kernel methods and relational learning in computational biology
TRANSCRIPT
Kernel Methods and Relational Learning inComputational Biology
ir. Michiel Stock
Faculty of Bioscience EngineeringGhent University
November 2014
KERMIT
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 1 / 36
Outline
1 Introduction
2 Kernel methodsTheoretical overviewDealing with sequencesDealing with graphsOther kernels
3 Learning relationsKronecker kernelsConditional ranking
4 Predicting enzyme functionDefining the problemResults
5 Conclusions
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 2 / 36
Introduction
Introduction
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 3 / 36
Introduction
Introductory example: drug design
Strategy for curing Alzheimer’s disease
Find compounds with good ADMET properties that selectively bindcholinesterase and amyloid precursor protein
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 4 / 36
Introduction
Labels: known protein-ligand interaction
GF
D
U YA
X
.6
B.5
ZT
E
.6
.8
.3
W
.3 1
V
.2C
ProteinsLigands
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 5 / 36
Introduction
The targets: features for proteins
Possible representations:
amino acid sequence
3D structure
gene expression
cellular location
phylogenetic profiles
...
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 6 / 36
Introduction
The ligands: features for compounds
Possible representations:
SMILE format and other text-basedrepresentations
coloured graph representation
fingerprints based on physicochemicaldescriptors
...
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 7 / 36
Introduction
Computational biology deals with interestingproblems
We deal with objects that are:
in large dimension (e.g. microarrays or proteomics data)
structured (e.g. gene sequences, small molecules, interactionnetworks, phylogenetic trees...)
heterogeneous (e.g. vectors, sequences, graphs to describe thesame protein)
in large quantities (e.g. more than 106 known proteinsequences)
noisy (e.g. many features are not relevant)
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 8 / 36
Introduction
Computational biology often deals with interactions
Relational learning
Predicting properties of two objects, which can be of a different type.
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 9 / 36
Kernel methods
Kernel methods
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 10 / 36
Kernel methods Theoretical overview
Formal definition of a kernel
Kernels are non-linear functions defined over objects x ∈ X .
Definition
A function k : X × X → R is called a positive definite kernel if it issymmetric, that is, k(x, x′) = k(x′, x) for any two objects x, x′ ∈ X , andpositive semi-definite, that is,
N∑
i=1
N∑
j=1
cicjk(xi , xj) ≥ 0
for any N > 0, any choice of N objects x1, . . . , xN ∈ X , and any choice ofreal numbers c1, . . . , cN ∈ R.
Can be seen as generalized covariances.
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 11 / 36
Kernel methods Theoretical overview
Interpretation of kernels
Suppose an object x has animplicit feature representationφ(x) ∈ F .A kernel function can be seenas a dot product in thisfeature space:
k(x, x′) = 〈φ(x), φ(x′)〉
Linear models in this featurespace F can be made:
y(x) = wTφ(x)
=∑
n
ank(xn, x)
�
X F
k h�(x),�(x0)i
dinsdag, 10 april 2012
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 12 / 36
Kernel methods Theoretical overview
Many kernel methods exist
Examples of popular kernelmethods:
Support vector machine(SVM)
Regularized least squares(RLS)
Kernel principalcomponent analysis(KPCA)
Learning algorithm isindependent of the kernelrepresentation!
SVM
KPCA
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 13 / 36
Kernel methods Dealing with sequences
Kernels using sequence alignment
sequence alignment optimises a score of how well the residues match
use this score as a kernel value (similarity for sequences)
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 14 / 36
Kernel methods Dealing with sequences
Kernels using substrings
Spectrum kernel (SK)
The SK considers the number of k-mers m two sequences si and sj have incommon.
SKk(si , sj) =∑
m∈Σk
N(m, si )∗N(m, sj)
with N(m, s) the number of k-mersm in sequence s.Many modifications exist.
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 15 / 36
Kernel methods Dealing with graphs
What is a graph?
Graph
Graphs are a set of interconnected objects, called vertices (or nodes), thatare connected through edges.
Graphs can show the structure of an object or interactions betweendifferent objects.
Graph are important in bioinformatics!Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 16 / 36
Kernel methods Dealing with graphs
Comparing nodes within a graph
Diffusion kernel
Constructing a similarity between vertices within the same graph.
Based on performing arandom walk on a graph.Captures the long-rangerelationships betweenvertices.Inspired by the heatequation. The kernelquantifies how quickly ‘heat’can spread from one node toanother.
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 17 / 36
Kernel methods Dealing with graphs
Comparing two separate graphs
Graph kernel
Constructing a similarity between graphs.
Also based on performing arandom walk on both graphsand counting the number ofmatching walks.Usually very computationallydemanding!
In chemoinformatics:
In structural bioinformatics:
A B
zaterdag, 28 april 2012
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 18 / 36
Kernel methods Other kernels
Kernels for fingerprints
Objects that can be describedby a long binary vector x canbe represented by theTanimoto kernel:
KTan(xm, xn) =
〈xm, xn〉〈xm, xm〉+ 〈xn, xn〉 − 〈xm, xn〉
.
Fingerprint representation ofa molecule:
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 19 / 36
Kernel methods Other kernels
Kernels for other objects
Kernels for texts: often based on word count (example: medicalpapers)
Kernels for point clouds (example: using 3D structure of proteins)
Fisher kernels: use information of a generative model (example: usinga Hidden Markov Model)
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 20 / 36
Learning relations
Learning relations
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 21 / 36
Learning relations Kronecker kernels
A little math...
A =
[a11 a12
a21 a22
]and B =
[b11 b12
b21 b22
]. (1)
We define the Vectorization operator:
vec(A) =
a11
a12
a21
a22
And the Kronecker product:
A⊗ B =
a11b11 a11b12 a12b11 a12b12
a11b21 a11b22 a12b21 a12b22
a21b11 a21b12 a22b11 a22b12
a21b21 a21b22 a22b21 a22b22
Key equation: (BT ⊗ A)vec(X ) = vec(AXB)Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 22 / 36
Learning relations Kronecker kernels
Kernels for pairs of objects
Pairwise kernel
Combine the kernel matrices of the individual objects to construct a kernelmatrix for pairs of objects.
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Extra Logo’s
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomics
Suppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. With no known mechanistic information one can build a statistical model based on a data set. Kernel methods allow for the generation of a joint feature representation of a pair containing a protein and a ligand.
proteins ligands
( , )( , )( , )
...
( , )( , )
EC 2.7.7.12
EC 4.2.3.90
EC ?.?.?.?EC 2.7.7.34
EC 4.6.1.11
EC 2.7.1.12
1
0
0
3
0
2
02
0
zondag, 13 mei 2012
h(e) = hw,�(e)i =X
e2E
aeK�(e, e)
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomicsSuppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. Our framework can be used to model pairwise relations between different types of objects.
Proteins Ligands
Object kernelsPairwise kernel
Data set
Conditional ranking algorithmThe ranking data can be seen as a graph, we want to predict some value using a feature representation of the edges:
h 2 H �(e)
Given a training dataset T, this function can be learned using the following algorithm:
A(T ) = argmaxh2H
L(h, T ) + �khk2H,
with an appropriate loss function and a regularization parameter. To train a model for conditional ranking a convex and differentiable approximation of the ranking loss is used:
L �
L(h, T ) =X
v2V
X
e,e2Ev
(ye � ye � h(e) + h(e))2
In the most general case the Kronecker product pairwise kernel is used for the edges, which is simply the product of some kernel between pairs of nodes:
K�(e, e) = K�(v, v0, v, v0) = K�(v, v)K�(v0, v0)
SVMRLS
...
Learning algorithm
By optimizing a ranking loss, our algorithms can also be used for conditional ranking, as shown on the right.In short, our framework is ideally suited for bioinformatics challenges:
- efficient learning process- can handle complex objects (graphs, trees, sequences...)- ability to deal with information retrieval problems
Database objects
Mor
e re
leva
nt
Query 1 Query 2M
ore
rele
vant
Functional ranking of enzymesGiven structural information of an enzyme we want to infer its function. This is done by ranking annotated proteins of a database according to their predicted catalytic similarity (derived from the EC number) with the query-protein.
Using five state of the art structural similarities, we showed that learning a conditional ranking model is always an improvement compared on the baseline ranking.
KERMIT
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Extra Logo’s
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomics
Suppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. With no known mechanistic information one can build a statistical model based on a data set. Kernel methods allow for the generation of a joint feature representation of a pair containing a protein and a ligand.
proteins ligands
( , )( , )( , )
...
( , )( , )
EC 2.7.7.12
EC 4.2.3.90
EC ?.?.?.?EC 2.7.7.34
EC 4.6.1.11
EC 2.7.1.12
1
0
0
3
0
2
02
0
zondag, 13 mei 2012
h(e) = hw,�(e)i =X
e2E
aeK�(e, e)
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomicsSuppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. Our framework can be used to model pairwise relations between different types of objects.
Proteins Ligands
Object kernelsPairwise kernel
Data set
Conditional ranking algorithmThe ranking data can be seen as a graph, we want to predict some value using a feature representation of the edges:
h 2 H �(e)
Given a training dataset T, this function can be learned using the following algorithm:
A(T ) = argmaxh2H
L(h, T ) + �khk2H,
with an appropriate loss function and a regularization parameter. To train a model for conditional ranking a convex and differentiable approximation of the ranking loss is used:
L �
L(h, T ) =X
v2V
X
e,e2Ev
(ye � ye � h(e) + h(e))2
In the most general case the Kronecker product pairwise kernel is used for the edges, which is simply the product of some kernel between pairs of nodes:
K�(e, e) = K�(v, v0, v, v0) = K�(v, v)K�(v0, v0)
SVMRLS
...
Learning algorithm
By optimizing a ranking loss, our algorithms can also be used for conditional ranking, as shown on the right.In short, our framework is ideally suited for bioinformatics challenges:
- efficient learning process- can handle complex objects (graphs, trees, sequences...)- ability to deal with information retrieval problems
Database objects
Mor
e re
leva
nt
Query 1 Query 2
Mor
e re
leva
nt
Functional ranking of enzymesGiven structural information of an enzyme we want to infer its function. This is done by ranking annotated proteins of a database according to their predicted catalytic similarity (derived from the EC number) with the query-protein.
Using five state of the art structural similarities, we showed that learning a conditional ranking model is always an improvement compared on the baseline ranking.
KERMIT
Kronecker kernel: KΦ = Kφ ⊗ Kψ
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 23 / 36
Learning relations Kronecker kernels
Kernel ridge regression for relations
set y = vec(Y ) andKΦ = Kφ ⊗ Kψ
We can just use the usualkernel ridge regression:
arg mina
(y−KΦa)T (y−KΦa)+
λaTKΦa
This is equivalent to solvingthe following linear system:
(KΦ + λINM×NM)a = y
N objects of type U (e.g.proteins)
M objects of type V(e.g. ligands)
Y : N ×M label matrix(e.g. molecularinteraction)
Kφ: N ×N kernel matrixfor objects of type UKψ: M ×M kernelmatrix for objects oftype V
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 24 / 36
Learning relations Conditional ranking
Conditional ranking
Motivation
Suppose one is not particularly interested in the exact value of theinteraction but in the order of the proteins for a given ligand.
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Extra Logo’s
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomics
Suppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. With no known mechanistic information one can build a statistical model based on a data set. Kernel methods allow for the generation of a joint feature representation of a pair containing a protein and a ligand.
proteins ligands
( , )( , )( , )
...
( , )( , )
EC 2.7.7.12
EC 4.2.3.90
EC ?.?.?.?EC 2.7.7.34
EC 4.6.1.11
EC 2.7.1.12
1
0
0
3
0
2
02
0
zondag, 13 mei 2012
h(e) = hw,�(e)i =X
e2E
aeK�(e, e)
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomicsSuppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. Our framework can be used to model pairwise relations between different types of objects.
Proteins Ligands
Object kernelsPairwise kernel
Data set
Conditional ranking algorithmThe ranking data can be seen as a graph, we want to predict some value using a feature representation of the edges:
h 2 H �(e)
Given a training dataset T, this function can be learned using the following algorithm:
A(T ) = argmaxh2H
L(h, T ) + �khk2H,
with an appropriate loss function and a regularization parameter. To train a model for conditional ranking a convex and differentiable approximation of the ranking loss is used:
L �
L(h, T ) =X
v2V
X
e,e2Ev
(ye � ye � h(e) + h(e))2
In the most general case the Kronecker product pairwise kernel is used for the edges, which is simply the product of some kernel between pairs of nodes:
K�(e, e) = K�(v, v0, v, v0) = K�(v, v)K�(v0, v0)
SVMRLS
...
Learning algorithm
By optimizing a ranking loss, our algorithms can also be used for conditional ranking, as shown on the right.In short, our framework is ideally suited for bioinformatics challenges:
- efficient learning process- can handle complex objects (graphs, trees, sequences...)- ability to deal with information retrieval problems
Database objects
Mor
e re
leva
nt
Query 1 Query 2
Mor
e re
leva
nt
Functional ranking of enzymesGiven structural information of an enzyme we want to infer its function. This is done by ranking annotated proteins of a database according to their predicted catalytic similarity (derived from the EC number) with the query-protein.
Using five state of the art structural similarities, we showed that learning a conditional ranking model is always an improvement compared on the baseline ranking.
KERMIT
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Extra Logo’s
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomics
Suppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. With no known mechanistic information one can build a statistical model based on a data set. Kernel methods allow for the generation of a joint feature representation of a pair containing a protein and a ligand.
proteins ligands
( , )( , )( , )
...
( , )( , )
EC 2.7.7.12
EC 4.2.3.90
EC ?.?.?.?EC 2.7.7.34
EC 4.6.1.11
EC 2.7.1.12
1
0
0
3
0
2
02
0
zondag, 13 mei 2012
h(e) = hw,�(e)i =X
e2E
aeK�(e, e)
Relational Learning and Ranking Algorithms for Bioinformatics Applications
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics
Michiel Stock, Willem Waegeman, Bernard De Baets
Introductory example: chemogenomicsSuppose one wants to model the binding interactions between a set of proteins and a database of ligands to aid the process of drug design. Our framework can be used to model pairwise relations between different types of objects.
Proteins Ligands
Object kernelsPairwise kernel
Data set
Conditional ranking algorithmThe ranking data can be seen as a graph, we want to predict some value using a feature representation of the edges:
h 2 H �(e)
Given a training dataset T, this function can be learned using the following algorithm:
A(T ) = argmaxh2H
L(h, T ) + �khk2H,
with an appropriate loss function and a regularization parameter. To train a model for conditional ranking a convex and differentiable approximation of the ranking loss is used:
L �
L(h, T ) =X
v2V
X
e,e2Ev
(ye � ye � h(e) + h(e))2
In the most general case the Kronecker product pairwise kernel is used for the edges, which is simply the product of some kernel between pairs of nodes:
K�(e, e) = K�(v, v0, v, v0) = K�(v, v)K�(v0, v0)
SVMRLS
...
Learning algorithm
By optimizing a ranking loss, our algorithms can also be used for conditional ranking, as shown on the right.In short, our framework is ideally suited for bioinformatics challenges:
- efficient learning process- can handle complex objects (graphs, trees, sequences...)- ability to deal with information retrieval problems
Database objects
Mor
e re
leva
nt
Query 1 Query 2
Mor
e re
leva
ntFunctional ranking of enzymes
Given structural information of an enzyme we want to infer its function. This is done by ranking annotated proteins of a database according to their predicted catalytic similarity (derived from the EC number) with the query-protein.
Using five state of the art structural similarities, we showed that learning a conditional ranking model is always an improvement compared on the baseline ranking.
KERMIT
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 25 / 36
Learning relations Conditional ranking
Conditional ranking
Suppose: e = (u, v) ∈ E = (U × V)
Train the model:
h(e) = wTΦ(e) =∑
e∈EaeK
Φ(e, e)
by solving:
A(T ) = arg minh∈H
L(h,T )+λ‖h‖2H.
Where we use a ranking loss:
L(h,T ) =∑
u,u′∈U
∑
v ,v ′∈V(yu,v−yu′,v ′−h(u, v)+h(u′, v ′))2.
preference graph:
*Figure 1 Example of a multi-graph. If this graph, on the left, would be used for ranking the elements conditioned on C, then A scores better than E, which ranks higher than E, which on its turn ranks higher than D and D ranks higher than B. There is no information about the relation between C and F and G, respectively, our model could be used to include these two instances in the ranking if features are available. Notice that in this setting unconditional ranking of these objects is meaningless as this graph is obviously intransitive. Figure reproduced from (Pahikkala et al., 2010). The proposed framework is based on the Kronecker product kernel for generating implicit joint feature representations of queries and the sets of objects to be ranked. Exactly this kernel construction will allow a straightforward extension of the existing framework to dyadic relations and multi-task learning problems (Objectives 1 and 2). It has been proposed independently by three research groups for modeling pairwise inputs in different application domains (Basilico et al. 2004, Oyana et al. 2004, Ben-Hur et al. 2005). From a different perspective, it has been considered in structured output prediction methods for defining joint feature representations of inputs and outputs (Tsochantaridis et al., 2005, Weston et al., 2007). While the usefulness of Kronecker product kernels for pairwise learning has been clearly established, computational efficiency of the resulting algorithms remains a major challenge. Previously proposed methods require the explicit computation of the kernel matrix over the data object pairs, hereby introducing bottlenecks in terms of processing and memory usage, even for modest dataset sizes. To overcome this problem, one typically applies sampling strategies of the kernel matrix for training. An alternative approach known as the Cartesian kernel has been proposed in (Kashima et al., 2009). This kernel exhibits interesting computational properties, but it can be solely employed in selected applications, because it cannot make predictions for (couples of) objects that are not observed in the training dataset. When modeling interactions between two types of objects one gets close to the field of collaborative filtering, as shown in (Pessiot et al., 2007). Matrix factorization methods, which are used especially in collaborative filtering, may be applied to conditional ranking problems, by exploiting the known labels for pairs of objects in order to generate a latent feature representation that allows predicting these labels for pairs for which this information is missing. Such methods can be combined with our machine learning approach, as a preprocessing step in which additional latent features are generated (part of Objectives 1 and 2).
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 26 / 36
Predicting enzyme function
Predicting enzyme function
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 27 / 36
Predicting enzyme function
The data set
Data:
two data sets of ca. 1600enzymes with 21different functions
five different similaritymeasures of the activesite
active site of anenzyme:
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 28 / 36
Predicting enzyme function
The enzyme commission number
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 29 / 36
Predicting enzyme function Defining the problem
Quantifying enzyme function similarity
EC 2.7.7.12
EC 4.2.3.90
EC ?.?.?.?EC 2.7.7.34
EC 4.6.1.11
EC 2.7.1.12
1
0
0
3
0
2
02
0
zondag, 13 mei 2012
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 30 / 36
Predicting enzyme function Defining the problem
Conditional ranking of enzymes
Ranking enzymes
For an unannotated enzyme, rank the annotated enzymes so that thetop has a similar function w.r.t. the query.
Minimize ranking error:number of switches neededfor a perfect ranking
Example: suppose one has anenzyme with unknownfunction: EC ?.?.?.?
1 EC 2.7.7.12
2 EC 2.7.7.12
3 EC 2.7.7.34
4 EC 2.7.1.12
5 EC 2.7.7.34
6 EC 4.2.3.90
7 EC 1.14.11
8 EC 4.6.1.11
⇒ EC 2.7.7.12
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 31 / 36
Predicting enzyme function Defining the problem
Learning the catalytic similarity
pair of enzymes:e = (v , v ′)
label ye ∈ {0, 1, 2, 3, 4}:the catalytic similarity
five different structuralsimilarities: Kφ(v , v ′)
A B C D E F GA 4 4 0 0 0B 4 4 0 0 0C 0 0 4 2 1D 0 0 2 4 3E 0 0 1 3 4FG
Enzymes
Enzymes
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 32 / 36
Predicting enzyme function Results
Qualitative improvement in the enzyme similarities
Example for CavBase structural similarity:
Ground truthSupervisedUnsupervised
Lighter color = higher similarity
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 33 / 36
Predicting enzyme function Results
Improvement of the ROC curves
ROC curves for the five different structural similarity measures:unsupervised and supervised
False positive rate
Ave
rage
true
pos
itive
rate
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
CB sup.FP sup.LPCS sup.MCS sup.SW sup.CB unsup.FP unsup.LPCS unsup.MCS unsup.SW unsup.
ROC curve for the different enzyme similarity measurements of data set I
Improve
ment
Increase of AUC from ca. 0.7 to more than 0.8!Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 34 / 36
Conclusions
Conclusions
kernels can be used to work with structured objects...
... and can encode your prior knowledge
many problems in computational biology can be seen as ‘learningrelations’
relations between objects can be learned elegantly and efficientlyusing Kronecker kernels
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 35 / 36
Conclusions
Kernel Methods and Relational Learning inComputational Biology
ir. Michiel Stock
Faculty of Bioscience EngineeringGhent University
November 2014
KERMIT
Michiel Stock (KERMIT) Kernels for Computational Biology November 2014 36 / 36