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Clustering_Biomedicine Students

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Susanne Gerber

on 23 March 2017

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Transcript of Clustering_Biomedicine Students

Clustering, Klassifikation and Dimensions Reduktion
Supervised versus unsupervised learning
Learning by examples
An
Enemy
is:
A
friend
is
Learning by rules:
A
friend
looks exactly
like us
is
smaller
than us
or - if larger -
has
hooves
is a big furry animal eating grass on a meadow
is an animal with feather
AND
either paddles or a very long neck/pecker (ideally both)
An
enemy

has sharp teeth
is larger than 20 cm - having paws
barks, howls or growls
is a bird of our size or larger with compact corpus (short neck) with claws
,...
(
size
in cm,
sharp

teeth
(1=yes, 0 =no),
#legs
,
feathers
(yes=1, no=0),
claws
(1=yes, 0 =no),
furry
(1=yes, 0 =no),
hooves
(1=yes, 0 =no), length of the
neck
in cm,...)
Supervised learning
is the machine learning task of inferring a function from labeled training data in order to make predictions for the future
Each example consists of an input vector (feature vector) and a desired output (label)
Feature vector:
Label
: (enemy, friend)
(100, 1, 4, 0,1 ,1,0,8)
Feature vector:
Label:
(150, 1, 4, 0, 1, 1, 0, 10)
(60, 1, 4, 0, 1, 1, 0, 7)
(30, 0, 2, 1, 1,0, 0, 3)
(140, 0, 4, 0, 0,1, 1, 5)
(8, 0, 4, 0, 1,1, 0, 2)
(6, 0, 2, 1, 1,0, 0, 1)
enemy
enemy
enemy
enemy
friend
friend
friend
Find a function that maps between the input and the desired output
allowing to classify (determine the correct class label) new/unseen instances.
? enemy or friend ?
(100, 0, 2, 1, 0, 0, 60)
(10, 0, 4,0,0,0,0)
? enemy or friend ?
? enemy or friend ?
(200, 0, 4,0,1,1,100)
unsupervised learning
is the machine learning task of inferring a function to describe cluster/groups of objects from
unlabeled
together according to their natural characteristics
clustering occurs without a priori knowledge
goal is to detect pattern or (hidden) structures in the (high-dimensional) data
Where do those rules come from ?
Reduction of Dimensions !
(50, 0,2,1,0,0,0,40)
This task is much more vage than supervised clustering.

In higher dimensions the categorization is neither unique nor canonical.

There exist a multitude of different approaches and concepts.
friend
Clustering algorithms
Why do we need clustering ?
In several situations we don't know the labeling and wish to learn rules from the data (data-driven modeling)
Clustering
approaches
Partitional
(or centroid-based)
clustering
Hierarchical
clustering
k-means
model-based
clustering
Spectral
clustering
agglomerative
algorithms
divisive
algorithms
density-based
clustering
or "how to optimize the grouping of objects by minimizing distances"
The k-means algorithm partitions the data for a given k into k mutually exclusive cluster
How k-mean works:
Fisher's iris data consists of measurements on the sepal length, sepal width, petal length, and petal width for 150 iris specimens. There are 50 specimens from each of three species.
Goal: minimize iteratively the variance (inner-cluster-distance) in each cluster
Formal definition: Minimization of the total-cluster variance
Tasks/Problems:
Fisher's iris data
Input:
K
and a set of data-points (
x1,...xn
)
Initialization
: place
K
centroid-seeds at random locations
Assign
each data point
x
i
to the nearest centroid
cj

(depends on the chosen distance measure)
Repeat
until convergence:
How to compute the centroids positions without knowing the cluster assignment of each point ?
How to assign the data points to a certain cluster without knowing the centroid positions ?
Calculate for
each cluster

j=1,...,K
the new centroid
cj

(the mean of all points
xi
assigned to cluster
j
in the
previous step

Stop
when the solution converges (none of the cluster assignment changes any more)
How to choose the correct number of cluster ?
Does the algorithm guarantee convergence to the global optimum ?
Sir Ronald Aylmer Fisher
Clustering
an English statistician and biologist who used mathematics to combine Mendelian genetics and natural selection.
(17 February 1890 – 29 July 1962),
Silhouette coefficient
Principal Component Analysis (PCA)
Pollen et. al. :Nature Biotechnology 32, 1053–1058 (2014) doi:10.1038/nbt.2967
Example:
PCA is a simple yet popular and useful linear transformation technique that is used in numerous applications (e.g. gene expression data).

It transforms the data to a new coordinate system such that the greatest variance by some projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on.
Main goals
:
identification and extraction of (hidden) patterns (correlation between variables) in the data -> allows for dimension reduction
Finding the directions of maximum variance in high-dimensional data and project it onto a smaller dimensional subspace while retaining most of the information.
Iris setosa
Iris versicolor
Iris virginica

The silhouette value of a point is a measure of how similar a point is to points in its own cluster compared to points in other clusters
where
a(i) is the average distance of the point
i
to the other points in its own cluster A
d(i, C)
is the average distance of the point
i
to the other points in the cluster C
b(i)
is the minimal
d(i, C)
over all clusters other than A
The silhouette coefficient is the average silhouette value over all points. A quantitative measure that can assess the quality of a clustering
Single linkage
complete linkage
average linkage
Connectivity-based clustering
Differential gene expression between the brachial and femoral artery based on microarray data: heat map showing the human orthologous genes of the 63 probe sets with a significant difference in gene expression (FDR < 0.05) as well as a 1.5-fold change between the brachial and the femoral artery.
Algorithm description:
Step 1:
Determine the distance between each pair of points m * (m - 1) / 2 different pairs -> adjacency matrix
Stop
:
Cut the hierarchical tree into cluster
Iteratively
group points into a binary hierarchical tree (linkage)
connect the closest pair of points and re-compute the distance matrix
Decicion trees
decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility.
Support vector machines
supervised learning models analyzing data used for classification and regression analysis.
Patients
Genes
Susanne Gerber
Computational Systems Genetics Group
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