# Anomaly score calculation for multidimensional data set

I'm currently using anomaly score calculation methods which work on single dimensional data sets (Timestamp & Value). I would like to calculate the same single anomaly score for multidimensional data set (Timestamp & Value 1 & Value 2 & ..... & Value N).

What method could compare all the values and calculate anomaly score based upon the relationship between them?

to make it more formal, if we denote $\vec{v}_{t0}$ as your data at timestamp $t_0$, we train a regression model $R$ that learns from $\{v_{t_0},\dots,v_{t_{n-1}}\}$.
Your anomaly score is a function of $R({v_{t_0},\dots,v_{t_{n-1}}})-v_{t_n}$
I think you can use a prediction model to predict next value $y_{pred}$ after that you have:
$e = |y_{pred} - y_t|$, use error to compare with "$alpha \times std$" of series. $alpha = [1, 10]$.