Algorithm 1: (Few-shot AI corrector [83]: 1NN version. Training). Input: sets $\mathcal{X}$, $\mathcal{Y}$; the number of clusters, k; threshold, $\theta$ (or thresholds ${\theta }_1,\dots ,{\theta }_k$).

Determining the centroid $\overline{\mathit{x}}$ of the $\mathcal{X}$. Generate two sets, ${\mathcal{X}}_c$, the centralised set $\mathcal{X}$, and ${\mathcal{Y}}^{\ast }$, the set obtained from $\mathcal{Y}$ by subtracting $\overline{\mathit{x}}$ from each of its elements. Construct Principal Components for the centralised set ${\mathcal{X}}_c$. Using Kaiser, broken stick, conditioning rule, or otherwise, select $m\le n$ Principal Components, $h_1,\dots ,h_m$, corresponding to the first largest eivenvalues ${\lambda }_1\ge \cdots \ge {\lambda }_m>0$ of the covariance matrix of the set ${\mathcal{X}}_c$, and project the centralized set ${\mathcal{X}}_c$ as well as ${\mathcal{Y}}^{\ast }$ onto these vectors. The operation returns sets ${\mathcal{X}}_r$ and ${\mathcal{Y}}_r^{\ast }$, respectively: $$\begin{array}{cc}\hfill {\mathcal{X}}_r& =\{\mathit{x}|\mathit{x}=H\mathit{z},\mathit{z}\in {\mathcal{X}}_c\}\hfill \\ \hfill {\mathcal{Y}}_r^{\ast }& =\{\mathit{y}|\mathit{y}=H\mathit{z},\mathit{z}\in {\mathcal{Y}}^{\ast }\},H=\left(\begin{array}{c}{h}_1^T\\ ⋮\\ h_m^T\end{array}\right).\hfill \end{array}$$ Construct matrix W $$W=\mathrm{diag}\left(\frac{1}{\sqrt{{\lambda }_1}},\dots ,\frac{1}{\sqrt{{\lambda }_m}}\right)$$ corresponding to the whitening transformation for the set ${\mathcal{X}}_r$. Apply the whitening transformation to sets ${\mathcal{X}}_r$ and ${\mathcal{Y}}_r^{\ast }$. This returns sets ${\mathcal{X}}_w$ and ${\mathcal{Y}}_w^{\ast }$: $$\begin{array}{cc}\hfill {\mathcal{X}}_w& =\{\mathit{x}|\mathit{x}=W\mathit{z},\mathit{z}\in {\mathcal{X}}_r\}\hfill \\ \hfill {\mathcal{Y}}_w^{\ast }& =\{\mathit{y}|\mathit{y}=W\mathit{z},\mathit{z}\in {\mathcal{Y}}_r^{\ast }\}.\hfill \end{array}$$ Cluster the set ${\mathcal{Y}}_w^{\ast }$ into k clusters ${\mathcal{Y}}_{w,1}^{\ast },\dots ,{\mathcal{Y}}_{w,k}^{\ast }$ (using e.g. the k-means algorithm or otherwise). Let ${\overline{\mathit{y}}}_1,\dots ,{\overline{\mathit{y}}}_k$ be their corresponding centroids. For each pair $({\mathcal{X}}_w,{\mathcal{Y}}_{w,i}^{\ast })$, $i=1,\dots ,k$, construct (normalised) Fisher discriminants ${\mathit{w}}_1,\dots ,{\mathit{w}}_k$: $${\mathit{w}}_i=\frac{{(\mathrm{Cov}({\mathcal{X}}_w)+\mathrm{Cov}({\mathcal{Y}}_{w,i}^{\ast }))}^{-1}{\overline{\mathit{y}}}_i}{\parallel {(\mathrm{Cov}({\mathcal{X}}_w)+\mathrm{Cov}({\mathcal{Y}}_{w,i}^{\ast }))}^{-1}{\overline{\mathit{y}}}_i\parallel }.$$ An element $\mathit{z}$ is associated with the set ${\mathcal{Y}}_{w,i}^{\ast }$ if $({\mathit{w}}_i,\mathit{z})>\theta$ and with the set ${\mathcal{X}}_w$ if $({\mathit{w}}_i,\mathit{z})\le \theta$. If multiple thresholds are given then an element $\mathit{z}$ is associated with the set ${\mathcal{Y}}_{w,i}^{\ast }$ if $({\mathit{w}}_i,\mathit{z})>{\theta }_i$ and with the set ${\mathcal{X}}_w$ if $({\mathit{w}}_i,\mathit{z})\le {\theta }_i$. Output: vectors ${\mathit{w}}_i$, $\overline{\mathit{x}}$, $i=1,\dots ,k$, matrices H and W.