# Support-Vector Networks

^{1}

##### Citations

40,826 citations

### Cites background from "Support-Vector Networks"

...{1,-1}, C-SVC [Boser et al. 1992; Cortes and Vapnik 1995] solves 4LIBSVM Tools: http://www.csie.ntu.edu.tw/~cjlin/libsvmtools. the following primal optimization problem: l t min 1 w T w +C .i (1) w,b,. 2 i=1 subject to yi(w T f(xi) +b) =1 -.i, .i =0,i =1,...,l, where f(xi)maps xi into a…...

[...]

[...]

38,208 citations

20,196 citations

^{1}

15,696 citations

### Cites background or methods from "Support-Vector Networks"

...Keywords: support vector machines, statistical learning theory, VC dimension, pattern recognition...

[...]

...For the pattern recognition case, SVMs have been used for isolated handwritten digit recognition (Cortes and Vapnik, 1995; Schölkopf, Burges and Vapnik, 1995; Schölkopf, Burges and Vapnik, 1996; Burges and Schölkopf, 1997), object recognition (Blanz et al., 1996), speaker identification…...

[...]

...This can be done by introducing positive slack variables ξi, i = 1, · · · , l in the constraints (Cortes and Vapnik, 1995), which then become: xi · w+ b ≥ +1 − ξi for yi = +1 (40) xi · w+ b ≤ −1 + ξi for yi = −1 (41) ξi ≥ 0 ∀i. (42) Thus, for an error to occur, the corresponding ξi must exceed…...

[...]

10,696 citations

### Cites methods from "Support-Vector Networks"

...Analogously to the “soft margin” loss function (Bennett and Mangasarian 1992) which was used in SV machines by Cortes and Vapnik (1995), one can introduce slack variables ξi , ξ ∗ i to cope with otherwise infeasible constraints of the optimization problem (2). Hence we arrive at the formulation stated in Vapnik (1995)....

[...]

...In its present form, the SV machine was largely developed at AT&T Bell Laboratories by Vapnik and co-workers (Boser, Guyon and Vapnik 1992, Guyon, Boser and Vapnik 1993, Cortes and Vapnik, 1995, Schölkopf, Burges and Vapnik 1995, 1996, Vapnik, Golowich and Smola 1997)....

[...]

...Analogously to the “soft margin” loss function (Bennett and Mangasarian 1992) which was used in SV machines by Cortes and Vapnik (1995), one can introduce slack variables ξi , ξ ∗ i to cope with otherwise infeasible constraints of the optimization problem (2)....

[...]

...Analogously to the “soft margin” loss function (Bennett and Mangasarian 1992) which was used in SV machines by Cortes and Vapnik (1995), one can introduce slack variables ξi , ξ ∗i to cope with otherwise infeasible constraints of the optimization problem (2)....

[...]

##### References

23,814 citations

17,604 citations

14,009 citations

### "Support-Vector Networks" refers background in this paper

...More than 60 years ago R.A. Fisher (Fisher, 1936) suggested the first algorithm for pattern recognition....

[...]

11,211 citations

7,426 citations