calculate interpolation value of pk according to *P(S)*i, get vk.

 let = ∣vk -dk ∣ , 
 let max=max(di) , min=min(di) i=0, 1, 2, …, N-1 let coef=(*max-min)/N*
 normalize di, dk and vk by i off k

 '
$$d_{i}^{\dag}=(d_{i}\,\mbox{-}m i n)\,/c o e f$$

 'k d = (dk *-min*) /*coef*
 'k
$$\dot{\nu_{k}}=(\nu_{k}\,\mbox{-}m i n)\,/c o e f$$
 denote (i, '
i d) by pi', (k, 'k d) by pk' and (k,'k v) by pj'

calculating angle $\angle p_{k}\cdot p_{i}\cdot p_{j}$: denoted by $\angle j$'$i$'$k$' (degree) $sim_{k}^{i}=exp$ (- $\angle j$'$i$'$k$'$2/50)
 = exp (-*j'i'k'^2/50)*

$\mathbf{a}\cdot\mathbf{t}$
$$\mathrm{\noted\by\}\ \ \angle j\,\ddot{\imath}\,\dddot{k}\,\mathrm{'}\ \ \ (\mathrm{degree)}$$
 }
$$\mathbf{\mu}_{\mathrm{f}}$$
}
3. Calculate RDDk by פ algorithm 

$$\mathrm{with~weight}\qquad w_{i}~=~\sum_{k=0}^{N-1}s i m_{k}^{i}$$

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

$$\mathrm{and}\;\;\;R D D_{k}=-\ln\;\;$$

 and 
4. Output outliers by Expanding Algorithm Note: To any series sets, since outliers deviate from others, they may disturb some order of the sets. 

So we can use kinds of order to descript the pattern. Definition 2 and corresponding algorithms hold true to any kinds of order. 

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