners select the most appropriate weighting mechanisms for their own problems.
To use neural networks in safety-critical settings it is paramount to provide assurances on their runtime operation. Recent work on ReLU networks has sought to verify whether inputs belonging to a bounded box can ever yield some undesirable output. Input-splitting procedures, a particular type of verification mechanism, do so by recursively partitioning the input set into smaller sets. The efficiency of these methods is largely determined by the number of splits the box must undergo before the property can be verified. In this work, we propose a new technique based on shadow prices that fully exploits the information of the problem yielding a more efficient generation of splits than the state-of-the-art. Results on the Airborne Collision Avoidance System (ACAS) benchmark verification tasks show a considerable reduction in the partitions generated which substantially reduces computation times. These results open the door to improved verification methods for a wide variety of machine learning applications including vision and control.
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