Example: Suppose we want to build a classifier that recognizes WebPages of graduate students.

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1 Exampe: Suppose we want to bud a cassfer that recognzes WebPages of graduate students. How can we fnd tranng data? We can browse the web and coect a sampe of WebPages of graduate students of varous unverstes. Now we have a coecton of postve exampes. How about negatve exampes? he negatve exampes are the rest of the web that s not a graduate student webpage. So: the negatves exampes come from an unnown number of dfferent negatves casses. hus: It s hopeess and wrong to tryng to characterze the dstrbuton of the negatves; they can beong to any cass. ( Each negatve exampes s negatve n ts own way. )

2 We ust cannot formuate ths probem as a two cass cassfcaton probem. It can be seen as a (x)-cass earnng probem: here are an unnown number (x) of casses but the user s nterested n one cass.e. the user s based toward one cass. Smary: n content-based mage retreva and document retreva n genera. How do we approach ths probem then? It s reasonabe to assume that postve exampes custer n a certan way. ( A postve exampe are ae. ) hus: We can attempt to capture the dstrbuton of the postve exampes. One-cass SVMs offer a souton to the (x)- cass probem.

3 One-Cass SVM for Learnng n Image Retreva Y. Chen. S. Zhou. Huang Unversty of Inos at Urbana-Champagn IEEE Internatona Conference on Image Processng 00 Undesrabe resut reached by a two-cass SVM 3

4 he Proposed Approach ry to ft a tght hyper-sphere (n a transformed space) to ncude most postve tranng exampes. Such hyper-sphere tres to capture the support wthn whch the postve exampes are custered n an effort to separate them from the rest of the word. he hyper-sphere w ncude most but not a tranng data to avod overfttng. One cass SVM 4

5 One cass SVM radus center One cass SVM 5

6 6 One cass SVM ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ζ β ν β ζ ζ ν ζ R R By substtutng () () (3) n L we obtan: One cass SVM ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Whch we want to maxmze wth respect to the s

7 7 One cass SVM hus: the dua obectve functon can be wrtten usng a erne functon: he souton of ths optmzaton probem gves the optma vaues s max One cass SVM ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) c Note :

8 8 One cass SVM ( ) ( ) ( ) ( ) ( ) R c R f o use the one - cass SVM to ran mages: he coser the mage s to the center of the hyper-sphere the hgher s the score and more ey the mage s to be a target mage. wo nce toy exampes

9 Lnear One cass SVM amount of outers (a) (b) In practce we cannot assume that rea data are custered n spherca shapes as n the prevous exampe. Rea data (e.g. mages) can have mut-mode dstrbutons. he use of a erne aows to hande the more genera case. We oo for spherca shapes n the transformed space. 9

10 Non-near One cass SVM Rea data Fuy abeed mage database; 5 casses wth 00 mages each; Casses: arpanes cars horses eages staned gasses; Each mage s a vector of 37 dmensons: statstca moments edge-based structure features etc; 0

11 Experment wth rea data For each cass 0 mages are randomy chosen as tranng exampes; he earned decson functon s used to ran a the 500 mages n the database; he ht rates n the top raned 0 and 00 mages are used as performance measures; For each cass the experment s repeated 00 tmes and average error rates are reported. Expermenta Resuts

12 Concusons Effectve tranng was performed wth a sma number of exampes; A Gaussan erne was used: how does t compare wth usng dfferent ernes? he method requres the tunng of two parameters: the spread of the Gaussan erne and the reguarzaton term for errors.

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