Optimization in pattern analysis Optimization approaches in pattern
- Slides: 37
Optimization in pattern analysis Optimization approaches in pattern analysis Patterns in vector spaces Tijl De Bie K. U. Leuven / Southampton University School on pattern analysis - Erice
Optimization in pattern analysis Pattern analysis Overview • Pattern analysis – Pattern functions – Pattern matching – Pattern discovery Patterns in discrete spaces • Patterns in discrete spaces – Patterns in sets – Patterns in strings – Patterns in graphs Patterns in vector spaces • Patterns in vector spaces – Least squares problems – Convex optimization – Eigenvalue problems 9/9/2020 School on pattern analysis - Erice 2
Optimization in pattern analysis Pattern functions Pattern matching A framework for pattern analysis? santic. vinym. thyi. thapna. mycym Pattern discovery halch. zethui. thivacl. cesasin. thumsa. cilva neri. canva. carsi. pytnam. thycal. atnam tei. lena. haustish. enac. eshi. catnis. heci spurta. sylsle. napti. thui. laiscla. hechz. neri une. mlach nthi acal vacl. vinum. shantishtsh. celi. pen. trytym thi. thapneshtsh. trytanasha. hanthin. celi Patterns in discrete spaces tyr. hetym. vinym. thic. vacl. hechz. etnam ich. matam. cnticn. thsepen. teshamitn murce. thi. nunthen. etnam. thi. tryth. etnam hanthin. etnam. celycn. etnam. athumitn pethereni. eslem. zathrum. mur. in. velthinesh cilthsh. vacl. ara. thui. useti. catneti. slapichyn slapinash. favin. yfli. spyrta. eisna. hinthy cla. thesns. eslem. cealchus. etnam. aisna. cesal tychlac. ethri. syntnam. cecha cntnam. thesan. fler. veivesh. thezeri etnam. aisna. esa. ich. huthish. zathrumish flerchve. trin. nethunshl. cn. thunt. eitylvar. thunem. cealchus. etnam. ich. eslem. cialchysh than etnam. thesan flanac. farsi tunt. enac. etnam. athymica. thlupcva ceshum. tei. lanti. ininc. eshi. tei. chimth streta. satrs. enash. ucy. hamphetish. rinush thui. arash. mucum. ania. chesh. rasna. hilar cateyth. hamphet. etnam Patterns in vector spaces aisna. ich. nac. reushce. aiserash. sheush thunchulem. muth. hilarthune. etertic cathre. chim. enach. unchva. methlumth. puts muth. hilarthuna. tecum. etrinthi. muth nafaucn. unchva. hetum. hilarthuna. thenth hyrsic. caplthy. cecham. enac. eisna. hinthy hetym. hilarthuma. etertic. cathra etnam. aisna. ich. matam /// vacltnam thunem. cialchush. masn. ynialti. ursmnal athre. acil. an. shacnicn. cilth. cecha. sal cus. cluce. caperi. zamtic. svem. thumsa matan. clyctrash. hilar. 9/9/2020 School on pattern analysis - Erice 3
Optimization in pattern analysis Pattern functions Pattern matching A framework for pattern analysis? Pattern discovery Patterns in discrete spaces Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 4
Optimization in pattern analysis Pattern functions Pattern matching A framework for pattern analysis? santic. vinym. thyi. thapna. mycym Pattern discovery halch. zethui. thivacl. cesasin. thumsa. cilva neri. canva. carsi. pytnam. thycal. atnam tei. lena. haustish. enac. eshi. catnis. heci spurta. sylsle. napti. thui. laiscla. hechz. neri une. mlach nthi acal vacl. vinum. shantishtsh. celi. pen. trytym thi. thapneshtsh. trytanasha. hanthin. celi Patterns in discrete spaces tyr. hetym. vinym. thic. vacl. hechz. etnam ich. matam. cnticn. thsepen. teshamitn murce. thi. nunthen. etnam. thi. tryth. etnam hanthin. etnam. celycn. etnam. athumitn pethereni. eslem. zathrum. mur. in. velthinesh cilthsh. vacl. ara. thui. useti. catneti. slapichyn slapinash. favin. yfli. spyrta. eisna. hinthy cla. thesns. eslem. cealchus. etnam. aisna. cesal tychlac. ethri. syntnam. cecha cntnam. thesan. fler. veivesh. thezeri etnam. aisna. esa. ich. huthish. zathrumish flerchve. trin. nethunshl. cn. thunt. eitylvar. thunem. cealchus. etnam. ich. eslem. cialchysh than etnam. thesan flanac. farsi tunt. enac. etnam. athymica. thlupcva ceshum. tei. lanti. ininc. eshi. tei. chimth streta. satrs. enash. ucy. hamphetish. rinush thui. arash. mucum. ania. chesh. rasna. hilar cateyth. hamphet. etnam Patterns in vector spaces aisna. ich. nac. reushce. aiserash. sheush thunchulem. muth. hilarthune. etertic cathre. chim. enach. unchva. methlumth. puts muth. hilarthuna. tecum. etrinthi. muth nafaucn. unchva. hetum. hilarthuna. thenth hyrsic. caplthy. cecham. enac. eisna. hinthy hetym. hilarthuma. etertic. cathra etnam. aisna. ich. matam /// vacltnam thunem. cialchush. masn. ynialti. ursmnal athre. acil. an. shacnicn. cilth. cecha. sal cus. cluce. caperi. zamtic. svem. thumsa matan. clyctrash. hilar. 9/9/2020 School on pattern analysis - Erice 5
Optimization in pattern analysis Pattern functions Pattern matching Pattern discovery Patterns in discrete spaces Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 6
Optimization in pattern analysis Pattern functions Pattern discovery? Pattern matching santic. vinym. thyi. thapna. mycym Pattern discovery halch. zethui. thivacl. cesasin. thumsa. cilva neri. canva. carsi. pytnam. thycal. atnam tei. lena. haustish. enac. eshi. catnis. heci spurta. sylsle. napti. thui. laiscla. hechz. neri une. mlach nthi acal vacl. vinum. shantishtsh. celi. pen. trytym thi. thapneshtsh. trytanasha. hanthin. celi Patterns in discrete spaces tyr. hetym. vinym. thic. vacl. hechz. etnam ich. matam. cnticn. thsepen. teshamitn murce. thi. nunthen. etnam. thi. tryth. etnam hanthin. etnam. celycn. etnam. athumitn pethereni. eslem. zathrum. mur. in. velthinesh cilthsh. vacl. ara. thui. useti. catneti. slapichyn slapinash. favin. yfli. spyrta. eisna. hinthy cla. thesns. eslem. cealchus. etnam. aisna. cesal tychlac. ethri. syntnam. cecha cntnam. thesan. fler. veivesh. thezeri etnam. aisna. esa. ich. huthish. zathrumish flerchve. trin. nethunshl. cn. thunt. eitylvar. thunem. cealchus. etnam. ich. eslem. cialchysh than etnam. thesan flanac. farsi tunt. enac. etnam. athymica. thlupcva ceshum. tei. lanti. ininc. eshi. tei. chimth streta. satrs. enash. ucy. hamphetish. rinush thui. arash. mucum. ania. chesh. rasna. hilar cateyth. hamphet. etnam Patterns in vector spaces aisna. ich. nac. reushce. aiserash. sheush thunchulem. muth. hilarthune. etertic cathre. chim. enach. unchva. methlumth. puts muth. hilarthuna. tecum. etrinthi. muth nafaucn. unchva. hetum. hilarthuna. thenth hyrsic. caplthy. cecham. enac. eisna. hinthy hetym. hilarthuma. etertic. cathra etnam. aisna. ich. matam /// vacltnam thunem. cialchush. masn. ynialti. ursmnal athre. acil. an. shacnicn. cilth. cecha. sal cus. cluce. caperi. zamtic. svem. thumsa matan. clyctrash. hilar. 9/9/2020 School on pattern analysis - Erice 7
Optimization in pattern analysis Pattern functions Pattern discovery Pattern matching Pattern discovery Patterns in discrete spaces Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 8
Optimization in pattern analysis Pattern functions But… Pattern matching Pattern discovery Patterns in discrete spaces Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 9
Optimization in pattern analysis Patterns in discrete spaces • Patterns in sets – Apriori algorithm Patterns in discrete spaces • Patterns in strings – Common/frequent substrings – More complex grammars – Probabilistic grammars Patterns in vector spaces • Patterns in graphs 9/9/2020 School on pattern analysis - Erice 10
Optimization in pattern analysis Patterns in sets Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 11
Optimization in pattern analysis Patterns in sets Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 12
Optimization in pattern analysis Patterns in sets Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 13
Optimization in pattern analysis Patterns in sets Patterns in discrete spaces Sets empty Strings Space of itemsets with items A, B, C, D Graphs AB A B C D AC AD BC BD ABC ABD ACD BCD CD Patterns in vector spaces ABCD 9/9/2020 School on pattern analysis - Erice 14
Optimization in pattern analysis Patterns in sets Patterns in discrete spaces Sets empty Strings Space of itemsets with items A, B, C, D Graphs AB A B C D AC AD BC BD ABC ABD ACD BCD CD Patterns in vector spaces ABCD 9/9/2020 School on pattern analysis - Erice 15
Optimization in pattern analysis Patterns in sets Patterns in discrete spaces Sets empty Strings Space of itemsets with items A, B, C, D Graphs A AB B D AD BD Patterns in vector spaces ABD 9/9/2020 School on pattern analysis - Erice 16
Optimization in pattern analysis Patterns in strings Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 17
Optimization in pattern analysis Patterns in strings Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 18
Optimization in pattern analysis Patterns in strings Patterns in discrete spaces Sets Strings Graphs A Patterns in vector spaces AA B AB … AAA 9/9/2020 AAB School on pattern analysis - Erice 19
Optimization in pattern analysis Patterns in strings Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 20
Optimization in pattern analysis Patterns in graphs, … Patterns in discrete spaces Sets Strings Graphs Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 21
Optimization in pattern analysis Patterns in vector spaces • Least squares problems – Linear regression (LSR/RR) – Fisher’s discriminant analysis (FDA) Patterns in discrete spaces • Convex optimization – Support vector machines (SVM) Patterns in vector spaces • Eigenvalue problems – Principal component analysis (PCA) 9/9/2020 School on pattern analysis - Erice 22
Optimization in pattern analysis Pattern analysis Least squares: LSR and FDA Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 23
Optimization in pattern analysis Pattern analysis Least squares: LSR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 24
Optimization in pattern analysis Pattern analysis Least squares: LSR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 25
Optimization in pattern analysis Pattern analysis Least squares: LSR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 26
Optimization in pattern analysis Pattern analysis Least squares: LSR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 27
Optimization in pattern analysis Pattern analysis Least squares: RR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 28
Optimization in pattern analysis Pattern analysis Least squares: RR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 29
Optimization in pattern analysis Pattern analysis Least squares: RR Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 30
Optimization in pattern analysis Pattern analysis Least squares: FDA Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 31
Optimization in pattern analysis Pattern analysis Least squares: FDA Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 32
Optimization in pattern analysis Pattern analysis Convex optimization: SVM Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 33
Optimization in pattern analysis Pattern analysis Eigenvalue problems: PCA Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 34
Optimization in pattern analysis Pattern analysis Eigenvalue problems: PCA Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 35
Optimization in pattern analysis Pattern analysis Eigenvalue problems: PCA Patterns in discrete spaces Patterns in vector spaces Least squares Convex Opt. Eigenproblems 9/9/2020 School on pattern analysis - Erice 36
Optimization in pattern analysis Pattern analysis Summary Patterns in discrete spaces Patterns in vector spaces 9/9/2020 School on pattern analysis - Erice 37
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