Unsupervised Learning: Agglomerative Clustering & Microarray Analysis, Assignments of Programming Languages

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Unsupervised Learning:

Clustering & Model Fitting

Administrivia

Reminder: office hours truncated tomorrow

“whenever I get in” until noon

HW3 due: Dec 2

Have an excellent Turkey Day!

The art of presentations

Do NOT tell us:

Every detail of every experiment

Choose the parts to show us carefully

Each thing you show us should be informative

about your conclusions

Place for excruciating detail is the paper

Every step of all the math

Every background reference

Focus on the “big picture” and the “take home

message”

Listeners will take home ~10 bytes. Make sure

they’re the right 10 bytes!

The unsupervised problem

Given:

Set of data points

Find:

Good description of the data

General unsup tasks

Given, data matrix

Which points are similar?

How do points cluster together?

How many groups are there?

Statistical description of distribution of data?

X =

x

11

x

12

· · · x

1 N

x

21

x

2 N

x

d 1

... x

dN

5 minutes of bioinformatics

Gene microarray (a.k.a., genechip, DNA chip, etc.)

Measure thousands (10s or 100s of thousands) of

genes simultaneously

Critical tool in bioinformatics

Understand function of genes, networks of gene

activity, response to stimuli, etc.

Leads to some very nasty analysis problems...

Only mRNA can be (easily measured)

When gene is “activated”, mRNA is produced

Can be “upregulated” or “downregulated” to

produce diff. concentrations of mRNA

Can be active or inactive under different

conditions:

External stimuli (food, ph, temperature, viral

infection, etc.)

Internal metabolic processes (cell cycles,

pathways, etc.)

mRNA measurements correlated with cell activity

5 minutes of bioinformatics

5 minutes of bioinformatics

measuring many mRNA...

Population A of cells

Population B of cells

mRNA pool A

mRNA pool B

Irradiation

5 minutes of bioinformatics

Imaging

[ x

1

, x

2

, ..., x

d

]

Data vector

5 minutes of bioinformatics

Measure populations over

time

Monitor development of

cell, metabolic processes,

response to introduction

of stimulus, etc.

Time series of data

     

x 11

x 12

· · · x 1 N

x 21

.

.

. x 2 N

.

.

.

.

.

.

x d 1

... x dN

     

timepoints

genes

Can consider either rows or

columns to be “points”, depending

on what you want to know

Similarity & distance

Most clust. algorithms based on distances between

points

Recall: distance (metric) function d ( x

1

, x

2

Symmetry: d ( x

1

, x

2

)= d ( x

2

, x

1

Identity: d ( x

1

, x

1

Triangle inequality: d ( x

1

, x

3

)<= d ( x

1

, x

2

)+ d ( x

2

, x

3

E.g., Euclidean distance, kernel distance, etc.

Sometimes have a natural similarity function instead

Can usually convert to a metric or semi-metric

Agglomerative clustering

Group clusters by mutual distance

“Bottom-up” method: start w/ points and combine

into groups, combine groups, etc.

Dist between clusters?

Problem: We have distance between pairs of points

Agglomerative clustering requires distance between

pairs of clusters

A number of measures are possible:

d

min

(c

1

, c

2

) = min

x∈c 1

;x

′ ∈c 2

d(x, x

′

c

c

Dist between clusters?

Problem: We have distance between pairs of points

Agglomerative clustering requires distance between

pairs of clusters

A number of measures are possible:

d

max

(c

1

, c

2

) = max

x∈c 1

;x

′ ∈c 2

d(x, x

′

c

c