Contents
What is variance in clustering?
In plain English, the cluster variance is the coordinate-wise squared deviations from the mean of the cluster of all the observations belonging to that cluster. The total within cluster scatter (for the entire set of observations) is simply W=K∑k=1∑xi∈Ck‖xi−ˉxk‖2 for K clusters and N observations with K
When computing variance Why do we square the deviations from the mean?
The calculation of variance uses squares because it weighs outliers more heavily than data closer to the mean. This calculation also prevents differences above the mean from canceling out those below, which would result in a variance of zero.
How is the variance of a cluster determined?
It says that minimizing the SSQ (and equivalent, minimizing variance of a cluster) increases the separation of clusters; and conversely. Intragroup variance is determining the variance within each cluster and combining them. Intergroup variance is determined by the distance between the cluster centers.
Is the standard deviation the same as the variance?
The Standard Deviation is a measure of how spread out numbers are. The formula is easy: it is the square root of the Variance. So now you ask, “What is the Variance?” The Variance is defined as: The average of the squared differences from the Mean.
Which is the square root of the variance?
Or, rather, standard deviation (the square root of the variance) is a measure of deviation. So it’s really standard deviation and average deviation you ought to compare. The normal average uses what is called the arithmetic mean, and the standard deviation uses what is called the quadratic mean.
When do you take sum of squares for clustering?
But now when looking at clusters, you want a cluster with many objects to have more influence. So for N objects, you take N times the variance. I.e., you take simply the sum of squares. It says that minimizing the SSQ (and equivalent, minimizing variance of a cluster) increases the separation of clusters; and conversely.