A companion set of lecture slides is available at

This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.

For many KDD applications, such as detecting criminal activities in E-commerce, finding the rare instances or the outliers, can be more interesting than finding the common patterns. Existing work in outlier detection regards being an outlier as a binary property. In this paper, we contend that for many scenarios, it is more meaningful to assign to each object a degree of being an outlier. This degree is called the local outlier factor (LOF) of an object. It is local in that the degree depends on how isolated the object is with respect to the surrounding neighborhood. We give a detailed formal analysis showing that LOF enjoys many desirable properties. Using realworld datasets, we demonstrate that LOF can be used to find outliers which appear to be meaningful, but can otherwise not be identified with existing approaches. Finally, a careful performance evaluation of our algorithm confirms we show that our approach of finding local outliers can be practical.

Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique

This paper describes a new approach to low level image processing; in particular, edge and corner detection and structure preserving noise reduction.

Abstract-There is considerable evidence that visual attention is concentrated at a single locus in the visual field, and that this locus can be moved independent of eye movements. Two studies are reported which suggest that, while certain aspects of attention require that locations\be scanned serially, at least one operation may be carried out in parallel across several independent loci in the visual field. That is the operation of indexing features and tracking their identity. The studies show that: (a) subjects are able to track a subset of up to 5 objects in a field of 10 'identical randomly-moving objects in order to distinguish a change in a target from a change in a distractor; and (b) when the speed and distance parameters of the display are designed so that, on the basis of some very conservative assumptions about the speed of attention movement and encoding times, the predicted performance of a serial scanning and updating algorithm would not exceed about 40 % accuracy, subjects still manage to do the task with 87 % accuracy. These findings are discussed in relation to an earlier, and independently motivated model of featurebinding-called the FINST model-which posits a primitive identity maintenance mechanism that indexes and tracks a limited number ofvisual objects in parallel. These indexes are hypothesized to serve the function of binding visual features prior to subsequent pattern recognition.

Wolford, and two anonymous reviewers for very useful comments on earlier drafts of the manuscript. Correspondence may be addressed to

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Finding structures in vast multidimensional data sets, be they measurement data, statistics, or textual documents, is difficult and time-consuming. Interesting, novel relations between the data items may be hidden in the data. The selforganizing map (SOM) algorithm of Kohonen can be used to aid the exploration: the structures in the data sets can be illustrated on special map displays. In this work, the methodology of using SOMs for exploratory data analysis or data mining is reviewed and developed further. The properties of the maps are compared with the properties of related methods intended for visualizing highdimensional multivariate data sets. In a set of case studies the SOM algorithm is applied to analyzing electroencephalograms, to illustrating structures of the standard of living in the world, and to organizing full-text document collections. Measures are proposed for evaluating the quality of different types of maps in representing a given data set, and for measuring the robu...

This paper investigates a variant of boosting, L 2 Boost, which is constructed from a functional gradient descent algorithm with the L 2 -loss function. Based on an explicit stagewise re tting expression of L 2 Boost, the case of (symmetric) linear weak learners is studied in detail in both regression and two-class classification. In particular, with the boosting iteration m working as the smoothing or regularization parameter, a new exponential bias-variance trade off is found with the variance (complexity) term bounded as m tends to infinity. When the weak learner is a smoothing spline, an optimal rate of convergence result holds for both regression and two-class classification. And this boosted smoothing spline adapts to higher order, unknown smoothness. Moreover, a simple expansion of the 0-1 loss function is derived to reveal the importance of the decision boundary, bias reduction, and impossibility of an additive bias-variance decomposition in classification. Finally, simulation and real data set results are obtained to demonstrate the attractiveness of L 2 Boost, particularly with a novel component-wise cubic smoothing spline as an effective and practical weak learner.