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===Unsupervised learning===
[[Unsupervised learning|Unsupervised]] multiple kernel learning algorithms have also been proposed by Zhuang et al. The problem is defined as follows. Let <math>U={x_i}</math> be a set of unlabeled data. The kernel definition is the linear combined kernel <math>K'=\sum_{i=1}^M\beta_iK_m</math>. In this problem, the data needs to be "clustered" into groups based on the kernel distances. Let <math>B_i</math> be a the group or cluster of which <math>x_i</math> is a member. We define the loss function as <math>\sum^n_{i=1}\left\Vert x_i - \sum_{x_j\in B_i} K(x_i,x_j)x_j\right\Vert^2</math>. Furthermore, we minimize the distortion by minimizing <math>\sum_{i=1}^n\sum_{x_j\in B_i}K(x_i,x_j)\left\Vert x_i - x_j \right\Vert^2</math>. Finally, we add a regularization term to avoid overfitting. Combining these terms, we can write the minimization problem as follows.
:<math>\min_{\beta,B}\sum^n_{i=1}\left\Vert x_i - \sum_{x_j\in B_i} K(x_i,x_j)x_j\right\Vert^2 + \gamma_1\sum_{i=1}^n\sum_{x_j\in B_i}K(x_i,x_j)\left\Vert x_i - x_j \right\Vert^2 + \gamma_2\sum_i |B_i|</math>
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