Mismatch string kernels for discriminative protein classification

By Leslie. et .al

Presented by Yan Wang

Outline

• Problem Definition

• Support Vector Machines

• Mismatch Kernel

• Mismatch Tree Data Structure

• Experiments

• Conclusions

Protein Classification

• Problem: classification of proteins sequences into functional and structural families based on sequence homology.

• Motivation: Many proteins have been sequenced, but often structure and function remains unknown. Discriminative supervised machine learning approach to infer proteins structure and function needs an efficient way to do the computation.

Protein Classification

• Given a new protein, can we place it in its “correct” position within an existing protein hierarchy?

Remote Homology

• Remote homology: Superfamily-level homology. Sequences that belong to the same superfamily but not the same family.

• Motivation: Classify proteins based on sequence data into homologous groups to understand the structure and functions of proteins.

• Previous known approaches: pairwise sequence alignment, profiles, HMM

• New approaches: Discriminative Models

Discriminative approach

• More direct way to the goal• Most accurate method

Protein sequences are seen as a set of labeled examples—positive if they are in the family and negative otherwise.

Discriminative Models -- SVM

0, bxwHyperplane:

margin

bxwxf ,)(

Assume training data linearly

separable in feature space,

Linear classification rule:

The Kernel Function

• The linear classifier relies on inner products between vectors <xi, xj>.

• If every data point in the input space is mapped into high-dimensional space called feature space via some transformation Φ: x→φ(x), the inner product becomes: K (xi,xj)= <φ(xi), φ(xj)> called kernel. Φ is called the feature map.

• A kernel function is some function that corresponds to an inner product into some feature space.

The k-Spectrum of a Sequence

• Feature map for SVM based on spectrum of a sequence.

• The k-spectrum of a sequence is the set of all k-length (contiguous, k>=1) subsequences that it contains. We refer to such a k-length subsequence as a k-mer.

• Dimension of k-mer feature space = l k (l =20 for the alphabet of amino acids).

AKQDYYYYEI

AKQ KQD QDY DYY YYY

YYY YYE YEI

k-Spectrum Feature Map

• Feature map is indexed by all possible k-mers. • k-spectrum feature map with no mismatches:

For sequence x, ,where = number of occurrences of in x.

kxxk

))(()( )(x

AKQDYYYYEI

( 0 , 0 , … , 1 , … , 1 , … , 2 , … 1) AAA AAC … AKQ … DYY … YYY … YEI

k-Spectrum Kernel

• k-spectrum kernel K (x, y) for two sequences x and y is obtained by taking the inner product in feature space:

• This kernel simply counts the occurrences of k-length subsequences for each of the sequence in consideration.

• This kernel gives a simple notion of sequence similarity: two sequences will have a large k-spectrum kernel value if they share many of the same k-mers.

)(),(),( yxyxK kkk

(k, m)-Mismatch Kernel

• Slight modification to the k-spectrum kernel.• Define a parameter m which allows up to m mismatches

in the counting of occurrences.• This means =>k-spectrum feature map, allowing m

mismatches: If is a fixed k-mer, , where

= 1 if is within m mismatches from , otherwise 0. Example: Mismatch neighborhood around .

kmk ))(()(),(

)(

(k,m)-Mismatch Kernel

extend additively to longer sequences x by summing over all k-mers in x:

xinmersk

mkmk x

)()( ),(),(

• (k, m)-mismatch kernel is once again just the inner product in feature space:

)(),(),( ),(),(),( yxyxK mkmkmk

• SVMs can be learned by supplying this kernel function. The learned SVM classifier is given by:

Example: (k, m)-Mismatch Feature Map

A Simple Application:

• We first normalize the kernels:

• Then consider the induced distance:

),(),(

),(),(

yyKxxK

yxKyxK

),(),(2),(),( yyKyxKxxKyxd

Efficient computation of kernel matrix with a mismatch tree data structure

• The entire kernel matrix can be computed in one depth-first traversal of the mismatch tree structure.

• The (k,m)-mismatch tree is a rooted tree of depth k, where each internal node has 20 branches. an amino acid is labeled with

each branch. a leaf node presents a k-mer. an internal node represented

the prefix of a k-mer.

A

L

(8,1)-mismatch tree for sequence

AVLALKAVLL

Example: Mismatch Tree Data Structure

AA AB AC BA BB BC CA CB CC

Experiments

• SCOP experiments with domain homologs

Experiments

• SCOP experiments without domain homologs

Conclusions

• Presented mismatch kernels that measure sequence similarity without requiring alignment and without depending upon a generative model.

• Presented a method for efficiently computing kernels.• In the SCOP experiments, this method performs

competitively when compare with state-of-the-art methods. Such as SVM-Fisher and SVM-pairwise. Mismatch kernel approach gives efficient kernel computation, linear

time prediction and maintains good performance even when there is little training data.

Mismatch kernel approach can extract high-scoring k-mers from a trained SVM-mismatch classifier in order to look for discriminative motif regions in the positive sequence family.