Beyond uniformity and independence: analysis of R-trees using the concept of fractal dimension
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The SR-tree: an index structure for high-dimensional nearest neighbor queries
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
Automatic subspace clustering of high dimensional data for data mining applications
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Self-spacial join selectivity estimation using fractal concepts
ACM Transactions on Information Systems (TOIS)
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
OPTICS: ordering points to identify the clustering structure
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Fast algorithms for projected clustering
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Finding generalized projected clusters in high dimensional spaces
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Using the fractal dimension to cluster datasets
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Clustering by pattern similarity in large data sets
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
A Monte Carlo algorithm for fast projective clustering
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Similarity Search without Tears: The OMNI Family of All-purpose Access Methods
Proceedings of the 17th International Conference on Data Engineering
M-tree: An Efficient Access Method for Similarity Search in Metric Spaces
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
Similarity Search in High Dimensions via Hashing
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
The X-tree: An Index Structure for High-Dimensional Data
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Deflating the Dimensionality Curse Using Multiple Fractal Dimensions
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Translated Poisson Mixture Model for Stratification Learning
International Journal of Computer Vision
REDUS: finding reducible subspaces in high dimensional data
Proceedings of the 17th ACM conference on Information and knowledge management
ACM Transactions on Knowledge Discovery from Data (TKDD)
Efficient layered density-based clustering of categorical data
Journal of Biomedical Informatics
Subspace sums for extracting non-random data from massive noise
Knowledge and Information Systems
Hierarchical density-based clustering of categorical data and a simplification
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Proximity algorithms for nearly-doubling spaces
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Fuzzy C-Means in High Dimensional Spaces
International Journal of Fuzzy System Applications
| Hi-index | 0.00 |
It is commonly assumed that high-dimensional datasets contain points most of which are located in low-dimensional manifolds. Detection of low-dimensional clusters is an extremely useful task for performing operations such as clustering and classification, however, it is a challenging computational problem. In this paper we study the problem of finding subsets of points with low intrinsic dimensionality. Our main contribution is to extend the definition of fractal correlation dimension, which measures average volume growth rate, in order to estimate the intrinsic dimensionality of the data in local neighborhoods. We provide a careful analysis of several key examples in order to demonstrate the properties of our measure. Based on our proposed measure, we introduce a novel approach to discover clusters with low dimensionality. The resulting algorithms extend previous density based measures, which have been successfully used for clustering. We demonstrate the effectiveness of our algorithms for discovering low-dimensional m-flats embedded in high dimensional spaces, and for detecting low-rank sub-matrices.