This lecture explores the significance and application of data clustering in bioinformatics, focusing on pattern recognition in various biological data analysis problems such as regulatory binding site identification, gene expression data analysis, and more. The process of clustering involves partitioning a dataset into clusters based on similarities and differences among data points. The lecture discusses multivariate statistics, cluster analysis, similarity matrices, and dendrograms, illustrating how clustering algorithms can solve complex biological problems. Through examples like multiple sequence alignment and distance matrices, the lecture demonstrates the practical implementation of clustering techniques in bioinformatics.
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PatternsSome are easy some are not • Knitting patterns • Cooking recipes • Pictures (dot plots) • Colour patterns • Maps In 2D and 3D humans are hard to be beat by a computational pattern recognition technique, but humans are not so consistent
Example of algorithm reuse: Data clustering • Many biological data analysis problems can be formulated as clustering problems • microarray gene expression data analysis • identification of regulatory binding sites (similarly, splice junction sites, translation start sites, ......) • (yeast) two-hybrid data analysis (experimental technique for inference of protein complexes) • phylogenetic tree clustering (for inference of horizontally transferred genes) • protein domain identification • identification of structural motifs • prediction reliability assessment of protein structures • NMR peak assignments • ......
Data Clustering Problems • Clustering: partition a data set into clusters so thatdata points of the same cluster are “similar” and points of different clusters are “dissimilar” • Cluster identification-- identifying clusters with significantly different features than the background
Application Examples • Regulatory binding site identification: CRP (CAP) binding site • Two hybrid data analysis • Gene expression data analysis These problems are all solvable by a clustering algorithm
Multivariate statistics – Cluster analysis C1 C2 C3 C4 C5 C6 .. 1 2 3 4 5 Raw table Any set of numbers per column • Multi-dimensional problems • Objects can be viewed as a cloud of points in a multidimensional space • Need ways to group the data
Multivariate statistics – Cluster analysis C1 C2 C3 C4 C5 C6 .. 1 2 3 4 5 Raw table Any set of numbers per column Similarity criterion Similarity matrix Scores 5×5 Cluster criterion Dendrogram
Comparing sequences - Similarity Score - • Many properties can be used: • Nucleotide or amino acid composition • Isoelectric point • Molecular weight • Morphological characters • But: molecular evolution through sequence alignment
Multivariate statistics – Cluster analysis Now for sequences 1 2 3 4 5 Multiple sequence alignment Similarity criterion Similarity matrix Scores 5×5 Cluster criterion Phylogenetic tree
Multivariate statistics – Cluster analysisWhy do it? • Finding a true typology • Model fitting • Prediction based on groups • Hypothesis testing • Data exploration • Data reduction • Hypothesis generation But you can never prove a classification/typology!
Cluster analysis – Clustering criteria • Start with N clusters of 1 object each • Apply clustering distance criterion iteratively until you have 1 cluster of N objects • Most interesting clustering somewhere in between distance Dendrogram (tree) 1 cluster N clusters
Single linkage clustering (nearest neighbour) Let Ci andCj be two disjoint clusters: di,j = Min(dp,q), where p Ci and q Cj Single linkage dendrograms typically show chaining behaviour (i.e., all the time a single object is added to existing cluster)
Complete linkage clustering (furthest neighbour) Let Ci andCj be two disjoint clusters: di,j = Max(dp,q), where p Ci and q Cj More ‘structured’ clusters than with single linkage clustering
Clustering algorithm • Initialise (dis)similarity matrix • Take two points with smallest distance as first cluster • Merge corresponding rows/columns in (dis)similarity matrix • Repeat steps 2. and 3. using appropriate cluster measure until last two clusters are merged
Average linkage clustering (Unweighted Pair Group Mean Averaging -UPGMA) Char 2 Char 1 Distance from cluster to cluster is defined as the average distance over all within-cluster distances
UPGMA Let Ci andCj be two disjoint clusters: 1 di,j = ————————pqdp,q, where p Ci and q Cj |Ci| × |Cj| Ci Cj In words: calculate the average over all pairwise inter-cluster distances
Multidimensional Scaling • Multidimensional scaling (MDS) can be considered to be an alternative to factor analysis • It starts using a set of distances (distance matrix) • MDS attempts to arrange "objects" in a space with a particular number of dimensions so as to reproduce the observed distances. As a result, we can "explain" the distances in terms ofunderlying dimensions
Multidimensional Scaling Measures of goodness-of-fit: Stress Phi = [dij – f(ij)]2 • Phi is stress value, dijis reproduced distance, ij is observed distance, f(ij) is a monotone transformation of the observed distances (good function preserves rank order of distances after scaling)
Multidimensional Scaling Different cell types are multi-dimensionally scaled. The colour codes indicate clear clustering.
Neighbour joining • Widely used method to cluster DNA or protein sequences • Global measure – keeps total branch length minimal, tends to produce a tree with minimal total branch length • At each step, join two nodes such that distances are minimal (criterion of minimal evolution) • Agglomerative algorithm • Leads to unrooted tree
Neighbour joining y x x x y (c) (a) (b) x x x y y (f) (d) (e) At each step all possible ‘neighbour joinings’ are checked and the one corresponding to the minimal total tree length (calculated by adding all branch lengths) is taken.
