Potential Data Mining Techniques for Flow Cyt Data Analysis

Li Xiong

Data Mining Functionalities

Association analysis Classification and prediction Cluster analysis Evolution analysis

Flow Cyt Data

Sample over time points Flow cyt data at each time point

cell – marker intensity matrix

Data Preprocessing

Data cleaning Reduce noise and handle missing values

Data transformation Discretization: discretize marker values into

ranges (gates?) Normalization

Marker based Cell based Sample based

Potential Analysis Marker-based clustering

Cluster markers based on their expression patterns Cell-based clustering

Cluster cells based on their expression patterns Marker-based frequent itemsets analysis

Find frequent co-elevated marker groups Sample-based clustering

Cluster samples based on their flow-cyt data Sample-based classification

Classify patient based on their flow-cyt data and other clinical data into pre-defined classes

Sample-based time series analysis Analyze how the flow cyt data evolves

Marker-Based Clustering

Plot each marker as a point in N-dimensional space (N = #of cells)

Define a distance metric between every two marker points in the N-dimensional space Euclidean distance Pearson correlation

Markers with a small distance share the same expression characteristics -> functionally related or similar?

Clustering -> functionally related markers?

Cell Based Clustering

Plot each cell as a point in N-dimensional space (N=# of markers)

Define a distance metric between every two cell points in the N-dimensional space

Cells with a small distance share the same expression characteristics -> functionally related or similar?

Clustering -> functionally related cells? Help with gating? (N-dimensional vs. 2-dimensional)

Clustering Techniques

Partition-based: Partition data into a set of disjoint clusters

Hierarchical: Organize elements into a tree (dendrogram), representing a hierarchical series of nested clusters

Agglomerative: Start with every element in its own cluster, and iteratively join clusters together

Divisive: Start with one cluster and iteratively divide it into smaller clusters

Graph-theoretical: Present data in proximity graph and solve graph-theoretical problems such as finding minimum cut or maximal cliques

Others

Partitioning Methods: K-Means Clustering

Input: A set, V, consisting of n points and a parameter k

Output: A set X consisting of k points (cluster centers) that minimizes the squared error distortion d(V,X) over all possible choices of X

• Given a data point v and a set of points X, define the distance from v to X, d(v, X), as the (Eucledian) distance from v to the closest point from X. Given a set of n data points V={v1…vn} and a set of k points X, define the Squared Error Distortion

d(V,X) = ∑d(vi, X)2 / n 1 < i < n

K-Means Clustering: Lloyd AlgorithmLloyd Algorithm1. Arbitrarily assign the k cluster centers2. while the cluster centers keep changing3. Assign each data point to the cluster Ci

corresponding to the closest cluster center (1 ≤ i ≤ k)

4. Update cluster centers according to the center of gravity of each cluster, that is, ∑v \ |C| for all v in C for every cluster C

*This may lead to merely a locally optimal clustering.

Some Discussion on k-means Clustering

May leads to a merely locally optimal clustering

Works well when the clusters are compact clouds that are rather well separated from one another.

Not suitable for clusters with nonconvex shapes or clusters of very different size.

Sensitive to noise and outlier data points Necessity for users to specify k

Hierarchical Clustering

Hierarchical Clustering Algorithm

Hierarchical Clustering (d , n) Form n clusters each with one element Construct a graph T by assigning one vertex to each cluster while there is more than one cluster Find the two closest clusters C1 and C2 Merge C1 and C2 into new cluster C with |C1| +|C2| elements Compute distance from C to all other clusters Add a new vertex C to T and connect to vertices C1 and C2 Remove rows and columns of d corresponding to C1 and C2 Add a row and column to d corrsponding to the new cluster

C return T

The algorithm takes a nxn distance matrix d of pairwise distances between points as an input.Different ways to define distances between clusters may lead to different clusters

Graph Theoretical Methods: Clique Graphs

Turn the distance matrix into a distance graph Cells are represented as vertices in the graph Choose a distance threshold θ If the distance between two vertices is below θ, draw

an edge between them Transform the distance graph into clique graph

by adding or removing edges The resulting graph may contain cliques that represent

clusters of closely located data points!

Marker Association Analysis Convert intensity values to present or absent The cell-marker intensity matrix can be transformed

to cell – list of present markers data

Mine for frequent marker sets that are co-present in cells

Potential association analysis for different gates (vs. present or absent)

B, E, F4

B, C, D, E, F5

A, D, E3

A, C, D2

A, B, D1

Present MarkersCell-id

Frequent Pattern Mining Methods

Three major approaches Apriori (Agrawal & Srikant@VLDB’94) Freq. pattern growth (FPgrowth—Han, Pei & Yin

@SIGMOD’00) Vertical data format approach (Charm—Zaki & Hsiao

@SDM’02)

Sample Based Classification Predict target attributes for patients based on a set of features:

e.g. is the patient healthy? Will the patient reject the transplant?

…

yes 5

no 4

no 3

yes 2

yes 1

Class1…Feature 2

Feature 1

Patient

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Classification: Model Construction

TrainingData

(w/ Label)

ClassificationAlgorithms

Classifier(Model)

NewData

(w/o Label)Labels

Feature Generation

Potential features Marker data Microarray data Clinical data

Marker Data Features

Cell distribution for each marker Histograms: % of cells for each range/gate

(corresponds to what users are currently plotting for pair-wise markers)

Min, max, average, variance of the intensity levels Distribution curves: % of cells for each intensity

value

Cell Distribution for Individual Marker (CD 62L)

Question

Is the cell distribution enough to represent the flow cyt data?

In other words, can we say two samples are similar or the same if they have the same cell distribution for each marker?

Cross-Marker Distribution

Pair-wise cell distribution? Can we use any results form the marker

based clustering, cell based clustering, and the marker based association analysis?

Others?

Feature Selection and Feature Extraction Problem: curse of dimensionality

Limited data samples Large set of features

Techniques: dimension reduction Feature selection Feature extraction

Feature Selection

Select a subset of features from feature space Theoretically - an optimal feature selection requires

exhaustive search of all possible subsets of features Practically - satisfactory set of features Approaches

Relevance analysis: remove redundant features based on correlation or mutual information (dependencies) among features

Greedy hill climbing: select an approximate “best” set of features using correlation and mutual information between features and class attributes

Feature Extraction

Map high dimensional feature space to low dimensional feature space

Approaches Principle Component Analysis: linear

transformation that maps projection of the data with greatest variance to the first coordinate (the first principal component), and so on.

Classification Methods

Decision tree induction

Bayesian classification

Neural network

Support Vector Machines (SVM)

Instance based methods

age?

overcast

IFM 1? IFM 2?

++ -- --++

<=30 >40

no noyes yes

yes

30..40

Decision Tree

Decision Tree - Comments

Relatively faster learning speed (than other classification methods)

Convertible to simple and easy to understand classification rules (e.g. if age<30 and IFM1 ++ then healthy)

Can use SQL queries for accessing databases Comparable classification accuracy with other

methods

Probabilistic Learning (Bayesian Classification)

Calculate explicit probabilities for hypothesis Characteristics

Incremental Standard Computationally intractable

Naïve Bayesian Classifier Conditional independency of attributes

Naïve Bayesian Classifier - Comments

Advantages Easy to implement Good results obtained in most of the cases

Disadvantages Assumption: conditional independence Practically, dependencies exist among variables

and cannot be modeled by Naïve Bayesian Classifier

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Discriminative Analysis

Learning a function of its inputs to base its decision on

x

xx

x

xx

x

x

x

x ooo

oo

o

o

o

o o

oo

o

Neural Network

Output nodes

Input nodes

Hidden nodes

Output vector

Input vector: xi

wij

SVM

Support Vectors

Small Margin Large Margin

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Discriminative Classifiers vs. Bayesian Classifiers

Advantages prediction accuracy is generally high robust, works when training examples contain errors fast evaluation of the learned target function

Criticism long training time difficult to understand the learned function (weights) not easy to incorporate domain knowledge

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Instance-Based Methods

Instance-based learning: Store training examples and delay the processing (“lazy

evaluation”) until a new instance must be classified Typical approaches

k-nearest neighbor approach Instances represented as points in a Euclidean space.

Locally weighted regression Constructs local approximation

Case-based reasoning Uses symbolic representations and knowledge-based

inference

Popular Implementations General

Weka: an open source toolkit written in Java with

implementations of many basic algorithms of classification,

clustering, association analysis, can be accessed through GUI

interface or Java API

Specialized ones SVM-light: simple implementation of SVM in C

KDNuggets: a good directory of data mining software (commercial as well as open source) http://www.kdnuggets.com/software/index.html

Summary

Potential adaptation and evaluation of a set of data mining techniques for flow cyt data analysis

Domain knowledge is important for each of the steps