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BioInformatics (3)

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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 analysis Structure 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)

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Data Warehousing : Mapping Biologic into Data Logic

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Structure Analysis : Alignments & Scores Global (e.g. haplotype) ACCACACA ::xx::x: ACACCATA Score= 5(+1) + 3(-1) = 2 Suffix (shotgun assembly) ACCACACA ::: ACACCATA Score= 3(+1) =3 Local (motif) ACCACACA :::: ACACCATA Score= 4(+1) = 4

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A comparison of the homology search and the motif search for functional interpretation of sequence information. Homology SearchMotif Search New sequence Retrieval Similar sequence Expert knowledge Sequence interpretation Sequence database (Primary data) Knowledge acquisition Motif library (Empirical rules) Expert knowledge New sequence Inference Sequence interpretation

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Search and learning problems in sequence analysis

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(Whole genome) Gene Expression Analysis Quantitative Analysis of Gene Activities (Transcription Profiles) Gene Expression

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Biotinylated RNA from experiment GeneChip expression analysis probe array Image of hybridized probe array Each probe cell contains millions of copies of a specific oligonucleotide probe Streptavidin- phycoerythrin conjugate

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(Sub)cellular inhomogeneity ( see figure) Cell-cycle differences in expression. XIST RNA localized on inactive X-chromosome

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Cluster Analysis Protein/protein complex Genes DNA regulatory elements

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Functional Analysis via Gene Expression Pairwise Measures Clustering Motif Searching/...

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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.

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Clusters of Two-Dimensional Data

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Key Terms in Cluster Analysis Distance & Similarity measures Hierarchical & non-hierarchical Single/complete/average linkage Dendrograms & ordering

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Distance Measures: Minkowski Metric ref

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Most Common Minkowski Metrics

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An Example 4 3 x y

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Manhattan distance is called Hamming distance when all features are binary. Gene Expression Levels Under 17 Conditions (1-High,0-Low)

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Similarity Measures: Correlation Coefficient

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Time Gene A Gene B Gene A Time Gene B Expression Level Time Gene A Gene B

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Distance-based Clustering Assign a distance measure between data Find a partition such that: –Distance between objects within partition (i.e. same cluster) is minimized –Distance between objects from different clusters is maximised Issues : –Requires defining a distance (similarity) measure in situation where it is unclear how to assign it –What relative weighting to give to one attribute vs another? –Number of possible partition is super-exponential

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Normalized Expression Data hierarchical & non-

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Hierarchical Clustering Techniques

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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.

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The distance between two clusters is defined as the distance between Single-Link Method / Nearest Neighbor Complete-Link / Furthest Neighbor Their Centroids. Average of all cross-cluster pairs.

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Computing Distances single-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.

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Single-Link Method b a Distance Matrix Euclidean Distance (1) (2) (3) a,b,c ccd a,b dd a,b,c,d

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Complete-Link Method b a Distance Matrix Euclidean Distance (1) (2) (3) a,b ccd d c,d a,b,c,d

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Compare Dendrograms Single-LinkComplete-Link

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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, or Chromosome positioning Eisen98

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Which clustering methods do you suggest for the following two-dimensional data?

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Nadler and Smith, Pattern Recognition Engineering, 1993

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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.

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Normalized Expression Data Tavazoie et al (http://arep.med.harvard.edu) Non-hierarchical clustering

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Clustering by K-means Given 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.

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K-Means Clustering Algorithm 1) Select an initial partition of k clusters 2) 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

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Time-point 1 Time-point 3 Time-point 2 Gene 1 Gene 2 Normalized Expression Data from microarrays T1 T2T3 Gene 1 Gene N. Representation of expression data d ij

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Identifying prevalent expression patterns (gene clusters) Time-point 1 Time-point 3 Time-point Time -point Normalized Expression Normalized Expression Normalized Expression

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Glycolysis Nuclear Organization Ribosome Translation Unknown GenesMIPS functional category Evaluate Cluster contents

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