# Community-EintragVersionsverlauf dieses EintragsURLDOIBibTeXEndNoteAPAChicagoDIN 1505HarvardMSOffice XML Greedy Algorithms for Matrix-Valued Kernels

, und . University of Stuttgart, (2018)

#### Zusammenfassung

We are interested in approximating vector-valued functions on a compact set \$ØmegaR^d\$. We consider reproducing kernel Hilbert spaces of \$R^m\$-valued functions which each admit a unique matrix-valued reproducing kernel \$k\$. These spaces seem promising, when modelling correlations between the target function components. The approximation of a function is a linear combination of matrix-valued kernel evaluations multiplied with coefficient vectors. To guarantee a fast evaluation of the approximant the expansion size, i.e. the number of centers \$n\$ is desired to be small. We thus present three different greedy algorithms by which a suitable set of centers is chosen in an incremental fashion: First, the \$P\$-Greedy which requires no function evaluations, second and third, the \$f\$-Greedy and \$f/P\$-Greedy which require function evaluations but produce centers tailored to the target function. The efficiency of the approaches is investigated on some data from an artificial model.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8291459083557129, "perplexity": 1232.8513459178787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540555616.2/warc/CC-MAIN-20191213122716-20191213150716-00299.warc.gz"}