Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
SVM-KM: Speeding SVMs Learning with a priori Cluster Selection and k-Means
SBRN '00 Proceedings of the VI Brazilian Symposium on Neural Networks (SBRN'00)
Classifying large data sets using SVMs with hierarchical clusters
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Gaussian Processes for Ordinal Regression
The Journal of Machine Learning Research
Making SVMs Scalable to Large Data Sets using Hierarchical Cluster Indexing
Data Mining and Knowledge Discovery
Block-quantized kernel matrix for fast spectral embedding
ICML '06 Proceedings of the 23rd international conference on Machine learning
Training linear SVMs in linear time
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning concepts from large scale imbalanced data sets using support cluster machines
MULTIMEDIA '06 Proceedings of the 14th annual ACM international conference on Multimedia
Prediction of Ordinal Classes Using Regression Trees
Fundamenta Informaticae - Intelligent Systems
Support Vector Ordinal Regression
Neural Computation
Learning to rank: from pairwise approach to listwise approach
Proceedings of the 24th international conference on Machine learning
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
ROC analysis in ordinal regression learning
Pattern Recognition Letters
Support vector machines based on K-means clustering for real-time business intelligence systems
International Journal of Business Intelligence and Data Mining
The Journal of Machine Learning Research
Representative sampling for text classification using support vector machines
ECIR'03 Proceedings of the 25th European conference on IR research
Large-Margin thresholded ensembles for ordinal regression: theory and practice
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Cost-Sensitive learning of SVM for ranking
ECML'06 Proceedings of the 17th European conference on Machine Learning
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Support vector ordinal regression (SVOR) is a recently proposed ordinal regression (OR) algorithm. Despite its theoretical and empirical success, the method has one major bottleneck, which is the high computational complexity. In this brief, we propose a both practical and theoretical guaranteed algorithm, block-quantized support vector ordinal regression (BQSVOR), where we approximate the kernel matrix K with K that is composed of k2 constant blocks. We provide detailed theoretical justification on the approximation accuracy of BQSVOR. Moreover, we prove theoretically that the OR problem with the block-quantized kernel matrix K could be solved by first separating the data samples in the training set into k clusters with kernel k-means and then performing SVOR on the k cluster representatives. Hence, the algorithm leads to an optimization problem that scales only with the number of clusters, instead of the data set size. Finally, experiments on several real-world data sets support the previous analysis and demonstrate that BQSVOR improves the speed of SVOR significantly with guaranteed accuracy.