Semi-supervised clustering is an very important topic in machine learning and computer vision. The key challenge of this problem is how to learn a metric, such that the instances sharing the same label are more likely close to each other on the embedded space. However, little attention has been paid to learn better representations when the data lie on non-linear manifold. Fortunately, deep learning has led to great success on feature learning recently. Inspired by the advances of deep learning, we propose a deep transductive semi-supervised maximum margin clustering approach. More specifically, given pairwise constraints, we exploit both labeled and unlabeled data to learn a non-linear mapping under maximum margin framework for clustering analysis. Thus, our model unifies transductive learning, feature learning and maximum margin techniques in the semi-supervised clustering framework. We pretrain the deep network structure with restricted Boltzmann machines (RBMs) layer by layer greedily, and optimize our objective function with gradient descent. By checking the most violated constraints, our approach updates the model parameters through error backpropagation, in which deep features are learned automatically. The experimental results shows that our model is significantly better than the state of the art on semi-supervised clustering.
The maximum margin clustering (MMC) aims to find the hyperplanes that can partition the data into different clusters over all possible labels with large margins @cite_10 @cite_28 @cite_12 . Nevertheless, the accuracy of the clustering results by MMC may not be good sometimes due to the nature of its unsupervised learning @cite_11 . Thus, it is interested to incorporate semi-supervised information, e.g. the pairwise constraints, into the recently proposed maximum margin clustering framework. Recent research demonstrates the advantages by leveraging pairwise constraints on the semi-supervised clustering problems @cite_30 @cite_13 @cite_2 @cite_17 @cite_1 @cite_8 . In particular, COPKmeans [11] is a semi-supervised variant of Kmeans, by following the same clustering procedure of Kmeans while avoiding violations of pairwise constraints. MPCKmeans @cite_8 extended Kmeans and utilized both metric learning and pairwise constraints in the clustering process. More recently, @cite_3 show that they can improve classification with pairwise constraints under maximum margin framework. @cite_4 leverage the margin-based approach on the semi-supervised clustering problems, and yield competitive results.
@cite_30 @cite_13 @cite_4 @cite_8 @cite_28 @cite_1 @cite_17 @cite_3 @cite_2 @cite_10 @cite_12 @cite_11
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Clustering is traditionally viewed as an unsupervised method for data analysis. However, in some cases information about the problem domain is available in addition to the data instances themselves. In this paper, we demonstrate how the popular k-means clustering algorithm can be protably modied to make use of this information. In experiments with articial constraints on six data sets, we observe improvements in clustering accuracy. We also apply this method to the real-world problem of automatically detecting road lanes from GPS data and observe dramatic increases in performance. We present an improved method for clustering in the presence of very limited supervisory information, given as pairwise instance constraints. By allowing instance-level constraints to have space-level inductive implications, we are able to successfully incorporate constraints for a wide range of data set types. Our method greatly improves on the previously studied constrained k-means algorithm, generally requiring less than half as many constraints to achieve a given accuracy on a range of real-world data, while also being more robust when over-constrained. We additionally discuss an active learning algorithm which increases the value of constraints even further. Semi-supervised clustering employs a small amount of labeled data to aid unsupervised learning. Previous work in the area has utilized supervised data in one of two approaches: 1) constraint-based methods that guide the clustering algorithm towards a better grouping of the data, and 2) distance-function learning methods that adapt the underlying similarity metric used by the clustering algorithm. This paper provides new methods for the two approaches as well as presents a new semi-supervised clustering algorithm that integrates both of these techniques in a uniform, principled framework. Experimental results demonstrate that the unified approach produces better clusters than both individual approaches as well as previously proposed semi-supervised clustering algorithms. Maximum margin clustering was proposed lately and has shown promising performance in recent studies [1, 2]. It extends the theory of support vector machine to unsupervised learning. Despite its good performance, there are three major problems with maximum margin clustering that question its efficiency for real-world applications. First, it is computationally expensive and difficult to scale to large-scale datasets because the number of parameters in maximum margin clustering is quadratic in the number of examples. Second, it requires data preprocessing to ensure that any clustering boundary will pass through the origins, which makes it unsuitable for clustering unbalanced dataset. Third, it is sensitive to the choice of kernel functions, and requires external procedure to determine the appropriate values for the parameters of kernel functions. In this paper, we propose "generalized maximum margin clustering" framework that addresses the above three problems simultaneously. The new framework generalizes the maximum margin clustering algorithm by allowing any clustering boundaries including those not passing through the origins. It significantly improves the computational efficiency by reducing the number of parameters. Furthermore, the new framework is able to automatically determine the appropriate kernel matrix without any labeled data. Finally, we show a formal connection between maximum margin clustering and spectral clustering. We demonstrate the efficiency of the generalized maximum margin clustering algorithm using both synthetic datasets and real datasets from the UCI repository. We present an approach to clustering based on the observa- tion that "it is easier to criticize than to construct." Our approach of semi- supervised clustering allows a user to iteratively provide feedback to a clus- tering algorithm. The feedback is incorporated in the form of constraints, which the clustering algorithm attempts to satisfy on future iterations. These constraints allow the user to guide the clusterer toward clusterings of the data that the user finds more useful. We demonstrate semi-supervised clustering with a system that learns to cluster news stories from a Reuters data set. 1 We address the problem of learning distance metrics using side-information in the form of groups of "similar" points. We propose to use the RCA algorithm, which is a simple and efficient algorithm for learning a full ranked Mahalanobis metric (, 2002). We first show that RCA obtains the solution to an interesting optimization problem, founded on an information theoretic basis. If the Mahalanobis matrix is allowed to be singular, we show that Fisher's linear discriminant followed by RCA is the optimal dimensionality reduction algorithm under the same criterion. We then show how this optimization problem is related to the criterion optimized by another recent algorithm for metric learning (, 2002), which uses the same kind of side information. We empirically demonstrate that learning a distance metric using the RCA algorithm significantly improves clustering performance, similarly to the alternative algorithm. Since the RCA algorithm is much more efficient and cost effective than the alternative, as it only uses closed form expressions of the data, it seems like a preferable choice for the learning of full rank Mahalanobis distances. Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar." For instance, we may ask them to provide examples. In this paper, we present an algorithm that, given examples of similar (and, if desired, dissimilar) pairs of points in ℝn, learns a distance metric over ℝn that respects these relationships. Our method is based on posing metric learning as a convex optimization problem, which allows us to give efficient, local-optima-free algorithms. We also demonstrate empirically that the learned metrics can be used to significantly improve clustering performance. We propose a new method for clustering based on finding maximum margin hyperplanes through data. By reformulating the problem in terms of the implied equivalence relation matrix, we can pose the problem as a convex integer program. Although this still yields a difficult computational problem, the hard-clustering constraints can be relaxed to a soft-clustering formulation which can be feasibly solved with a semidefinite program. Since our clustering technique only depends on the data through the kernel matrix, we can easily achieve nonlinear clusterings in the same manner as spectral clustering. Experimental results show that our maximum margin clustering technique often obtains more accurate results than conventional clustering methods. The real benefit of our approach, however, is that it leads naturally to a semi-supervised training method for support vector machines. By maximizing the margin simultaneously on labeled and unlabeled training data, we achieve state of the art performance by using a single, integrated learning principle. The pairwise constraints specifying whether a pair of samples should be grouped together or not have been successfully incorporated into the conventional clustering methods such as k-means and spectral clustering for the performance enhancement. Nevertheless, the issue of pairwise constraints has not been well studied in the recently proposed maximum margin clustering (MMC), which extends the maximum margin framework in supervised learning for clustering and often shows a promising performance. This paper therefore proposes a pairwise constrained MMC algorithm. Based on the maximum margin idea in MMC, we propose a set of effective loss functions for discouraging the violation of given pairwise constraints. For the resulting optimization problem, we show that the original nonconvex problem in our approach can be decomposed into a sequence of convex quadratic program problems via constrained concave-convex procedure (CCCP). Subsequently, we present an efficient subgradient projection optimization method to solve each convex problem in the CCCP sequence. Experiments on a number of real-world data sets show that the proposed constrained MMC algorithm is scalable and outperforms the existing constrained MMC approach as well as the typical semi-supervised clustering counterparts.