Converting between two SVM problem setups












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I am trying to implement an SVM solver and have two related, but apparently different SVM setups. They are:
1. Equation (2) of http://proceedings.mlr.press/v5/li09c/li09c.pdf [A] and Equation (26) of https://arxiv.org/pdf/1404.7203.pdf [B]
2. SVM setup from An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, Cristianini, Shawe-Taylor
soft margin SVM with squared hinge loss



I can understand how Equation (26) of the latter paper is derived from the first problem setup. Similarly, I can see how the Lagrange method applied to the primal problem gives the setup as in the screenshot.



What I don't understand is




  1. why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function

  2. Why the constraints (namely simplex constraint in [A] and [B]) differs from the inner product type constraint from the textbook.


There is perhaps an easy translation which I am missing so if someone is able to point it out I would really appreciate it.










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    0












    $begingroup$


    I am trying to implement an SVM solver and have two related, but apparently different SVM setups. They are:
    1. Equation (2) of http://proceedings.mlr.press/v5/li09c/li09c.pdf [A] and Equation (26) of https://arxiv.org/pdf/1404.7203.pdf [B]
    2. SVM setup from An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, Cristianini, Shawe-Taylor
    soft margin SVM with squared hinge loss



    I can understand how Equation (26) of the latter paper is derived from the first problem setup. Similarly, I can see how the Lagrange method applied to the primal problem gives the setup as in the screenshot.



    What I don't understand is




    1. why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function

    2. Why the constraints (namely simplex constraint in [A] and [B]) differs from the inner product type constraint from the textbook.


    There is perhaps an easy translation which I am missing so if someone is able to point it out I would really appreciate it.










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I am trying to implement an SVM solver and have two related, but apparently different SVM setups. They are:
      1. Equation (2) of http://proceedings.mlr.press/v5/li09c/li09c.pdf [A] and Equation (26) of https://arxiv.org/pdf/1404.7203.pdf [B]
      2. SVM setup from An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, Cristianini, Shawe-Taylor
      soft margin SVM with squared hinge loss



      I can understand how Equation (26) of the latter paper is derived from the first problem setup. Similarly, I can see how the Lagrange method applied to the primal problem gives the setup as in the screenshot.



      What I don't understand is




      1. why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function

      2. Why the constraints (namely simplex constraint in [A] and [B]) differs from the inner product type constraint from the textbook.


      There is perhaps an easy translation which I am missing so if someone is able to point it out I would really appreciate it.










      share|cite|improve this question









      $endgroup$




      I am trying to implement an SVM solver and have two related, but apparently different SVM setups. They are:
      1. Equation (2) of http://proceedings.mlr.press/v5/li09c/li09c.pdf [A] and Equation (26) of https://arxiv.org/pdf/1404.7203.pdf [B]
      2. SVM setup from An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, Cristianini, Shawe-Taylor
      soft margin SVM with squared hinge loss



      I can understand how Equation (26) of the latter paper is derived from the first problem setup. Similarly, I can see how the Lagrange method applied to the primal problem gives the setup as in the screenshot.



      What I don't understand is




      1. why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function

      2. Why the constraints (namely simplex constraint in [A] and [B]) differs from the inner product type constraint from the textbook.


      There is perhaps an easy translation which I am missing so if someone is able to point it out I would really appreciate it.







      optimization convex-optimization machine-learning






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 14 at 21:25









      Charlie DickensCharlie Dickens

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