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1
K-means and
Hierarchical
Clustering
K-means and Hierarchical Clustering: Slide 2
Some
Data
This could easily be
modeled by a
Gaussian Mixture
(with 5 components)
But let’s look at an
satisfying, friendly and
infinitely popular
alternative…
2
K-means and Hierarchical Clustering: Slide 3
Lossy Compression
Suppose you transmit the
coordinates of points drawn
randomly from this dataset.
You can install decoding
software at the receiver.
You’re only allowed to send
two bits per point.
It’ll have to be a “lossy
transmission”.
Loss = Sum Squared Error
between decoded coords and
original coords.
What encoder/decoder will
lose the least information?
K-means and Hierarchical Clustering: Slide 4
Suppose you transmit the
coordinates of points drawn
randomly from this dataset.
You can install decoding
software at the receiver.
You’re only allowed to send
two bits per point.
It’ll have to be a “lossy
transmission”.
Loss = Sum Squared Error
between decoded coords and
original coords.
What encoder/decoder will
lose the least information?
Idea One
00
1110
01
Break into a grid,
decode each bit-pair
as the middle of
each grid-cell
A
n
y
B
e
t
t
e
r
I
d
e
a
s
?
3
K-means and Hierarchical Clustering: Slide 5
Suppose you transmit the
coordinates of points drawn
randomly from this dataset.
You can install decoding
software at the receiver.
You’re only allowed to send
two bits per point.
It’ll have to be a “lossy
transmission”.
Loss = Sum Squared Error
between decoded coords and
original coords.
What encoder/decoder will
lose the least information?
Idea Two
00
11
10
01
Break into a grid, decode
each bit-pair as the
centroid of all data in
that grid-cell
A
n
y
F
u
r
t
h
e
r
I
d
e
a
s
?
K-means and Hierarchical Clustering: Slide 6
K-means
1. Ask user how many
clusters they’d like.
(e.g. k=5)
4
K-means and Hierarchical Clustering: Slide 7
K-means
1. Ask user how many
clusters they’d like.
(e.g. k=5)
2. Randomly guess k
cluster Center
locations
K-means and Hierarchical Clustering: Slide 8
K-means
1. Ask user how many
clusters they’d like.
(e.g. k=5)
2. Randomly guess k
cluster Center
locations
3. Each datapoint finds
out which Center it’s
closest to. (Thus
each Center “owns”
a set of datapoints)
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