In order to highlight the asymmetries in the distributions, Mitrovic et al. has introduced embeddings on the conditional distributions $P_{Y | X}$ and $P_{X | Y}$ instead of the joint distribution. This allows for distinguishing asymmetries along with building an embedding of the distribution. The proposed conditional embedding is based on the Gaussian kernel along with an α quantity that performs as conditioning: $\mu_{k,M}(P_{S_j}) = \{ \sum_{j=1}^{n_j} \alpha_j (y)k_m(\cdot , x_j), \sum_{j=1}^{n_j} \alpha_j (x) k_m(\cdot , y_j) \}_{m\in M}$ with $α ( y ) = ( L + nλ I )^{−1} l_y$, $L = [l(y_i, y_j)]_{i,j=1}^n$, $l_y = [ l ( y_1 , y ), …, l ( y_n , y )]^T$ , $α (⋅) = [ α_1 (⋅), …, α_n (⋅)]^T$, regularization parameter λ , identity matrix $I$ , and $M$ the set of parameters for the kernel $k$ .