Weighted Parzen Windows for Pattern Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Support vector density estimation
Advances in kernel methods
Support vector domain description
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
The accuracy and the computational complexity of a multivariate binned kernel density estimator
Journal of Multivariate Analysis
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Density-Based Multiscale Data Condensation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Parzen Density Estimation Using Clustering-Based Branch and Bound
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse Greedy Matrix Approximation for Machine Learning
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Multivariate Density Estimation: an SVM Approach
Multivariate Density Estimation: an SVM Approach
Efficient Biased Sampling for Approximate Clustering and Outlier Detection in Large Data Sets
IEEE Transactions on Knowledge and Data Engineering
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
Enhancing Density-Based Data Reduction Using Entropy
Neural Computation
Estimating the Support of a High-Dimensional Distribution
Neural Computation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Segmentation Based on Adaptive Cluster Prototype Estimation
IEEE Transactions on Fuzzy Systems
Probability density estimation from optimally condensed data samples
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Core Vector Machines
IEEE Transactions on Neural Networks
INDIE: An Artificial Immune Network for On-Line Density Estimation
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
On minimum class locality preserving variance support vector machine
Pattern Recognition
Robust relief-feature weighting, margin maximization, and fuzzy optimization
IEEE Transactions on Fuzzy Systems
Multivariate online kernel density estimation with Gaussian kernels
Pattern Recognition
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Reduced set density estimator (RSDE) is an important technique that can be used to replace the classical Parzen window estimator (PW) for saving the computational cost. Though RSDE demonstrates a nicer performance in the density accuracy and the computational time compared with several existing methods, it still faces the critical challenge for practical applications because of its high time complexity (no less than O(N^2)) and space complexity (O(N^2)) in training the model weighting coefficients on large data sets. In order to overcome this shortcoming, a fast reduced set density estimator algorithm (FRSDE) is proposed in this study. First, the relationship between RSDE and the minimal enclosing ball problems (MEB) in computational geometry is revealed. Then, the finding that RSDE is equivalent to a special MEB problem is derived. With this finding, the fast core-set based MEB approximation algorithm is introduced to develop the proposed algorithm FRSDE. Compared with RSDE, FRSDE has the following distinctive advantage: it can guarantee that the upper bound of the time complexity is linear with the size N of a large data set and the upper bound of the space complexity is independent of N. Our experimental results show that the proposed FRSDE has a competitive performance in the density accuracy and an overwhelming advantage over RSDE for large data sets in the data condensation rate and the training time for the weighting coefficients.