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Visualization and Microarray

• Complement to numerical analysis

• Offers insightful information

• Detects the structure of dataset

• Early / late stage of data mining• Challenges of Microarray Visualization

– High dimensionality– Large data size– Intuitive layout– Low time complexity

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An Example – Early Stage

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General Approaches• Global Visualizations

– Encode each dimension uniformly by the same visual cue

Parallel coordinates

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General Approaches, con’t• Optimal Visualizations

– Estimate the parameters and assess the fit of various spatial distance models for proximity data

– Multidimensional scaling (MDS)• Sammon’s mapping: topology preservation. Two samples that

are close to each other have to stay close when projected.

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Sammon’s mapping

• Sammon’s mapping is a classical case of MDS• MDS optimizes 2-D presentation to preserve

distances in original N-dimensional space

• Sammon’s mapping iteratively minimizes

i ij ij

i ijij d

ddd

ijijE *

2

*

)( *1

dij* is the distance between points i and j in the N-dimensional spacedij* is the distance between points I and j in the visualization.

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2D to 1D

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A method for achieving this projection 1. D1, D2 and D3 (the interpoint distances in the higher

dimensional space) are calculated. 2. P1', P2' and P3' are generated randomly in the lower

dimensional space. 3. The mapping error, E, is calculated for all the

interpoint distances in the lower dimensional space.4. The gradient showing the direction which minimizes

the error is calculated. 5. The points in the lower dimensional space are moved

according to the direction given by the gradient. 6. Steps 3 to 5 are repeated until E is below a given

limit.

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Sammon’s mapping, con’t

• Some drawbacks – Computationally intensive, time complexity O(n2) – How to determine the best initialization– No user interaction is permitted– Addition of new data points requires rerun the process to get

new minimized projection– Information loss

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General Approaches, con’t• Projective Visualizations

– Use projection functions to achieve a low dimensional display

– Radial Visualizations• RadViz• Star Coordinates• VizStruct

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Comparison of ApproachesAdvantages Disadvantages

Global visualization Display all dimensional information, no computation

Severe overlapping, large space to display

Optimal visualization

Achieve optimal result, sound theoretical basis

Lack user interaction, heavy computation

Projection visualization

Concise display, little computation

Lack regorous proof, may not be optimal

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Challenges of Microarray Visualization

• High dimensionality• Large data size• Intuitive layout• Low time complexity

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Density or Heat Plots

Ge

nes

0

1

Sample

Increased

Before IFN After IFN

• Widely used with arrays

• Works well only for structured data

• Quantitative information is lost

• Gets easily cluttered

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TreeView Visualization

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Principal component analysisPCA: • linear projection of data onto major principal components defined by the eigenvectors of the covariance matrix.• PCA is also used for reducing the dimensionality of the data.• Criterion to be minimised: square of the distance between the original and projected data. This is fulfilled by the Karhuven-Loeve transformation

Px Px

1( )( )

1

ti i

i

x xn

C

P is composed by eigenvectors of the covariance matrix

Example: Leukemia data sets by Golub et al.: Classification of ALL and AML

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Sammon`s mapping:• Non-linear multi-dimensional scaling such as Sammon's mapping aim to optimally conserve the distances in an higher dimensional space in the 2/3-dimensional space.• Mathematically: Minimalisation of error function E by steepest descent method:

Multi-linear scaling

Example: DLBCL prognosis – cured vs featal cases

2( )1

Nij ij

Ni j ijiji j

D dE

DD

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Our Visualization Approach

Gene Space

Sample Space

Fourier Harmonic Projection

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Geometric Interpretation

N-dimensional space Two-dimensional space

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An Example of the Mapping

P=[a,a,…a] -> ?

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First Fourier Harmonic Projection

N-dimensional space Two-dimensional space

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Analytical Properties

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Scaling and Transpose Property

Original

Shift

Scaling

Transpose

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Time Shifting Property

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Visual Exploration Framework

• Explorative Visualization – Sample space

• Confirmative Visualization – Gene space

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VizStruct Architecture

WebBrowser WebBrowser

Internet

Client

ClientClient

Web Server

MatlabWeb Server

MatlabLibraries

Intranet

MatlabApplications

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VizStruct User Interface

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VizStruct User Interface (3)

Cartesian Plot Polar plot

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VizStruct User Interface (2)

EM Mixture Density contour

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Sample Classification

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Binary Classification

Leukemia-A

72 samples with 7129 genes 38(27+11)Training,34(20+14) Testing, hold out evaluation

Multiple Sclerosis

44 samples, 4132 genes MS_IFN(28), MS_CON(30), cross validation evaluation

Binary classification: two sample classes

Evaluation: hold out and cross validation

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Multiple Classification

Breast Cancer

22 samples with 3226 genes 3 Classes: BRCA1 (7), BRCA2 (8), Sporadic (7) cross validation evaluation

88 samples with 2308 genes 4 classes: RMS, BL, NB, EWS, 63 Training and 25 Testing

SRBCT

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Classification Summary

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Temporal Pattern (1)

10-OH NortryptylineNortryptyline

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Temporal Pattern (2)

• Rat Kidney data set of Stuart et al. (2001) contains 873 genes of 7 time points during kidney development

• There are 5 patterns or gene groups classified by the author

• Parallel coordinate shows the actual data comply to the profiles but with some noise

Parallel coordinates for each of the gene groups

Idealized temporal gene expression profiles

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Temporal Pattern (3)

Genes having very high relative levels of expression in early development

Genes having arelatively steady increase in expression throughout development

The first Fourier harmonic projection

Genes are somewhat symmetric to the middle time point, i.e., they are transposing each other

Genes are very similar except the last time point

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VizStruct vs. Sammon’s Mapping

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147148149 150

Ima

gin

ary

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rt o

f F

1(x[n

])

Real Part of F1(x[n])

VizStruct

-4

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0

2

4

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123

45

67

89 1011

1213

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1920

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gin

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rt o

f F

1(x

[n])

Real Part of F1(x[n])

Sammon's Mapping

• VizStruct is similar to Sammon’s mapping

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VizStruct - Dimension Tour

Interactively adjust dimension parameters

Manually or automatically

May cause false clusters to break

Create dynamic visualization

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Visualized Results for a Time Series Data Set

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Interrelated Dimensional Clustering

The approach is applied on classifying multiple-sclerosis patients and IFN-drug treated patients.

– (A) Shows the original 28 samples' distribution. Each point represents a sample, which is a mapping from the sample's 4132 genes intensity vectors.

– (B) Shows 28 samples' distribution on 2015 genes.– (C) Shows 28 samples' distribution on 312 genes. – (D) Shows the same 28 samples distribution after using our approach. We reduce

4132 genes to 96 genes.

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References• Li Zhang, Aidong Zhang, and Murali Ramanathan VizStruct: Exploratory

Visualization for Gene Expression Profiling. Bioinformatics 2004 20: 85-92, 2004.• Li Zhang, Chun Tang, Yuqing Song, and Aidong Zhang, Murali Ramanathan.

VizCluster and Its Application on Clustering Gene Expression Data. International Journal of Distributed and Parallel Database, 13(1): 73-97, 2003

• Li Zhang, Aidong Zhang, and Murali Ramanathan: Enhanced Visualization of Time Series through Higher Fourier Harmonics. In proceeding of BIOKDD 2003, Washington DC, August 2003, pp 49-56.

• Li Zhang, Aidong Zhang, and Murali Ramanathan: Fourier Harmonic Approach for Visualizing Temporal Patterns of Gene Expression Data. In proceeding of IEEE Computer Society Bioinformatics Conference (CSB 2003). Stanford, CA, August 2003, pp131-141.

• Li Zhang, Aidong Zhang, and Murali Ramanathan. Visualized Classification of Multiple Sample Types. In proceeding of BIOKDD 2002, Edmonton, Alberta, Canada, July 2002, pp 55-62.

• Li Zhang, Chun Tang, Yong Shi, Yuqing Song, and Aidong Zhang, Murali Ramanathan. VizCluster: An Interactive Visualization Approach to Cluster Analysis and Its Application on Microarray Data. In proceeding of the Second SIAM International Conference on Data Mining (SDM02). Arlinton, VA. April 2002, pp 29-51.