StatQuest: K-means clustering
Summary
TLDRIn this episode of Stat Quest, Josh Starmer introduces k-means clustering, a method for organizing data points into distinct groups. The tutorial covers selecting the number of clusters (K), randomly choosing initial points, calculating distances to assign points to the nearest cluster, and iteratively updating cluster means until convergence. It also explores determining the optimal K value using an 'elbow plot' and discusses the difference between k-means and hierarchical clustering. The video concludes with examples of applying k-means to data on a number line, in two dimensions, and on a heatmap, illustrating the versatility of this clustering technique.
Takeaways
- π The video is an educational tutorial on k-means clustering, a method used to group data points into clusters.
- π It explains how to identify the optimal number of clusters, 'K', for the data set, which is a crucial step in k-means clustering.
- π― The process begins by randomly selecting 'K' distinct data points as initial clusters and then iteratively refining these clusters.
- π The script describes how to calculate the distance of each data point from the centroids of the clusters to assign them to the nearest cluster.
- βοΈ It discusses the importance of calculating the mean of each cluster to update the centroids and reassign points based on these new values.
- π The iterative process continues until the clusters no longer change, indicating that the clustering has converged to a stable solution.
- π The quality of clustering can be assessed by measuring the total variation within each cluster, with lower variation indicating better clustering.
- π The 'elbow method' is introduced as a way to determine the best value for 'K' by observing the point where the reduction in variance per additional cluster diminishes.
- π€ The video highlights that k-means clustering is different from hierarchical clustering in that it aims to partition data into a specified number of clusters.
- π The script also covers how to apply k-means clustering to data that is not on a number line, using Euclidean distance in two or more dimensions.
- π‘οΈ It mentions that k-means can be used with data represented as a heatmap, by treating the data points in a two-dimensional space and applying the same clustering principles.
- πΆ The video ends with a call to action for viewers to subscribe for more content and support the channel by liking the video and considering purchasing the creator's songs.
Q & A
What is the main topic of the video?
-The main topic of the video is k-means clustering, a method used to group data into clusters based on their similarities.
Who is the presenter of the video?
-The presenter of the video is Josh Stormer.
What is the purpose of using k-means clustering in the video?
-The purpose of using k-means clustering in the video is to identify clusters in data without relying on visual inspection, such as distinguishing between different types of tumors or cell types.
What is the 'K' in k-means clustering?
-The 'K' in k-means clustering represents the number of clusters that the algorithm is instructed to identify in the data.
How does k-means clustering start the clustering process?
-K-means clustering starts by randomly selecting 'K' distinct data points as the initial clusters.
What is the method used to assign data points to clusters in k-means clustering?
-Data points are assigned to the nearest cluster based on the calculated distance between the point and the centroids of the clusters.
How does the k-means algorithm determine the best value for K?
-The best value for K can be determined by trying different values and observing the total variation within the clusters, often using an elbow plot to identify the point where the reduction in variance decreases significantly.
What is an elbow plot in the context of k-means clustering?
-An elbow plot is a graphical representation that shows the reduction in variance as the number of clusters increases, helping to identify the optimal number of clusters by finding the 'elbow' point where the decrease in variance slows down.
How does k-means clustering differ from hierarchical clustering?
-K-means clustering aims to partition the data into a specified number of clusters, whereas hierarchical clustering builds a tree of clusters and does not require a predetermined number of clusters.
Can k-means clustering be applied to data that is not plotted on a number line?
-Yes, k-means clustering can be applied to data in two or more dimensions using the Euclidean distance to measure the distance between points.
How is the Euclidean distance calculated for data with more than two dimensions?
-The Euclidean distance for data with more than two dimensions is calculated as the square root of the sum of the squared differences between corresponding coordinates of points in the multidimensional space.
What is the significance of calculating the mean of each cluster in k-means clustering?
-Calculating the mean of each cluster is important because it helps to reassign the data points to the nearest updated cluster center, which is essential for the iterative process of refining the clusters.
Outlines
π Introduction to K-Means Clustering
Josh Stormer introduces the concept of k-means clustering, a method for organizing data points into clusters based on their similarity. The video aims to demonstrate how to apply this technique to data that can be plotted on a line, an XY graph, or a heatmap. The process begins by selecting the number of clusters (K), choosing initial cluster centers, and iteratively refining the clusters by reassigning points to the nearest mean until no changes occur. The video also hints at a more sophisticated method for determining the optimal value of K.
π Exploring K-Means Clustering Techniques and Cluster Quality Assessment
This paragraph delves deeper into the k-means clustering process, emphasizing the iterative nature of the algorithm and the importance of selecting the right value for K. It explains how to assess the quality of clustering by measuring the total variation within clusters. The video introduces the concept of an 'elbow plot' to help determine the optimal number of clusters by observing the rate of variance reduction. Additionally, it touches on the differences between k-means and hierarchical clustering, and how k-means can be applied to data in two or more dimensions using Euclidean distance. The summary concludes with a mention of how to handle heatmap data by treating it as a two-dimensional case for clustering.
Mindmap
Keywords
π‘StatQuest
π‘K-means Clustering
π‘Cluster
π‘XY Graph
π‘Heat Map
π‘K (in k-means)
π‘Euclidean Distance
π‘Centroid
π‘Iteration
π‘Elbow Plot
π‘Hierarchical Clustering
Highlights
Introduction to k-means clustering and its application in grouping data on a line or an XY graph and even on a heatmap.
The necessity of choosing the best value for K in k-means clustering to identify the correct number of clusters.
Step-by-step explanation of the k-means clustering process starting from selecting the number of clusters.
The method of randomly selecting initial clusters and the importance of this step in the k-means algorithm.
Calculating the distance between data points and clusters to assign points to the nearest cluster.
The iterative process of recalculating the mean of each cluster and re-clustering based on the new means.
Assessing the quality of clustering by measuring the total variation within each cluster.
The concept of using multiple starting points to improve the reliability of k-means clustering results.
The use of an elbow plot to determine the optimal value for K by observing the reduction in variance.
Comparing k-means clustering with hierarchical clustering and their distinct approaches to data grouping.
Application of k-means clustering in two-dimensional space using Euclidean distance.
Explanation of how to handle data that is not plotted on a number line by using Euclidean distance in higher dimensions.
Approach to clustering heatmap data by renaming samples as x and y and plotting them on an XY graph.
The significance of calculating Euclidean distances for clustering data with more than two dimensions.
Encouragement for viewers to subscribe for more educational content on statistical methods.
Invitation for viewers to support the channel by liking the video and considering purchasing original songs.
Transcripts
statcast
[Music]
stat quest stat quest stat quest hello
I'm Josh stormer and welcome to stat
quest today we're going to be talking
about k-means clustering we're gonna
learn how to cluster samples that can be
put on a line on an XY graph and even on
a heat map and lastly we'll also talk
about how to pick the best value for K
imagine you had some data that you could
plot on a line and you knew you needed
to put it into three clusters maybe they
are measurements from three different
types of tumors or other cell types in
this case the data make three relatively
obvious clusters but rather than rely on
our eye let's see if we can get a
computer to identify the same three
clusters to do this we'll use k-means
clustering we'll start with raw data
that we haven't yet clustered step one
select the number of clusters you want
to identify in your data this is the K
in k-means clustering in this case we'll
select K equals three that is to say we
want to identify three clusters there is
a fancier way to select a value for K
but we'll talk about that later
step two randomly select three distinct
data points these are the initial
clusters
step 3 measure the distance between the
first point and the three initial
clusters this is the distance from the
first point to the blue cluster this is
the distance from the first point to the
green cluster
and this is the distance from the first
point to the orange cluster well it's
kind of yellow but we'll just call it
orange for now step 4 assign the first
point to the nearest cluster in this
case the nearest cluster is the blue
cluster now we do the same thing for the
next point we measure the distances and
then assign the point to the nearest
cluster now we figure out which cluster
the third point belongs to we measure
the distances and then assign the point
to the nearest cluster the rest of these
points are closest to the orange cluster
so they'll go in that one two now that
all the points are in clusters we go on
to step 5 calculate the mean of each
cluster then we repeat what we just did
measure and cluster using the mean
values
since the clustering did not change at
all during the last iteration were done
BAM the k-means clustering is pretty
terrible compared to what we did by eye
we can assess the quality of the
clustering by adding up the variation
within each cluster here's the total
variation within the clusters since
k-means clustering can't see the best
clustering it's only option is to keep
track of these clusters and their total
variance and do the whole thing over
again with different starting points so
here we are again back at the beginning
k-means clustering picks three initial
clusters and then clusters all the
remaining points calculates the mean of
each cluster and then re clusters based
on the new means it repeats until the
cluster is no longer change bit bit bit
of bit of boop boop boop now that the
data are clustered we sum the variation
within each cluster
and then we do it all again
at this point k-means clustering knows
that the second clustering is the best
clustering so far but it doesn't know if
it's the best overall so it will do a
few more clusters it does as many as you
tell it to do and then come back and
return that one if it is still the best
question how do you figure out what
value to use for K with this data it's
obvious that we should set K to three
but other times it is not so clear one
way to decide is to just try different
values for K
we'll start with k equals 1 k equals 1
is the worst case scenario we can
quantify its badness with the total
variation now try K equals 2 K equals 2
is better and we can quantify how much
better by comparing the total variation
within the two clusters to K equals 1
now try K equals 3 k equals 3 is even
better we can quantify how much better
by comparing the total variation within
the three clusters to k equals 2 now try
k equals 4 the total variation within
each cluster is less than when K equals
3 each time we add a new cluster the
total variation within each cluster is
smaller than before and when there is
only one point per cluster the variation
equals 0 however if we plot the
reduction in variance per value for K
there is a huge reduction in variation
with K equals three but after that the
variation doesn't go down as quickly
this is called an elbow plot and you can
pick K by finding the elbow in the plot
question how is k-means clustering
different from hierarchical clustering
k-means clustering specifically tries to
put the data into the number of clusters
you tell it to hierarchical clustering
just tells you pairwise what two things
are most similar question what if our
data isn't plotted on a number line just
like before you pick three random points
and we use the Euclidean distance in two
dimensions the Euclidean distance is the
same thing as the Pythagorean theorem
then just like before we assign the
point to the nearest cluster and just
like before we then calculate the center
of each cluster and re cluster BAM
although this looks good the computer
doesn't know that until it does the
clustering a few more times question
what if my data is a heatmap well if we
just have two samples we can rename them
x and y and we can then plot the data in
an XY graph then we can cluster just
like before note we don't actually need
to plot the data in order to cluster it
we just need to calculate the distances
between things when we have two samples
or two axes the Euclidean distance is
the square root of x squared plus y
squared when we have three samples or
three axes the Euclidean distance is the
square root of x squared plus y squared
plus Z squared and when we have four
samples or four axes the Euclidean
distance is the square root of x squared
plus y squared plus Z squared plus a
squared etc etc etc hooray
we've made it to the end of another
exciting stat quest if you like this
stat quest and want to see more please
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next time for another exciting stat
quest
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