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
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
- why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function
- 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
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add a comment |
$begingroup$
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
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
- why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function
- 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
$endgroup$
add a comment |
$begingroup$
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
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
- why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function
- 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
$endgroup$
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
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
- why the authors in [A] and [B] remove the $sum_i alpha_i$ term from the objective function
- 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
optimization convex-optimization machine-learning
asked Jan 14 at 21:25
Charlie DickensCharlie Dickens
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