2 Computational Issues Data Warehousing: Organising Biological Information into a Structured Entity (World’s Largest Distributed DB)Function Analysis (Numerical Analysis) :Gene Expression Analysis : Applying sophisticated data mining/Visualisation to understand gene activities within an environment (Clustering )Integrated Genomic Study : Relating structural analysis with functional analysisStructure Analysis (Symbolic Analysis) :Sequence Alignment: Analysing a sequence using comparative methods against existing databases to develop hypothesis concerning relatives (genetics) and functions (Dynamic Programming and HMM)Structure prediction : from a sequence of a protein to predict its 3D structure (Inductive LP)
3 Data Warehousing : Mapping Biologic into Data Logic
5 A comparison of the homology search and the motif search for functional interpretation of sequence information.Homology SearchMotif SearchNew sequenceNew sequenceKnowledgeacquisitionMotif library(Empirical rules)Sequence database(Primary data)RetrievalSimilarsequenceInferenceExpertknowledgeExpertknowledgeSequence interpretationSequence interpretation
6 Search and learning problems in sequence analysis
8 Biotinylated RNAfrom experimentGeneChip expressionanalysis probe arrayEach probe cell containsmillions of copies of a specificoligonucleotide probeStreptavidin-phycoerythrinconjugateImage of hybridized probe array
9 (Sub)cellular inhomogeneity Cell-cycle differences in expression.XIST RNA localized on inactiveX-chromosome( see figure)
10 Cluster AnalysisProtein/protein complexGenesDNA regulatory elements
11 Functional Analysis via Gene Expression Pairwise MeasuresClusteringMotif Searching/...
12 Clustering Algorithms A clustering algorithm attempts to find natural groups of components (or data) based on some similarity. Also, the clustering algorithm finds the centroid of a group of data sets.To determine cluster membership, most algorithms evaluate the distance between a point and the cluster centroids. The output from a clustering algorithm is basically a statistical description of the cluster centroids with the number of components in each cluster.
21 Distance-based Clustering Assign a distance measure between dataFind a partition such that:Distance between objects within partition (i.e. same cluster) is minimizedDistance between objects from different clusters is maximisedIssues :Requires defining a distance (similarity) measure in situation where it is unclear how to assign itWhat relative weighting to give to one attribute vs another?Number of possible partition is super-exponential
24 Hierarchical Clustering Given a set of N items to be clustered, and an NxN distance (or similarity) matrix, the basic process hierarchical clustering is this:1.Start by assigning each item to its own cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters equal the distances (similarities) between the items they contain.2.Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one less cluster.3.Compute distances (similarities) between the new cluster and each of the old clusters.4.Repeat steps 2 and 3 until all items are clustered into a single cluster of size N.
25 The distance between two clusters is defined as the distance between Single-Link Method / Nearest NeighborComplete-Link / Furthest NeighborTheir Centroids.Average of all cross-cluster pairs.
26 Computing Distancessingle-link clustering (also called the connectedness or minimum method) : we consider the distance between one cluster and another cluster to be equal to the shortest distance from any member of one cluster to any member of the other cluster. If the data consist of similarities, we consider the similarity between one cluster and another cluster to be equal to the greatest similarity from any member of one cluster to any member of the other cluster.complete-link clustering (also called the diameter or maximum method): we consider the distance between one cluster and another cluster to be equal to the longest distance from any member of one cluster to any member of the other cluster.average-link clustering : we consider the distance between one cluster and another cluster to be equal to the average distance from any member of one cluster to any member of the other cluster.
27 Single-Link Method Euclidean Distance a a,b b a,b,c a,b,c,d c d c d d (1)(2)(3)Distance Matrix
28 Complete-Link Method Euclidean Distance a a,b a,b b a,b,c,d c,d c d c (1)(2)(3)Distance Matrix
30 Ordered dendrograms 2 n-1 linear orderings of n elements (n= # genes or conditions)Maximizing adjacent similarity is impractical. So order by:Average expression level,Time of max induction, orChromosome positioningEisen98
31 Which clustering methods do you suggest for the following two-dimensional data?
32 Nadler and Smith, Pattern Recognition Engineering, 1993
33 Problems of Hierarchical Clustering It concerns more about complete tree structure than the optimal number of clusters.There is no possibility of correcting for a poor initial partition.Similarity and distance measures rarely have strict numerical significance.
34 Non-hierarchical clustering Normalized Expression DataTavazoie et al (http://arep.med.harvard.edu)
35 Clustering by K-meansGiven a set S of N p-dimension vectors without any prior knowledge about the set, the K-means clustering algorithm forms K disjoint nonempty subsets such that each subset minimizes some measure of dissimilarity locally. The algorithm will globally yield an optimal dissimilarity of all subsets.K-means algorithm has time complexity O(RKN) where K is the number of desired clusters and R is the number of iterations to converges.Euclidean distance metric between the coordinates of any two genes in the space reflects ignorance of a more biologically relevant measure of distance. K-means is an unsupervised, iterative algorithm that minimizes the within-cluster sum of squared distances from the cluster mean.The first cluster center is chosen as the centroid of the entire data set and subsequent centers are chosen by finding the data point farthest from the centers already chosen iterations.
36 K-Means Clustering Algorithm 1) Select an initial partition of k clusters2) Assign each object to the cluster with the closest center:3) Compute the new centers of the clusters:4) Repeat step 2 and 3 until no object changes cluster
37 Representation of expression data Gene 1Time-point 1Time-point 3dijGene N.Time-point 2Normalized Expression Data from microarraysGene 1Gene 2