# Clustering using using min,max,mean and standard deviation

I have read some papers on clustering application to detect outliers in the data set. In many places the euclidean distance between any 2 data points is calculated using minimum , maximum , mean and standard deviation of the data unit. Let's say the data set consists of multiple samples each of 1 hour duration. Now 1 hour of data is summarized to minimum , maximum , mean and standard deviation and euclidean distance is calculated on these parameters.
My doubt is what is the significance and rationale behind selecting the above 4 descriptive statistical parameters for subsequent use in clustering application.

• Could you add a reference? This practice is non standard, though to be clear any distance metric can be used – Harsh Feb 20 '16 at 18:41
• I have never heard of using min, max, mean & SD to calculate Euclidean distance, & I cannot see how it is possible. The Euclidean distance between 2 points is the square root of the sum of the squared distances on each dimension. Can you say more about your situation & your data? – gung - Reinstate Monica Feb 20 '16 at 19:19
• @Harsh and @gung It was used like d(X,Y) = sqrt( (avgx - avgy )^2 + (stdx - stdy )^2 + (maxx - maxy )^2 + (minx - miny )^2 – Soumajit Feb 21 '16 at 2:54
• @Harsh [ arc.aiaa.org/doi/book/10.2514/MSPOPS12 ] Here you can find the paper "New Telemetry Monitoring Paradigm with Novelty Detection" – Soumajit Feb 21 '16 at 3:03

• @Johnson Thanks for the reference. But the rationale for selecting "min,max,mean and std deviation" is not mentioned in the paper. – Soumajit Feb 21 '16 at 3:06