4' Molecular Similarity

1
4. Molecular Similarity
2
Similarity and Searching

• Historical Progression
• Similarity Measures
• Fingerprint Construction
• Pathological Cases
• MinMax- Counts
• Pruning Search Space
• Aggregate Queries
• LSH

3
Historical Progression

• Maximum Common Subgraph-Isomorphism (MCS)
• maximum common substructure between to molecules.
• NP-complete
• Structural Keys
• dictionary of predetermined, domain-specific
  sub-structures keyed to particular positions in a
  bit-vector constructed for each molecule
• similarity computed between bit-vectors (fast
  O(D) scan)
• 2D Compressed Fingerprints
• ALL substructures stored in a bit-vector using a
  hashing scheme plus lossy compression (modulo
  operator)
• Similarity computed between bit-vectors or count
  vectors
• Faster Searches
• database pruning
• locality sensitive hashing (LSH) towards O(log
  n) similarity searching

4
Superstructure and Substructure Searches
B
A

• A is a superstructure of B (ignoring H)
• B is a substructure of A
• Tversky similarity

5
The Similarity Problem

• How similar?

6
Spectral Similarity

• Count substructures
• Compare the count/bit vectors

7
2D Graph Substructures

• For chemical compounds
• atom/node labels
• A C,N,O,H,
• bond/edge labels
• B s, d, t, ar,
• Trace ALL Paths
• O(Ndl)
• Cycles and trees
• Combinatorial Space

(CsNsCdO)
8
Mapping Structures to Bits

• Compact data representation
• Hash each path to bit vector Feature space ? Bit
  space
• Resolve clashes with OR operator (i.e 111)

9
Similarity Measures

• There are many ways of measuring similarity (or
  distance) between bit/count vectors
• Euclidean
• Cosine
• Exponentials
• Tanimoto/Jaccard
• Tversky
• MinMax
• And many more (L1,L2,Lp,Hamming, Manhattan,.)

10
(No Transcript)
11
(No Transcript)
12
Similarity Measures Tanimoto

• Tally features
• Unique (a,b)
• Both on (c)
• Both off (d)
• Similarity Formula
• Tanimotoc/(abc)

13
The Fingerprint Approximation

• Fingerprint bit similarity approximates chemical
  feature similarity.

14
Similarity Measures Tversky

• Tally features
• Unique (a,b)
• Both on (c)
• Both off (d)
• Similarity Formula
• Tanimotoc/(abc)
• Tversky(a,ß)c/(aaßbc)

15
Pathological Cases

• On the Properties of Bit String-Based Measures of
  Chemical Similarity. Flower DR, J. Chem. Inf.
  Comput. Sci. 1998, 38, 379-386

16
Pathological Cases

• Issue of labeling scheme.

17
Counts

• MinMax similarity is a generalization of Tanimoto
  which uses the counts.
• MinMax can work better than Tanimoto.

18
Pruning Search Space Using Bounds

• Linear speedup (search CxD) for fixed threshold,
  often by one order of magnitude or more.
• Sub-linear speedup (search CxD0.6) for top K.

19
(No Transcript)
20
Speedup from Pruning

• Speedup depends on
• Threshold
• Query
• Fingerprint length
• Database size

21
(No Transcript)
22
(No Transcript)
23
Bias in Query Distribution
24
(No Transcript)
25
(No Transcript)
26
Aggregate Queries (Profiles)
27
Two Basic Strategies

• Similar to bioinformatics
• Aggregate individual pairwise measures
• Build a fingerprint profile
• Linear approaches
• Non-linear approaches (consensus, modal, etc)
• Hybrid (profile aggregation/scaling))
• Profile-profile

28
Aggregations
29
Consensus Fingerprints

• Create consensus fingerprint
• Search database using the consensus

30
Local Sensitive Hashing

• Bin fingerprints based on projections onto
  randomly directed vectors
• log D random vectors ? O(log D)
• Search for neighbors by returning bin
  corresponding to the querys projection
• Has been used for clustering. May be useful for
  building diverse data sets. Not yet developed for
  searching

31
Outline

• Historical Progression
• Similarity Measures
• Fingerprint Construction
• Pathologic Cases
• MinMax- Counts
• Pruning Search Space
• Aggregate Queries
• LSH