Confusion on calculating Mahalanobis distance between a point and a cluster I am slightly confused as to how you calculate Mahalanobis distance given a set of data. I have tried asking my tutor for help but he does not seem interested in helping what so ever and I am continuously insulted. I thought I would turn to the community for help.
I have a set of data here and I have performed distance calculation once using Euclidean distance to group the data. Now I am looking to calculate distance using Mahalanobis distance. I have calculated the means and also calculated a Pooled covariance matrix. I am unsure as to what I need to do from here to begin calculating distances for each point.
I think what I need to do is take a point and subtract the mean values. I then calculate a Pooled Covariance Matrix for each group and use this to calculate the distance between the point and the clusters data distribution. Whichever one yields the smallest distance out of the clusters, that will be the cluster the point belongs to.
Data clustered into 3 clusters after performing Euclidean distance to place points into initial groups

Pooled Covariance matrix
\begin{bmatrix}1.394&1.702\\1.702&6.62\end{bmatrix}
Inverse Pooled Covariance
\begin{bmatrix}1.046&-0.269\\-0.269&0.221\end{bmatrix}
Mahalanobis Formula

Pooled covariance matrix for each cluster
Cluster1
\begin{bmatrix}0.873&-0.234\\-0.234&0.158\end{bmatrix}
Cluster2
\begin{bmatrix}6.060&-3.030\\-3.030&6.060\end{bmatrix}
Cluster3
\begin{bmatrix}1.189&-0.573\\-0.573&0.722\end{bmatrix}
Calculating distance for point (1,1)and Cluster 1 distribution

Since cluster1 distribution has a smaller distance compared to cluster2, this point will belong to cluster1.


Why not pooling all raw data into one main sample, calculating a common covariance C from there?  (I'm assuming that to be different from pooling the samples' covariances together.) Would not that always take care of all data being measured in the same scale?
From there you could proceed by introducing C and inverting it  in your formula for D2 shown above?
Juan F.
