Dataset: supporting-data-code-1.zip, 1017.77 KB Access Condition: Open access Description: Part one - Supporting data and code (English)
Dataset: supporting-data-code-2.zip, 1017.75 KB Access Condition: Open access Description: Part two: Supporting data and code (English)
Documentation: readme.txt, 387 bytes Access Condition: Open access
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Kopriva, I., Brbić, M., Tolić, D., Antulov Fantulin, N. & Xinjian, C. (2019). Fast clustering in linear independent 1D subspaces: segmentation of multi-channel images with high spatial resolution [Data set]. https://urn.nsk.hr/urn:nbn:hr:241:579539.
Kopriva, Ivica, et al. Fast clustering in linear independent 1D subspaces: segmentation of multi-channel images with high spatial resolution. Institut Ruđer Bošković, 2019. 24 Oct 2024. https://urn.nsk.hr/urn:nbn:hr:241:579539.
Kopriva, Ivica, Marija Brbić, Dijana Tolić, Nino Antulov Fantulin, and Chen Xinjian. 2019. Fast clustering in linear independent 1D subspaces: segmentation of multi-channel images with high spatial resolution. Institut Ruđer Bošković. https://urn.nsk.hr/urn:nbn:hr:241:579539.
Kopriva, I., et al. 2019. Fast clustering in linear independent 1D subspaces: segmentation of multi-channel images with high spatial resolution. Institut Ruđer Bošković. [Online]. [Accessed 24 October 2024]. Available from: https://urn.nsk.hr/urn:nbn:hr:241:579539.
Kopriva I, Brbić M, Tolić D, Antulov Fantulin N, Xinjian C. Fast clustering in linear independent 1D subspaces: segmentation of multi-channel images with high spatial resolution. [Internet]. Institut Ruđer Bošković: , HR; 2019, [cited 2024 October 24] Available from: https://urn.nsk.hr/urn:nbn:hr:241:579539.
I. Kopriva, M. Brbić, D. Tolić, N. Antulov Fantulin and C. Xinjian, Fast clustering in linear independent 1D subspaces: segmentation of multi-channel images with high spatial resolution, Institut Ruđer Bošković, 2019. Accessed on: Oct 24, 2024. Available: https://urn.nsk.hr/urn:nbn:hr:241:579539.
Scientific / art field, discipline and subdiscipline
NATURAL SCIENCES Mathematics Applied Mathematics and Mathematical Modeling
Abstract (english)
Algorithms for subspace clustering (SC) such as sparse and low- rank representation SC are effective in terms of the accuracy but suffer from high computational complexity. We propose algorithm for SC of (highly) similar data points drawn from union of linear independent one-dimensional subspaces with computational complexity that is linear in number of data points. The algorithm finds a dictionary that represents data in reproducible kernel Hilbert space (RKHS). Afterwards, data are projected into RKHS by using empirical kernel map (EKM). Segmentation into subspaces is realized by applying the max operator on projected data. We provide rigorous proof that for noise free data proposed approach yields exact clustering into subspaces. We also prove that EKM-based projection yields less correlated data points. Due to nonlinear projection, the proposed method can adopt to linearly nonseparable data points. We demonstrate accuracy and computational efficiency of the proposed algorithm on synthetic dataset as well as on segmentation of tissue components from image of unstained specimen in histopathology.