Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Object Recognition from Local Scale-Invariant Features
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Kernel k-means: spectral clustering and normalized cuts
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
A Bayesian Hierarchical Model for Learning Natural Scene Categories
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
One-Shot Learning of Object Categories
IEEE Transactions on Pattern Analysis and Machine Intelligence
Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Approximate kernel k-means: solution to large scale kernel clustering
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Euler Principal Component Analysis
International Journal of Computer Vision
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By always mapping data from lower dimensional space into higher or even infinite dimensional space, kernel k-means is able to organize data into groups when data of different clusters are not linearly separable. However, kernel k-means incurs the large scale computation due to the representation theorem, i.e. keeping an extremely large kernel matrix in memory when using popular Gaussian and spatial pyramid matching kernels, which largely limits its use for processing large scale data. Also, existing kernel clustering can be overfitted by outliers as well. In this paper, we introduce an Euler clustering, which can not only maintain the benefit of nonlinear modeling using kernel function but also significantly solve the large scale computational problem in kernel-based clustering. This is realized by incorporating Euler kernel. Euler kernel is relying on a nonlinear and robust cosine metric that is less sensitive to outliers. More important it intrinsically induces an empirical map which maps data onto a complex space of the same dimension. Euler clustering takes these advantages to measure the similarity between data in a robust way without increasing the dimensionality of data, and thus solves the large scale problem in kernel k-means. We evaluate Euler clustering and show its superiority against related methods on five publicly available datasets.