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I am using libSVM on a subset of the MNIST, and I am struggling to interpret the output. I have learned that rho is the bias term, and that sv_coef is the multiplier used to get to the weight term. What is confusing me is the dimensions of the outputs:

    Parameters: [5×1 double]
      nr_class: 10
       totalSV: 4282
           rho: [45×1 double]
         Label: [10×1 double]
    sv_indices: []
         ProbA: [45×1 double]
         ProbB: [45×1 double]
           nSV: [10×1 double]
       sv_coef: [4282×9 double]
           SVs: [4282×784 double]

Why do we end up with dimensions of 45 for rho and 9 for the second dimension of sv_coef?

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As described in here, libsvm uses 1 vs 1 classifiers for multi-class classification (it's not the only option). So, it uses $n(n-1)/2$ binary SVM classifiers internally. Here, that makes $45$ classifiers, which explains the number of bias terms.

sv_coef contains $n-1$ columns. Number of rows is equal to number of SVs. The number of SVs belonging to each class is stored in nSV. For example, let nSV be $[m_1\ m_2\ ...\ m_{10}]$. Then, first $m_1$ rows of sv_coef are $\alpha_iy_i$ coefficients belonging to $1$ vs $x$ classifiers, where $x$ change from $2$ to $10$, making it $9$ columns. The second $m_2$ rows belong to $2$ vs $x$ classifiers, where $x$ is all other classes but $2$ and so on.

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