Locally adaptive metrics for clustering high dimensional data

Clustering suffers from the curse of dimensionality, and similarity functions that use all input features with equal relevance may not be effective. We introduce an algorithm that discovers clusters in subspaces spanned by different combinations of dimensions via local weightings of features. This approach avoids the risk of loss of information encountered in global dimensionality reduction techniques, and does not assume any data distribution model. Our method associates to each cluster a weight vector, whose values capture the relevance of features within the corresponding cluster. We experimentally demonstrate the gain in perfomance our method achieves with respect to competitive methods, using both synthetic and real datasets. In particular, our results show the feasibility of the proposed technique to perform simultaneous clustering of genes and conditions in gene expression data, and clustering of very high-dimensional data such as text data.     

An effective double-bounded tree-connected Isomap algorithm for microarray data classification

Isometric mapping (Isomap) is a popular nonlinear dimensionality reduction technique which has shown high potential in visualization and classification. However, it appears sensitive to noise or scarcity of observations. This inadequacy may hinder its application for the classification of microarray data, in which the expression levels of thousands of genes in a few normal and tumor sample tissues are measured. In this paper we propose a double-bounded tree-connected variant of Isomap, aimed at being more robust to noise and outliers when used for classification and also computationally more efficient. It differs from the original Isomap in the way the neighborhood graph is generated: in the first stage we apply a double-bounding rule that confines the search to at most k nearest neighbors contained within an ε-radius hypersphere; the resulting subgraphs are then joined by computing a minimum spanning tree among the connected components. We therefore achieve a connected graph without unnaturally inflating the values of k and ε. The computational experiences show that the new method performs significantly better in terms of accuracy with respect to Isomap, k-edge-connected Isomap and the direct application of support vector machines to data in the input space, consistently across seven microarray datasets considered in our tests.     

Composite kernels for semi-supervised clustering

A critical problem related to kernel-based methods is how to select optimal kernels. A kernel function must conform to the learning target in order to obtain meaningful results. While solutions to the problem of estimating optimal kernel functions and corresponding parameters have been proposed in a supervised setting, it remains a challenge when no labeled data are available, and all we have is a set of pairwise must-link and cannot-link constraints. In this paper, we address the problem of optimizing the kernel function using pairwise constraints for semi-supervised clustering. We propose a new optimization criterion for automatically estimating the optimal parameters of composite Gaussian kernels, directly from the data and given constraints. We combine our proposal with a semi-supervised kernel-based algorithm to demonstrate experimentally the effectiveness of our approach. The results show that our method is very effective for kernel-based semi-supervised clustering.     

Projective clustering ensembles

A considerable amount of work has been done in data clustering research during the last four decades, and a myriad of methods has been proposed focusing on different data types, proximity functions, cluster representation models, and cluster presentation. However, clustering remains a challenging problem due to its ill-posed nature: it is well known that off-the-shelf clustering methods may discover different patterns in a given set of data, mainly because every clustering algorithm has its own bias resulting from the optimization of different criteria. This bias becomes even more important as in almost all real-world applications, data is inherently high-dimensional and multiple clustering solutions might be available for the same data collection. In this respect, the problems of projective clustering and clustering ensembles have been recently defined to deal with the high dimensionality and multiple clusterings issues, respectively. Nevertheless, despite such two issues can often be encountered together, existing approaches to the two problems have been developed independently of each other. In our earlier work Gullo et al. (Proceedings of the international conference on data mining (ICDM), 2009a) we introduced a novel clustering problem, called projective clustering ensembles (PCE): given a set (ensemble) of projective clustering solutions, the goal is to derive a projective consensus clustering, i.e., a projective clustering that complies with the information on object-to-cluster and the feature-to-cluster assignments given in the ensemble. In this paper, we enhance our previous study and provide theoretical and experimental insights into the PCE problem. PCE is formalized as an optimization problem and is designed to satisfy desirable requirements on independence from the specific clustering ensemble algorithm, ability to handle hard as well as soft data clustering, and different feature weightings. Two PCE formulations are defined: a two-objective optimization problem, in which the two objective functions respectively account for the object- and feature-based representations of the solutions in the ensemble, and a single-objective optimization problem, in which the object- and feature-based representations are embedded into a single function to measure the distance error between the projective consensus clustering and the projective ensemble. The significance of the proposed methods for solving the PCE problem has been shown through an extensive experimental evaluation based on several datasets and comparatively with projective clustering and clustering ensemble baselines.     

On the composition of the essential oils of Artemisia genipi Weber and Artemisia umbelliformis Lam

Summary A comparison was made between the essential oil ofArtemisia genipi Weber, a rare and expensive plant employed in manufacturing liqueurs in Piemonte and Aosta Valley, and that ofArtemisia unbelliformis Lam., a less rare and costly plant, which often is used substitute the former. The essential oils, obtained by steam-distillation of the aerial parts of the two plants, after separation into fractions on a silica gel column, were investigated by means of GLC and GLC-MS. -Pinene,-thujone,-thujone and terpinen-4-ol were the main components ofArtemisia genipi Weber, totalling 63.1%.-Thujone,-thujone, sabinyl isovalerate and spathulenol were the main components ofArtemisia unbelliformis Lam., totalling 71.3%. Several other minor constituents have been identified and are reported.

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Über die Zusammensetzung der ätherischen Öle von Artemisia genipi Weber und Artemisia umbelliformis Lam

Zusammenfassung Es wurde ein Vergleich zwischen dem ätherischen Öl derArtemisia genipi Weber, einer seltenen und wertvollen in der Likörproduktion in Piemont und im Aostatal verwendeten Pflanze und dem vonA. umbelliformis Lam., einer weniger seltenen und weniger kostspieligen Pflanze gemacht. Die ätherischen Öle, durch Wasserdampfdestillation aus Blättern und Blüten von den zwei Pflanzen erhalten, wurden nach Säulenchromatographie an Kieselgel mittels GLC und GLC-MS analysiert.-Pinen,-Thujon,-Thujon und Terpinen-4-ol bilden 63,1% des Öls vonArtemisia genipi Weber;-Thujon,-Thujon, Sabinylisovalerianat und Spathuleol bilden 71,3% des Öls vonA. umbelliformis Lam. Darüber hinaus wurden weitere Bestandteile identifiziert und beschrieben.

     

Selectivity estimators for multidimensional range queries over real attributes

Estimating the selectivity of multidimensional range queries over real valued attributes has significant applications in data exploration and database query optimization. In this paper, we consider the following problem: given a table of d attributes whose domain is the real numbers and a query that specifies a range in each dimension, find a good approximation of the number of records in the table that satisfy the query. The simplest approach to tackle this problem is to assume that the attributes are independent. More accurate estimators try to capture the joint data distribution of the attributes. In databases, such estimators include the construction of multidimensional histograms, random sampling, or the wavelet transform. In statistics, kernel estimation techniques are being used. Many traditional approaches assume that attribute values come from discrete, finite domains, where different values have high frequencies. However, for many novel applications (as in temporal, spatial, and multimedia databases) attribute values come from the infinite domain of real numbers. Consequently, each value appears very infrequently, a characteristic that affects the behavior and effectiveness of the estimator. Moreover, real-life data exhibit attribute correlations that also affect the estimator. We present a new histogram technique that is designed to approximate the density of multidimensional datasets with real attributes. Our technique defines buckets of variable size and allows the buckets to overlap. The size of the cells is based on the local density of the data. The use of overlapping buckets allows a more compact approximation of the data distribution. We also show how to generalize kernel density estimators and how to apply them to the multidimensional query approximation problem. Finally, we compare the accuracy of the proposed techniques with existing techniques using real and synthetic datasets. The experimental results show that the proposed techniques behave more accurately in high dimensionalities than previous approaches.Received: 30 January 2001, Accepted: 9 June 2003, Published online: 4 March 2004Edited by: Y. IoannidisDimitrios Gunopulos: Supported by NSF ITR-0220148, NSF IIS-9907477 CAREER Award, NSF IIS-9984729, and NRDRP.George Kollios: Supported by NSF IIS-0133825 CAREER Award.Vassilis J. Tsotras: Supported by NSF IIS-9907477 and the US Dept. of Defense.     

Rotation-minimizing osculating frames

An orthonormal frame (_f1,_f2,_f3)$({\mathbf{f}}_1,{\mathbf{f}}_2,{\mathbf{f}}_3)$ is rotation-minimizing   with respect to _fi${\mathbf{f}}_i$ if its angular velocity ω   satisfies ω⋅_fi≡0$\mathit{\omega }\cdot {\mathbf{f}}_i\equiv 0$ — or, equivalently, the derivatives of _fj${\mathbf{f}}_j$ and _fk${\mathbf{f}}_k$ are both parallel to _fi${\mathbf{f}}_i$. The Frenet frame (t,p,b)$(\mathbf{t},\mathbf{p},\mathbf{b})$ along a space curve is rotation-minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation-minimizing with respect to the tangent t have attracted much interest. This study is concerned with rotation-minimizing osculating   frames (f,g,b)$(\mathbf{f},\mathbf{g},\mathbf{b})$ incorporating the binormal b, and osculating-plane vectors f, g that have no rotation about b. These frame vectors may be defined through a rotation of t, p by an angle equal to minus the integral of curvature with respect to arc length. In aeronautical terms, the rotation-minimizing osculating frame (RMOF) specifies yaw-free rigid-body motion along a curved path. For polynomial space curves possessing rational Frenet frames, the existence of rational RMOFs is investigated, and it is found that they must be of degree 7 at least. The RMOF is also employed to construct a novel type of ruled surface, with the property that its tangent planes coincide with the osculating planes of a given space curve, and its rulings exhibit the least possible rate of rotation consistent with this constraint.     

Adverse pregnancy outcomes in a population exposed to the emissions of a municipal waste incinerator

Some contaminants emitted by municipal waste incinerators are believed to adversely affect reproductive health in the exposed populations; yet only limited and conflicting epidemiologic evidence on this issue has been provided so far. In this study we analyzed rates of spontaneous abortion and prevalence at birth of congenital anomalies in women residing or working near the municipal solid waste incinerator of Modena, northern Italy, during the 2003--2006 period and who experienced higher levels of exposure to polychlorinated dibenzo-p-dioxins and dibenzofurans, compared to the remaining municipal population. In women residing in two areas close to the incinerator plant with increasing exposure to dioxins, we did not detect an excess risk of miscarriage (relative risk [RR] 1.00, 95% confidence interval [CI] 0.65-1.48) and of birth defects (RR 0.64, 95% CI 0.20-1.55), nor did any indication of dose-response relation emerge. Among female workers employed in the factories located in the exposed areas, we did not observe a higher risk of spontaneous abortion (RR 1.04, 95% CI 0.38-2.30); however, an increase in prevalence of birth defects was noted (RR 2.26), although this risk estimate was statistically very unstable (95% CI 0.57-6.14). Overall, the study results provide little evidence of an excess risk of adverse pregnancy outcomes in women exposed to emissions from a modern municipal solid waste incinerator.