1 / 39

BioInformatics (3)

BioInformatics (3). Computational Issues. Data Warehousing: Organising Biological Information into a Structured Entity (World’s Largest Distributed DB) Function Analysis (Numerical Analysis) :

vivien
Download Presentation

BioInformatics (3)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BioInformatics (3)

  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 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)

  3. Data Warehousing : Mapping Biologic into Data Logic

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

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

  6. Search and learning problems in sequence analysis

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

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

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

  10. Cluster Analysis Protein/protein complex Genes DNA regulatory elements

  11. Functional Analysis via Gene Expression Pairwise Measures Clustering Motif 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.

  13. Clusters of Two-Dimensional Data

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

  15. Distance Measures: Minkowski Metric ref

  16. Most Common Minkowski Metrics

  17. An Example x 3 y 4

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

  19. Similarity Measures: Correlation Coefficient

  20. Similarity Measures: Correlation Coefficient Expression Level Expression Level Gene A Gene B Gene B Gene A Time Time Expression Level Gene B Gene A Time

  21. 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 Distance-based Clustering

  22. hierarchical & non- Normalized Expression Data

  23. Hierarchical Clustering Techniques

  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 Neighbor • Complete-Link / Furthest Neighbor • Their Centroids. • Average of all cross-cluster pairs.

  26. 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.

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

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

  29. Compare Dendrograms Single-Link Complete-Link 0 2 4 6

  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, or • Chromosome positioning Eisen98

  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 Data Tavazoie et al. 1999 (http://arep.med.harvard.edu)

  35. 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. 200-400 iterations.

  36. 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 K-Means Clustering Algorithm

  37. Representation of expression data T2 T3 T1 Gene 1 Time-point 1 Time-point 3 dij Gene N . Time-point 2 Normalized Expression Data from microarrays Gene 1 Gene 2

  38. Identifying prevalent expression patterns (gene clusters) 1.5 1 0.5 0 1 2 3 -0.5 -1 -1.5 1.5 1 1.2 0.5 0.7 0 0.2 1 2 3 -0.5 -0.3 1 2 3 -1 -0.8 -1.5 -2 -1.3 -1.8 Time-point 1 Normalized Expression Time-point 3 Time -point Time-point 2 Normalized Expression Normalized Expression Time -point Time -point

  39. Evaluate Cluster contents Genes MIPS functional category Glycolysis Nuclear Organization Ribosome Translation Unknown

More Related