UPGMA
UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is a simple agglomerative (bottom-up) hierarchical clustering method. The method is generally attributed to Sokal and Michener.
The UPGMA method is similar to its weighted variant, the WPGMA method.
Algorithm
The UPGMA algorithm constructs a rooted tree (dendrogram) that reflects the structure present in a pairwise similarity matrix (or a dissimilarity matrix).
At each step, the nearest two clusters are combined into a higher-level cluster. The distance between any two clusters A and B, each of size (i.e., cardinality) 
and 
, is taken to be the average of all distances 
between pairs of objects 
in 
and 
in 
, that is, the mean distance between elements of each cluster:
In other words, at each clustering step, the updated distance between the joined clusters 
and a new cluster 
is given by the proportional averaging of the 
and 
distances:
The UPGMA algorithm produces rooted dendrograms and requires a constant-rate assumption - that is, it assumes an ultrametric tree in which the distances from the root to every branch tip are equal. When the tips are molecular data (i.e., DNA, RNA and protein), the ultrametricity assumption is called the molecular clock.
Podcasts:
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by My Epic
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by Duosway
You Became I
by: My EpicI once knew that everything around me leapt for you
And I spoke with fiery tongue of heavens fall and of
your kingdom come
The words I was saying were leaving with ease but
countered the actions that follow my feet
Oh the seduction of meaningless things
I've been eating from gravesides
Swearing oaths to the fairest of moons
Trading masters by firelight
And sleeping in their tombs
All creation waits - Aching for the day
(Earth, the sky, and savage tide will vanish under
heavens rise - falling, fading)
There is no escape - From what the author fates
(Greater souls than we conceive - Concern themselves
with our retreat)
I've been drifting in my words
I've been shifting my affection to whatever love may
call my name
Babel were your men so dim
To build their gods and worship them
Erect escape in increments
And place their faith in intellect
Now we've been weeping at gravesides
Swearing hope is an island away
Just a spark for the firelight
To keep despair at bay
My brothers, we are foolish
If this is how we think we can exist, there is no hope
We are all hopeless, we are broken
No tower built could ever save our souls
There is no hope, there is no
All creation waits
Aching for the day
(Falling, fading)
There is no escape
From what the author fates
(Falling, fading)
We've been living in shadows
Soon exposed to the light
Our existence will rupture
When the maker arrives
Every vanity shattered
Every galaxy frayed
We will suffer no longer
In these delicate frames
But no man knows the season or the time
And fault will find us all in guilty lives
And only mercy can a hope provide
Return, Repent,