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CENTR
FORINTEGRATIVE
BIOINFORMATICSVU
E
Lecture 6
Machine Learning
Bioinformatics Data Analysis and Tools
2
Supervised Learning
Train dataset
ML algorithm
model predictionnew observation
System (unknown)observationsproperty of interest
?
supervisor
Classification
3
Unsupervised Learning
ML for unsupervised learning attempts to discover interesting structure in the available data
Data mining, Clustering
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What is your question?• What are the targets genes for my knock-out gene?• Look for genes that have different time profiles between different cell types.
Gene discovery, differential expression
• Is a specified group of genes all up-regulated in a specified conditions?Gene set, differential expression
• Can I use the expression profile of cancer patients to predict survival?• Identification of groups of genes that predictive of a particular class of tumors?
Class prediction, classification
• Are there tumor sub-types not previously identified? • Are there groups of co-expressed genes?
Class discovery, clustering
• Detection of gene regulatory mechanisms. • Do my genes group into previously undiscovered pathways?
Clustering. Often expression data alone is not enough, need to incorporate sequence and other information
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Predefined Class
{1,2,…K}
1 2 K
Objects
Basic principles of discrimination•Each object associated with a class label (or response) Y {1, 2, …, K} and a feature vector (vector of predictor variables) of G measurements: X = (X1, …, XG)
Aim: predict Y from X.
X = {red, square} Y = ?
Y = Class Label = 2
X = Feature vector {colour, shape}
Classification rule ?
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Discrimination and PredictionLearning Set
Data with known classes
ClassificationTechnique
Classificationrule
Data with unknown classes
ClassAssignment
Discrimination
Prediction
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Example: A Classification Problem
• Categorize images of fish—say, “Atlantic salmon” vs. “Pacific salmon”
• Use features such as length, width, lightness, fin shape & number, mouth position, etc.
• Steps1. Preprocessing (e.g., background
subtraction)2. Feature extraction 3. Classification
example from Duda & Hart
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Classification in Bioinformatics
• Computational diagnostic: early cancer detection
• Tumor biomarker discovery
• Protein folding prediction
• Protein-protein binding sites prediction
• Gene function prediction
• …
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?Bad prognosis
recurrence < 5yrsGood Prognosis
recurrence > 5yrs
ReferenceL van’t Veer et al (2002) Gene expression profiling predicts clinical outcome of breast cancer. Nature, Jan..
ObjectsArray
Feature vectorsGene
expression
Predefine classesClinical
outcome
new array
Learning set
Classificationrule
Good PrognosisMatesis > 5
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Classification Techniques
• K Nearest Neighbor classifier
• Support Vector Machines
• …
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Instance Based LearningKey idea: just store all training examples <xi,f(xi)>
Nearest neighbor:• Given query instance xq, first locate nearest
training example xn, then estimate f(xq)=f(xn)
K-nearest neighbor:
• Given xq, take vote among its k nearest neighbors (if discrete-valued target function)
• Take mean of f values of k nearest neighbors (if
real-valued) f(xq)=i=1k f(xi)/k
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K-Nearest Neighbor
• A lazy learner …
• Issues: – How many neighbors?– What similarity measure?
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Which similarity or dissimilarity measure?
• A metric is a measure of the similarity or dissimilarity between two data objects
• Two main classes of metric:– Correlation coefficients (similarity)
• Compares shape of expression curves• Types of correlation:
– Centered.– Un-centered.– Rank-correlation
– Distance metrics (dissimilarity)• City Block (Manhattan) distance• Euclidean distance
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• Pearson Correlation Coefficient (centered correlation)
Sx = Standard deviation of x
Sy = Standard deviation of y
n
i y
i
x
in S
yy
S
xx
11
1
Correlation (a measure between -1 and 1)
Positive correlation Negative correlation
You can use absolute correlation to capture both positive and negative correlation
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Potential pitfalls
Correlation = 1
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Distance metrics• City Block (Manhattan)
distance:– Sum of differences across
dimensions– Less sensitive to outliers – Diamond shaped clusters
• Euclidean distance:– Most commonly used
distance– Sphere shaped cluster– Corresponds to the
geometric distance into the multidimensional space
i
ii yxYXd ),( i
ii yxYXd 2)(),(
where gene X = (x1,…,xn) and gene Y=(y1,…,yn)
X
Y
Condition 1
Co
nd
itio
n 2
Condition 1
X
Y
Co
nd
itio
n 2
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Euclidean vs Correlation (I)
• Euclidean distance
• Correlation
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When to Consider Nearest Neighbors
• Instances map to points in RN
• Less than 20 attributes per instance• Lots of training data
Advantages:• Training is very fast • Learn complex target functions• Do not loose information
Disadvantages:• Slow at query time • Easily fooled by irrelevant attributes
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Voronoi Diagram
query point qf
nearest neighbor qi
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3-Nearest Neighbors
query point qf
3 nearest neighbors
2x,1o
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7-Nearest Neighbors
query point qf
7 nearest neighbors
3x,4o
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Nearest Neighbor (continuous)
1-nearest neighbor
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Nearest Neighbor (continuous)
3-nearest neighbor
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Nearest Neighbor (continuous)
5-nearest neighbor
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Nearest Neighbor
• Approximate the target function f(x) at the single query point x = xq
• Locally weighted regression = generalization of IBL
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Curse of DimensionalityImagine instances are described by 20 attributes but only 10 are
relevant to target function
Curse of dimensionality: nearest neighbor is easily misled when the instance space is high-dimensional
One approach: weight the features according to their relevance!
• Stretch j-th axis by weight zj, where z1,…,zn chosen to minimize prediction error
• Use cross-validation to automatically choose weights z1,…,zn
• Note setting zj to zero eliminates this dimension alltogether (feature subset selection)
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Practical implementations
• Weka – IBk
• Optimized – Timbl
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Example: Tumor Classification
• Reliable and precise classification essential for successful cancer treatment
• Current methods for classifying human malignancies rely on a variety of morphological, clinical and molecular variables
• Uncertainties in diagnosis remain; likely that existing classes are heterogeneous
• Characterize molecular variations among tumors by monitoring gene expression (microarray)
• Hope: that microarrays will lead to more reliable tumor classification (and therefore more appropriate treatments and better outcomes)
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Tumor Classification Using Gene Expression Data
Three main types of ML problems associated with tumor classification:
• Identification of new/unknown tumor classes using gene expression profiles (unsupervised learning – clustering)
• Classification of malignancies into known classes (supervised learning – discrimination)
• Identification of “marker” genes that characterize the different tumor classes (feature or variable selection).
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B-ALL T-ALL AML
ReferenceGolub et al (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286(5439): 531-537.
ObjectsArray
Feature vectorsGene
expression
Predefine classes
Tumor type
?
new array
Learning set
ClassificationRule
T-ALL
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Nearest neighbor rule
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SVM• SVMs were originally proposed by Boser, Guyon and Vapnik
in 1992 and gained increasing popularity in late 1990s.• SVMs are currently among the best performers for a number
of classification tasks ranging from text to genomic data.• SVM techniques have been extended to a number of tasks
such as regression [Vapnik et al. ’97], principal component analysis [Schölkopf et al. ’99], etc.
• Most popular optimization algorithms for SVMs are SMO [Platt ’99] and SVMlight
[Joachims’ 99], both use decomposition to hill-climb over a subset of αi’s at a time.
• Tuning SVMs remains a black art: selecting a specific kernel and parameters is usually done in a try-and-see manner.
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SVM
• In order to discriminate between two classes, given a training dataset– Map the data to a higher dimension
space (feature space)
– Separate the two classes using an optimal linear separator
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Feature Space Mapping• Map the original data to some higher-
dimensional feature space where the training set is linearly separable:
Φ: x → φ(x)
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The “Kernel Trick”• The linear classifier relies on inner product between vectors K(xi,xj)=xi
Txj
• If every datapoint is mapped into high-dimensional space via some transformation Φ: x → φ(x), the inner product becomes:
K(xi,xj)= φ(xi) Tφ(xj)
• A kernel function is some function that corresponds to an inner product in some expanded feature space.
• Example:
2-dimensional vectors x=[x1 x2]; let K(xi,xj)=(1 + xiTxj)2
,
Need to show that K(xi,xj)= φ(xi) Tφ(xj):
K(xi,xj)=(1 + xiTxj)2
,= 1+ xi12xj1
2 + 2 xi1xj1 xi2xj2+ xi2
2xj22 + 2xi1xj1 + 2xi2xj2=
= [1 xi12 √2 xi1xi2 xi2
2 √2xi1 √2xi2]T [1 xj12 √2 xj1xj2 xj2
2 √2xj1 √2xj2] =
= φ(xi) Tφ(xj), where φ(x) = [1 x1
2 √2 x1x2 x22 √2x1 √2x2]
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Linear Separators
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Optimal hyperplane
ρ
Support vector
margin
Optimal hyper-plane
Support vectors uniquely characterize optimal hyper-plane
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Optimal hyperplane: geometric view
11
11
ii
ii
yforbxw
yforbxw
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Soft Margin Classification • What if the training set is not linearly separable?
• Slack variables ξi can be added to allow misclassification of difficult or noisy examples.
ξjξk
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Weakening the constraints
Weakening the constraints
Allow that the objects do not strictly obey the constraints
Introduce ‘slack’-variables
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Influence of C
Erroneous objects can still have a (large) influence on the solution
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SVM
• Advantages:– maximize the margin between two classes in the
feature space characterized by a kernel function– are robust with respect to high input dimension
• Disadvantages:– difficult to incorporate background knowledge– Sensitive to outliers
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SVM and outliersoutlier
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Classifying new examples
• Given new point x, its class membership is
sign[f(x, *, b*)], where ***
1
***** ),,( bybybbfSVi iii
N
i iii xxxxxwx
Data enters only in the form of dot products!
**** ),(),,( bKybfSVi iii
xxx
and in general
Kernel function
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Classification: CV error
• Training error– Empirical error
• Error on independent test set – Test error
• Cross validation (CV) error– Leave-one-out (LOO)– N-fold CV
N samples
splitting
1/n samples for testing
Summarize CV error rate
N-1/n samples for training
Count errors
