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Mismatch String Kernals for SVM Protein Classification

Mismatch String Kernals for SVM Protein Classification. Christina Leslie, Eleazar Eskin, Jason Weston, William Stafford Noble Presented by Pradeep Anand Ravindranath Mei Sze Lam. Introduction. Problem in Computational Biology

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Mismatch String Kernals for SVM Protein Classification

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  1. Mismatch String Kernals for SVM Protein Classification Christina Leslie, Eleazar Eskin, Jason Weston, William Stafford Noble Presented by Pradeep Anand Ravindranath Mei Sze Lam

  2. Introduction • Problem in Computational Biology • Classification of Proteins into functional and structural classes based on homology of protein sequence data

  3. Methods for Protein Classification and Homology Detection • Pairwise sequence alignment • Profiles for protein families • Consensus patterns using motifs • Profiles HMMs

  4. Focus • Remote Homology Detection

  5. How is the problem handled currently? • Fisher-SVM One of the successful discriminative techniques for protein classification and Best performing method for remote homology detection

  6. Fisher-SVM • Build a profile HMM for the positive training sequences, defining loglikelihood function [log P(x/θ)] for any protein sequence x. • θ0 - maximum likelihood for model parameters

  7. Gradient vector d(log P(x/θ)/θ=θ0)/dθassigns to each (positive or negative) training sequence x an explicit vector feature called fisher scores. • This feature mapping defines a kernel function, called the fisher kernel. • This Fisher kernel can then be used to train a SVM classifier.

  8. Strengths • Combines biological information encoded in a HMM with the discriminative power of the SVM algorithm.

  9. Negatives • Needs lots of data or sophisticated priors to train the HMM. • It is expensive to compute the kernel matrix, as calculating the fisher scores requires computing forward and backward probabilities from the Baun-Welch algorithm.

  10. Mismatch-SVM • The (k,m)-mismatch kernel is based on a feature map to a vector space indexed by all possible subsequence of amino acids of a fixed length k. • Each instance of a fixed k-length subsequence in an input sequence attributes to all feature coordinates differing from it by at most m mismatches.

  11. Thus, the mismatch kernel adds the biologically important idea of mismatching to the computationally simpler • In this paper, it is described how to compute the new kernel efficiently using a for values of (k,m) useful in this application. spectrum kernel mismatch tree data structure Mismatch kernel

  12. Advantages • By using mismatch tree data structure the kernel is fast enough to use on real datasets. • Considerabily less expensive than the fisher kernel. • Performance equal to Fisher-SVM. • Outperforms other methods.

  13. This kernel does not depend on any generative model and can be used for other sequence based classification problems.

  14. Feature Maps for Strings • (k,m)-mismatch kernel is based on a feature map from the space of all finite sequences from an alphabet A of size |A| = l to the lk –dimensional vector space indexed by the set of k-length subsequences (“k-mers”) from A. where, A - alphabet representing amino acids. l - no. of amino acids.

  15. If α is a k-mer βis all k length sequences N(k,m) (α) – set of all k length sequences differing from αby at most m mismatches. we define our feature map Φ(k,m) as Φ(k,m) (α) = (φβ(α))βЄAk where φβ(α) = 1if βbelongs to N(k,m) (α) , φβ(α) = 0 otherwise.

  16. For a sequence x of any length, we extends the map additively by summing the feature vectors for all the k-mers in x: Φ(k,m) (x) = Σ(k-mers α in x)Φ(k,m) (α) • The (k,m)-mismatch kernal is given by K (k,m) (x,y) = ‹Φ(k,m) (x), Φ(k,m) (y)›. For m = 0, we retrieve the k-spectrum kernal.

  17. Fisher Scores and Spectrum Kernel • Even though the spectrum and mismatch feature maps are defined without any reference to a generative model, there is some similarity between the k-spectrum feature map and the fisher scores associated to an order k-1 markov chain model.

  18. Efficient computation of the Mismatch Kernel: Mismatch Tree Data Structure • Mismatch tree data structure is used to represent the feature space(the set of all k-mers) and perform a lexical traversal of all k-mers occurring in the sample dataset match with up to m of mismatches.

  19. Example: Traversing the Mismatch Tree • Traversal for input sequence: AVLALKAVLL, k=8, m=1

  20. Example: Computing the Kernel for Pair of Sequences • Traversal of trie for k=3 (m=0) A S1: EADLALGKAVF EADLALGKAVF EADLALGKAVF D S2: ADLALGADQVFNG ADLALGADQVFNG ADLALGADQVFNG L Update kernel value for K(s1,s2) by adding contribution for feature ADL

  21. Efficiency Issues for Kernel Computation • Depth first search • Recursive function efficient use of memory no problem for large data sets

  22. Computational Cost Number of mismatches, m. This increases, computational cost increases exponentially Theoretical Computational Cost, O Total length of the sample data, N Number of different amino acids in the body The number of characters in the sequence, k. The classifier breaks up proteins into lengths of 5~6. (Longer strings are broken down by summing the feature vectors)

  23. = M x M x n = M X N • Where is just the M number of sequences to be processed. • Supposing M number of sequences are all equal with max. no of non zero entities Computational Cost (cont’d) • Worst case scenario for M sequences ?

  24. Training and Test Data 33 Classes of Superfamily Proteins (taken from SCOP database) Class we are interested in Any other class other than Class 1 Class 1 Class 2 Class 3 .. - - + - + - - + - - + - - - Families of Proteins, each belonging to 1 of 33 Superfamilies • For each class, we want to know whether a given protein sequence belongs to that class – Y/N? • 160 experiments were performed on 33 classes.

  25. Implementation and Comparison of Methods • We test the mismatch kernel with a publicly available SVM implementation • 4 methods • Mismatch Kernel • Fisher Kernel • SAM-T98 • PSI-BLAST Uses SVM implementation HMM Alignment Scoring

  26. Peformance Measurement - ROC ROC • Show on board: • The closer to 1, the better the score – more true positives to false positives ROC50

  27. Performance Comparison Many of the Mismatch SVM and Fisher Kernel classifications fall close to 1, meaning there is a low FP error rate; Both classifiers manage to classify almost all of the 33 classes with ROC score > 0.85 threshold Comparison of four homology detection methods

  28. Mismatch VS Spectrum ROC ROC50  Mismatch kernel outperforms the Spectrum kernel

  29. Mismatch VS Fisher ROC ROC50  No Significant Difference!

  30. Discussion & Conclusion • What was it for? • Constructing kernel for homology detection • What was achieved? • A kernel that was equal in performance to the best known classifier but with a lower computational cost • Future Work • Since does not depend on generative model (unlike Fisher), can be easily used for other stuff, eg. Splice site prediction • Since it is computationally cheaper (ie. faster), can be used for practical biological purposes, eg. multiclass prediction

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