Approximate Similarity Search in Genomic Sequence Databases using

Approximate Similarity Search in Genomic Sequence Databases using Landmark-Guided Embedding Ahmet Sacan and I. Hakki Toroslu email: [ahmet, toroslu]@ceng. metu. edu. tr Computer Engineering Department, Middle East Technical University Ankara, TURKEY SISAP’ 08 – 20080411

Outline • Background – Sequence Alignment – Blast • Embedding Subsequences – Fastmap, LMDS – Analysis of parameters to achieve stable and accurate mapping • Indexing Subsequences 2 SISAP’ 08 – 20080411

Sequence Similarity Search • Sequence similarity search is at the heart of bioinformatics research – Similarity information allows: structural, functional, and evolutionary inferences 3 SISAP’ 08 – 20080411

Sequence Alignment • Goal: maximize “alignment score” • Score of aligning two residues: – Substitution matrix • Optimal solution: Dynamic Programming – Global: Needleman-Wunsch (1970) – Local: Smith-Waterman (1981) 4 SISAP’ 08 – 20080411

Blast (Basic Local Alignment Search Tool) • Popular tool for similarity search in sequence databases 1) Generate “k-tuples” (“k-mers”, “words”) from query • • CDEFG CDE, DEF, EFG CDE ADE, CDC, CCE, CDE, … 2) Find (exact) matching k-tuples in the database 3) For each candidate sequence, extend the k-tuple match in both directions. 5 SISAP’ 08 – 20080411

Time-accuracy trade-off Proteins (203 tuples) DNA (411 tuples) 1 2 3 4 … 11 k: Too many k-tuple hits to process Slows down the extension phase Few/none k-tuple hits Fast execution Exact k-tuple matching not sensitive Too many false negatives • Challenge: – Allow flexible matching for larger words at reasonable time 6 SISAP’ 08 – 20080411

Raising the bar for k 1. Map k-tuples to a vector space • Mapping cannot be perfect, thus “approximate results” 2. Use Spatial Access Methods (e. g. R-tree, Xtree) to index and retrieve k-tuples 7 SISAP’ 08 – 20080411

Mapping k-tuples • Requirements: – Need to support out of sample extension – Speed • Candidate methods: – Fastmap (Faloutsos, 1995) – Landmark MDS (de Silva, 2003) 8 SISAP’ 08 – 20080411

Fastmap 1. Select two pivots • Distant pivots heuristic 2. Obtain projection using cosine law 3. Project objects to new hyperplane 4. Repeat 9 SISAP’ 08 – 20080411

Fastmap • Fast! O(Nd) – N: number of data points – d is the target dimensionality • For query, need only to calculate distances to set of pivots • Unstable (esp. if original space is non. Euclidean) 10 SISAP’ 08 – 20080411

Landmark MDS 1. Select n landmarks (pivots) 2. Embed landmarks using classical MDS 3. For the remaining objects, apply distance-based triangulation based on distances to landmarks 11 SISAP’ 08 – 20080411

Landmark MDS • Provides stable results • Good selection of landmarks is critical. – LMDSrandom – LMDSmaxmin • Add new landmarks that maximizes the minimum distance to already selected landmarks – LMDSfastmap • Use the same landmarks as found by Fastmap 12 SISAP’ 08 – 20080411

Evaluation • Synthetic datasets – Randomly generate k-tuples for a given k and alphabet size σ • Real dataset – Yeast proteins benchmark (σ=20) – 6, 341 proteins, 2. 9 million residues – 103 query proteins, 38 -884 residues • Weighted Hamming distance • CB-EUC substitution matrix (Sacan, 2007) 13 SISAP’ 08 – 20080411

Target dimensionality (d) k=5, synthetic dataset, identity matrix • Sammon’s metric stress: • Breaking point dimensionality SISAP’ 08 – 20080411 14

Subsequence length (k) and alphabet size (σ) 15 SISAP’ 08 – 20080411

Number of landmarks k=5, d=7, synthetic dataset, identity matrix SISAP’ 08 – 20080411 16

Approximate k-tuple search performance • Find all k-tuples within a specified radius from a query k-tuple k=6, d=8, real dataset, CB-EUC matrix 17 SISAP’ 08 – 20080411

Homology search k=6, d=8, real dataset, CB-EUC matrix 18 SISAP’ 08 – 20080411

Search time search radius=7 Database size=100, 000 19 SISAP’ 08 – 20080411

Conclusion • Applied an embedding-based approach to approximate sequence similarity search for the first time • Significant time improvements with negligible degradation in accuracy • Achieved more stable embedding with combined pivot selection strategy • Defined intrinsic Euclidean dimensionality of the dataset 20 SISAP’ 08 – 20080411