Graph preprocessing

Introduction Noise removal and data enhancement problem Noise removal and data enhancement on binary data Noise removal and data enhancement on graph data Noise removal and data enhancement tools Current research problems Future directions

Common Neighborhood Similarity (CNS) measures

We evaluated a variety of CNS measures in our study For the purpose of defining each of these measures, we

will use the following standard notation

u and v are the nodes between which the similarity is being computed.

Nu and Nv are the direct interaction partners of u and v

respectively, and Nuv = Nu ∩ Nv

a u,v the (positive) weight of the edge between u and v

Jaccard similarity

Nu and Nv here, is the Jaccard coefficient, which is defined as follows

o Jaccard(u,v) =|Nuv|/|Nu intersection Nv |

Jaccard coefficient measures how similar the two sets are

assumes a value of 1 only if Nu = Nv

it can only be used for unweighted graphs

this measure does not incorporate the presence or absence of an interaction between u and v

(au,v)

Pvalue

Samanta et al. [11] proposed a probabilistic measure for the statistical significance of the common neigh-borhood configuration of two nodes u and v in an unweighted graph −log10 value of the probability of u and v having a certain number of common neighbors by random chance Pvalue(u,v) = −log10(p(N, |Nu|, |Nv |, |Nuv|)) N is the total number of proteins in the network, and p(N, |Nu|, |Nv |, |Nuv|) is computed on the basis of a Binomial distribution Pvalue is expected to have a high value (low value of p) for the non-random common neighbor configurations in a network this measure is unable to take edge weights into account it does not incorporate the value of au,v

Functional Similarity (FS)

Chua et al. [13] proposed a measure named Functional Similarity (FS) for measuring the common neigh-borhood similarity of two proteins in an interaction network

FS.binary(u,v) =2|Nuv|/(|Nu − Nv | + 2|Nuv| + λu,v) ×

2|Nuv|/(|Nv − Nu| + 2|Nuv λv,u)

where λ u,v = max(0,navg − (|Nu − Nv | + |Nuv|)) and navg is the average number of neighbors of each protein in the network

λ factor is to penalize the score between proteins pairs

where at least one of the proteins has too few neighbors

Topological Overlap Measure (TOM)

TOM measures the strength of the association between two nodes in a graph based on the similarity of their common neighborhood to the smaller of the individual neighborhoods of the two nodes

o TOM.binary(u,v) =|Nuv| + au,v/(min{|Nu|, |Nv|} + 1 − au,v)

First, each of the above CNS measures is used to compute the

similarity (strength of the association) between each pair of proteins in the input interaction network

a threshold is chosen for each score such that the number of pairs

with a score higher than this threshold is as close as possible to the number of interactions in the original network

The pairs that score higher than the threshold are structured as a network, and constitute the transformed network for

the corresponding measure

Pair-wise H-Confidence

• Measure of the affinity of two items in terms of the transactions in which they appear simultaneously [Xiong et al, 2006]

• For an interaction network represented as an adjacency matrix:

– Unweighted Networks: n1,n2=# neighbors of p1,p2

m=# shared neighbors of p1,p2

– Weighted Networks: n1,n2=sum(weights) of edges incident on p1,p2

m = sum of min(weights) of edges to common neighbors of p1,p2

H-confidence Example

p1 p2 p3 p4 p5

p10 0 1 0 1

p20 0 1 1 0

p31 1 0 0 1

p41 1 0 0 1

p51 0 1 1 0

p1 p2 p3 p4 p5

p10 0 0.5 0 0.1

p20 0 1 0.2 0

p

3

0.5 1 0 0 0.1

p40 0.2 0 0 0.5

p50.1 0 0.1 0.5 0

Unweighted Network Weighted Network

Hconf(p1,p2)= min(0.5,0.5) = 0.5

Hconf(p1,p2)= min(0.5/0.6,0.5/1.2) = 0.416

Validation of Final Network

• Use FunctionalFlow algorithm [Nabieva et al, 2005] on the original and transformed graph(s)– One of the most accurate algorithms for predicting function from

interaction networks– Produces likelihood scores for each protein being annotated with one

of 75 MIPS functional labels• Likelihood matrix evaluated using two metrics

– Multi-label versions of precision and recall:

– mi = # predictions made, ni = # known annotations, ki = # correct predictions

– Precision/accuracy of top-k predictions• Useful for actual biological experimental scenarios

Test Protein Interaction Networks

• Three yeast interaction networks with different types of weighting schemes used for experiments– Combined

• Composed from Ito, Uetz and Gavin (2002)’s data sets• Individual reliabilities obtained from EPR index tool of DIP• Overall reliabilities obtained using a noisy-OR

– [Krogan et al, 2006]’s data set• 6180 interactions between 2291 annotated proteins• Edge reliabilities derived using machine learning techniques

– DIPCore [Deane et al, 2002]• ~5K highly reliable interactions in DIP• No weights assigned: assumed unweighted

Results on Combined data set

Precision-Recall Accuracy of top-k predictions

Results on Krogan et al’s data set

Precision-Recall Accuracy of top-k predictions

Results on DIPCore

Precision-Recall Accuracy of top-k predictions

Noise removal capabilities of H-confidence

• H-confidence and hypercliques have been shown to have noise removal capabilities [Xiong et al, 2006]

• To test its effectiveness, we added 50% random edges to DIPCore, and re-ran the transformation process

• Fall in performance of transformed network is significantly smaller than that in the original network

Summary of Results

• H-confidence-based transformations generally produce more accurate and more reliably weighted interaction graphs: Validated function prediction

• Generally, the less reliable the weights assigned to the edges in the raw network, the greater improvement in performance obtained by using an h-confidence-based graph transformation.

• Better performance of the h-confidence-based graph transformation method is indeed due to the removal of spurious edges, and potentially the addition of biologically viable ones and effective weighting of the resultant set of edges.

Conclusions and future directions different protein function prediction algorithms are run on the

original as well as the transformed networks

Nabieva et al.’s FunctionalFlow algorithm

o neighborhood-based algorithm inspired by Schwikowski et al.’s function prediction algorithm

o The predictions from both these algorithms are evaluated within

a five-fold cross-validation setup by computing the Area Under the ROC Curve (AUC) score for each class separately

o common neighborhood similarity information is that it can be

used for filtering out noisy or spurious interactions in a network

evaluated the use of a variety of common neighborhood similarity (CNS) measures to quantify the relationship of two proteins based on their common neighborhood

used them within the framework of graph transformation for the task

of pre-processing protein interaction networks

Conclusions and future directions

validation of the noisy edges removed and the functional linkages added to the network during the graph transformation process using experimental PPI

assessment methods examine how the CNS measures evaluated here perform for other types of network data, such as genetic interaction networks which have their own characteristics, such as the presence of both positively and negatively weighted edges

it is possible to develop hybrid CNS measures that

combine the best properties of all these measures

References (I)

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