SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Matrix computations (3rd ed.)
Computing depth contours of bivariate point clouds
Computational Statistics & Data Analysis - Special issue on classification
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
Large data series: modeling the usual to identify the unusual
Computational Statistics & Data Analysis
Geometric methods and applications: for computer science and engineering
Geometric methods and applications: for computer science and engineering
Properties of Embedding Methods for Similarity Searching in Metric Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A method of relational fuzzy clustering based on producing feature vectors using FastMap
Information Sciences: an International Journal
A Matrix Computation View of FastMap and RobustMap Dimension Reduction Algorithms
SIAM Journal on Matrix Analysis and Applications
Descriptive matrix factorization for sustainability Adopting the principle of opposites
Data Mining and Knowledge Discovery
Utilising wireless sensor networks towards establishing a method of sleep profiling
International Journal of Computers in Healthcare
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FastMap is a dimension reduction technique that operates on distances between objects. Although only distances are used, implicitly the technique assumes that the objects are points in a p\hbox{-}{\rm{dimensional}} Euclidean space. It selects a sequence of k\leq p orthogonal axes defined by distant pairs of points (called pivots) and computes the projection of the points onto the orthogonal axes. We show that FastMap uses only the outer envelope of a data set. Pivots are taken from the faces, usually vertices, of the convex hull of the data points in the original implicit Euclidean space. This provides a bridge to results in robust statistics, where the convex hull is used as a tool in multivariate outlier detection and in robust estimation methods. The connection sheds new light on the properties of FastMap, particularly its sensitivity to outliers, and provides an opportunity for a new class of dimension reduction algorithms, RobustMaps, that retain the speed of FastMap and exploit ideas in robust statistics.