In this paper, we focus on finding clusters in partially categorized data sets. We propose a semi-supervised version of Gaussian mixture model, called C3L, which retrieves natural subgroups of given categories. In contrast to other semi-supervised models, C3L is parametrized by user-defined leakage level, which controls maximal inconsistency between initial categorization and resulting clustering. Our method can be implemented as a module in practical expert systems to detect clusters, which combine expert knowledge with true distribution of data. Moreover, it can be used for improving the results of less flexible clustering techniques, such as projection pursuit clustering. The paper presents extensive theoretical analysis of the model and fast algorithm for its efficient optimization. Experimental results show that C3L finds high quality clustering model, which can be applied in discovering meaningful groups in partially classified data.
Clustering with pairwise constraints was introduced by @cite_37 , who created a variant of k-means, which focuses on preserving all constraints. @cite_13 constructed a version of Gaussian mixture model, which gathers data points into equivalence classes (called chunklets) using must-link relation and then applied EM algorithm on such generalized data set of chunklets. This approach was later modified to multi-modal clustering models @cite_27 . The aforementioned methods work well with noiseless side information, but deteriorate the results when some constraints are mislabeled. To overcome this problem, the authors of @cite_17 @cite_7 applied hidden Markov random fields (HMRF) to construct more sophisticated dependencies between linked points. However, the use of HMRF leads to complex solutions, which are difficult to optimize. In recent years, Asafi and Cohen-Or. @cite_22 suggested reducing distances between data points with a must-link constraint and adding a dimension for each cannot-link constraint. After updating all other distances to, e.g., satisfy the triangle inequality, the thus obtained pairwise distance matrix can be used for unsupervised learning. Wang and Davidson @cite_32 proposed a version of spectral clustering, which relies on solving a generalized eigenvalue problem.
@cite_37 @cite_22 @cite_7 @cite_32 @cite_27 @cite_13 @cite_17
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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. In this paper, we introduce a new approach to constrained clustering which treats the constraints as features. Our method augments the original feature space with additional dimensions, each of which derived from a given Cannot-link constraints. The specified Cannot-link pair gets extreme coordinates values, and the rest of the points get coordinate values that express their spatial influence from the specified constrained pair. After augmenting all the new features, a standard unconstrained clustering algorithm can be performed, like k-means or spectral clustering. We demonstrate the efficacy of our method for active semi-supervised learning applied to image segmentation and compare it to alternative methods. We also evaluate the performance of our method on the four most commonly evaluated datasets from the UCI machine learning repository. Constrained clustering has been well-studied for algorithms like K-means and hierarchical agglomerative clustering. However, how to encode constraints into spectral clustering remains a developing area. In this paper, we propose a flexible and generalized framework for constrained spectral clustering. In contrast to some previous efforts that implicitly encode Must-Link and Cannot-Link constraints by modifying the graph Laplacian or the resultant eigenspace, we present a more natural and principled formulation, which preserves the original graph Laplacian and explicitly encodes the constraints. Our method offers several practical advantages: it can encode the degree of belief (weight) in Must-Link and Cannot-Link constraints; it guarantees to lower-bound how well the given constraints are satisfied using a user-specified threshold; and it can be solved deterministically in polynomial time through generalized eigendecomposition. Furthermore, by inheriting the objective function from spectral clustering and explicitly encoding the constraints, much of the existing analysis of spectral clustering techniques is still valid. Consequently our work can be posed as a natural extension to unconstrained spectral clustering and be interpreted as finding the normalized min-cut of a labeled graph. We validate the effectiveness of our approach by empirical results on real-world data sets, with applications to constrained image segmentation and clustering benchmark data sets with both binary and degree-of-belief constraints. Density estimation with Gaussian Mixture Models is a popular generative technique used also for clustering. We develop a framework to incorporate side information in the form of equivalence constraints into the model estimation procedure. Equivalence constraints are defined on pairs of data points, indicating whether the points arise from the same source (positive constraints) or from different sources (negative constraints). Such constraints can be gathered automatically in some learning problems, and are a natural form of supervision in others. For the estimation of model parameters we present a closed form EM procedure which handles positive constraints, and a Generalized EM procedure using a Markov net which handles negative constraints. Using publicly available data sets we demonstrate that such side information can lead to considerable improvement in clustering tasks, and that our algorithm is preferable to two other suggested methods using the same type of side information. Unsupervised clustering can be significantly improved using supervision in the form of pairwise constraints, i.e., pairs of instances labeled as belonging to same or different clusters. In recent years, a number of algorithms have been proposed for enhancing clustering quality by employing such supervision. Such methods use the constraints to either modify the objective function, or to learn the distance measure. We propose a probabilistic model for semi-supervised clustering based on Hidden Markov Random Fields (HMRFs) that provides a principled framework for incorporating supervision into prototype-based clustering. The model generalizes a previous approach that combines constraints and Euclidean distance learning, and allows the use of a broad range of clustering distortion measures, including Bregman divergences (e.g., Euclidean distance and I-divergence) and directional similarity measures (e.g., cosine similarity). We present an algorithm that performs partitional semi-supervised clustering of data by minimizing an objective function derived from the posterior energy of the HMRF model. Experimental results on several text data sets demonstrate the advantages of the proposed framework.