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[ sign(z)(|z| - \gamma)_{+} = ] (6)
[ \frac{1} {N} \sum_{i=1}^N x_{ij}(y_i - \tilde{y}i^{(j)}) = \frac {1} {N} \sum{i=1}^N x_{ij} r_i + \tilde{\beta}_j ] (8)
[ \sum_{i=1}^N x_{ij} r_i = (x_j,y) - \sum_{k:|\tilde{\beta}_k | greater 0 }} (x_j, x_k) \tilde{\beta}_k ] (9)