Improved prediction of missing protein interactome links via anomaly detection
 Kushal Veer Singh^{1} and
 Lovekesh Vig^{1}Email author
DOI: 10.1007/s4110901700227
© The Author(s) 2017
Received: 24 August 2016
Accepted: 14 January 2017
Published: 28 January 2017
Abstract
Interactomes such as Protein interaction networks have many undiscovered links between entities. Experimental verification of every link in these networks is prohibitively expensive, and therefore computational methods to direct the search for possible links are of great value. The problem of finding undiscovered links in a network is also referred to as the link prediction problem. A popular approach for link prediction has been to formulate it as a binary classification problem in which class labels indicate the existence or absence of a link (we refer to these as positive links or negative links respectively) between a pair of nodes in the network. Researchers have successfully applied such supervised classification techniques to determine the presence of links in protein interaction networks. However, it is quite common for proteinprotein interaction (PPI) networks to have a large proportion of undiscovered links. Thus, a link prediction approach could incorrectly treat undiscovered positive links as negative links, thereby introducing a bias in the learning. In this paper, we propose to denoise the class of negative links in the training data via a Gaussian process anomaly detector. We show that this significantly reduces the noise due to mislabelled negative links and improves the resulting link prediction accuracy. We evaluate the approach by introducing synthetic noise into the PPI networks and measuring how accurately we can reconstruct the original PPI networks using classifiers trained on both noisy and denoised data. Experiments were performed with five different PPI network datasets and the results indicate a significant reduction in bias due to label noise, and more importantly, a significant improvement in the accuracy of detecting missing links via classification.
Keywords
Link prediction Anomaly detection Protein protein interaction networksIntroduction
Graphical networks can depict many complex systems involving biological, social and informational connections between entities. At the most abstract level, these networks are modelled by graphs in which nodes represent individuals or agents and links denote the interactions or relationships between nodes. Structural properties of biological networks are of great interest as they directly correlate with biological function (Qi and Ge 2006; Wuchty et al. 2003). Various attempts have been made to understand the topological evolution of networks (Albert and Barabási 2002; Dorogovtsev and Mendes 2002). The evolution of networks involves two processes: i) the addition or deletion of nodes and ii) The addition or deletion of edges (links) between nodes. The second process of topological evolution particularly when new connections are added to the existing network has not yet been concretely formalised and revolves around the linkprediction problem. Many applications utilize link prediction to identify new links in large, sparse networks armed only with knowledge of network topology. Therefore, improvements in link prediction accuracy will be of great significance in both science and engineering applications. Meanwhile, linkprediction also reflects the extent to which the evolution of a network can be modelled by topological features intrinsic to the network itself.
The link prediction task can be stated as follows: given a network, or a graph, predict what edges will form between nodes in the future. Alternatively, in domains where data collection is costly and the resulting networks are noisy and incomplete, link prediction can be used to identify unobserved edges. In such cases, the problem is also known as the missing link problem.
The objective of this work is to better identify undiscovered (missing and suspicious) links between pairs of nodes in a proteinprotein interaction (PPI) network. Link prediction uses the existing protein interaction topology to predict missing links. Discovery of links in biological networks such as gene networks, proteinprotein interaction networks, metabolic networks etc. are very costly and timeconsuming if done via laboratory experiments and hence the known connections within these networks remains largely incomplete (Martinez et al. 1999; Sprinzak et al. 2003). Instead of identifying links between all possible pairs of nodes, predictions that focus on already known interactions and are accurate enough can sharply reduce the experimental costs. Discovering protein protein interactions is a pivotal task for understanding the underlying biological processes behind tasks such as protein function prediction, drug delivery control and disease diagnosis.
Researchers have formulated link prediction as a binary classification problem, where class labels indicate the presence or absence of a link (referred to as positive links or negative links respectively) between pairs of nodes in the network. In this approch, features based on network topology such as common neighbors, Jaccard coefficient, etc. of the two nodes under consideration are fed to the classifier which predicts the presence or absence of a link. This paper also formulates the link prediction problem as a binary classification problem based on topological features, with a view to improve classification performance. Recently it was found that local communitybased features were most effective for link prediction in biological networks both in monopartite (Cannistraci et al. 2013b) and bipartite networks (Daminelli et al. 2015). Therefore, we have included these in our feature list for the PPI network datasets under consideration.
An unresolved issue with formulating the link prediction problem as a classification problem is the label noise present in the training data. Typically, a set of positive and negative links are randomly chosen from the existing graph and are used for training a classifier, which is then used to predict links on the remaining network. However, the absence of a link in the network does not necessarily mean it is a negative link; it may be the case that the link exists but is undiscovered (as commonly occurs with PPI networks). Therefore, to include this pair of nodes in the training data as a negative link may introduce label noise and bias the resulting classifier. In this paper, we claim that by using anomaly detection on the negative links of the training data, and by subsequently filtering out the detected anomalous negative links from training data, we can obtain better classifiers that yield superior link prediction performance. The suggested approach is evaluated on five different PPI networks, with four different classifiers. A comparison with classification with and without anomaly detection is provided and results demonstrate that utilizing anomaly detection for filtering suspicious negative links yields superior classifier performance on test data.
Related work
General purpose neighborhood based methods have been proposed for link prediction in different kinds of networks: collaboration, social, citation, roadmaps, etc. (Liben Nowell and Kleinberg 2007; Zhou et al. 2009). Various bioinspired methods were created to either assess reliability of interactions in PPI networks such as Interaction Generality (IG1) (Saito et al. 2002), IG2 (Saito et al. 2003) and IRAP (Chen et al. 2005) or predict protein function such as the CzekanowskiDice Dissimilarity (CDD) (Brun et al. 2003) and FSW (Chen et al. 2006). Later, these techniques were applied to protein interaction prediction (Cannistraci et al. 2013b; Chua et al. 2006). Both approaches rely on the number of neighbors that two nondirectly connected nodes have and assign a likelihood score to this pair of nodes.
The simplest techniques are Jaccard’s coefficient (Jaccard 1912), Common Neighbors and Preferential Attachment (Newman 2001). Jaccard’s coefficient assigns higher likelihood scores to the node pairs for which the set of common interactors as a proportion of all available neighbors is higher and Common Neighbors does the same for pairs of nodes that simply share more interactors. Preferential Attachment, on the other hand, gives high scores when both nodes have a large number of neighbors: if one of the nodes has a low number of interactors, the score is reduced. In contrast, Adamic and Adar (2003) and Resource Allocation (Ou et al. 2007) are two similar indices that give more importance to Common Neighbors with low degree.
Various other methods have been proposed to assess the reliability of highthroughput protein interaction data. In 2009, Kuchaiev et al. (2009) proposed a method for geometric denoising of PPI networks. Cannistraci et al. in (2010) proposed topologybased link prediction method using minimum curvilinear embedding. In 2013, Cannistraci et al. (2013a) proposed a new valid variation of minimum curvilinear embedding, named noncentred minimum curvilinear embedding. AlanisLobato et al. in (2013) utilized several measures for the proximity of genes based on the common neighborhood structure of a GI network. However these methods do not explicitly utilize a classification based approach to the problem of identifying missing interactions.
Hasan et al. (2006) formulated the link prediction problem into binary classification problem. The method extracted a set of topological features of the network as input for supervised learning for link prediction. A binary classification approach integrated information from multiple measures to get a better prediction. In 2011 Fire M et al. (2011) utilized topological features for supervised learning, and ranked the importance of each feature. They proposed a set of simple, computationally efficient topological features that could be analyzed to identify missing links. In 2013 Cannistraci et al. (2013b) proposed a new paradigm to support link formation called the Local Community Paradigm (LCP), which emphasizes the role of the local network community structure in link formation. They proposed local communitybased Cannistraci features for linkprediction in PPI networks. Yu et al. (2006) in 2006 predicted missing links in PPI networks by completing defective cliques. Some methods have been reviewed in Lü and Zhou (2011) and some have been successfully applied for link detection in PPI networks.
Several anomaly detection techniques have been proposed for detecting outlier nodes, edges or substructures in graph data. The techniques may broadly be classified as: i) Featurebased approaches which utilize structural graphcentric features for outlier detection in the constructed feature space. Essentially, these methods transform the graph anomaly detection problem to the wellunderstood outlier detection problem (Akoglu et al. 2010; Henderson et al. 2011). ii) Proximitybased approaches that exploit the graph structure to measure closeness (or proximity) of objects in the graph. These methods capture the simple autocorrelation between these objects, where similar objects are likely to belong to the same class (Jeh and Widom 2002; Brin and Page 1998). iii) Communitybased approaches that utilize clustering methods for graph anomaly detection and rely on finding densely connected groups of ’closeby’ nodes in the graph to discover anomalies that have connections across communities (Chakrabarti 2004; Sun et al. 2005; Tong and Lin 2011). iv) Relational learning based approaches consist of networkbased collective classification algorithms, the main idea of which is to exploit the relationships between the objects to assign them into classes, where the number of classes is often two: anomalous and normal (Getoor et al. 2001; Jensen et al. 2004). Further details on these approaches can be found in a thorough survey (Akoglu et al. 2015). In this paper we use featurebased anomaly detection techniques to discover suspicious negative links, thereby reducing the impact of label noise introduced by assigning undiscovered positive links to the class of negative links in the training data.
Materials and methods
Network Datasets
Network datasets
Network  Type  No. of nodes  No. of edges 

Arabidopsis thaliana  Undirected  7550  19962 
Caenorhabditis elegans  Undirected  5758  14829 
Mus musculus  Undirected  6236  13865 
Rattus norvegicus  Undirected  2448  3804 
Methods
Our objective was to minimize the classification bias arising due to currently undiscovered edges (positive links) being incorrectly labeled as negative links. To address this bias, we use anomaly detection for removing suspicious negative links (which may be undiscovered positive links) from the training set before classifier training. Finally, we train a link classifier on the filtered dataset after removal of these detected suspicious negative links. Since we focused on predicting links based only on network topology, we extracted a set of features for nodepairs (edges) from the corresponding PPI network with the goal of developing a network topological featurebased classifier. We then performed supervised learning, using different machine learning classifiers. The network topology based features utilized for classification are described here.
Topologybased Measures
We briefly describe the set of topologybased measures or features that were used during our experiment. A graph theoretic approach is used to model the proteinprotein interaction as a network. In this method, a PPI network is represented by an undirected graph G=(V,E), with a set of nodes or vertices V and a set of links or edges E, where vertices represent proteins and edges represent interactions between proteins respectively. In this paper, G will always be an unweighted, undirected graph. Graphs can be characterized by many different topologybased measures, each one reflecting some particular traits of the studied structure. The topologybased measures were chosen based on their successful application in prior work on link prediction (Cannistraci et al. 2013b; Fire et al. 2011; Zhou et al. 2009).

Node degree : The degree of a node in a network is the number of links the node has to other nodes. For an undirected network, degree of a node is defined as:
Let v∈V and$$ deg(v)= N(v) $$(3) 
Node subgraphs: This measure denotes the number of links within the open and closed nbhdsubgraphs for each node v, which is defined as:$$ \begin{aligned} subgraphedgeno(v) &= nbhdsubgraph(v)\\ subgraphedgeno[\!v] &= nbhdsubgraph[\!v] \end{aligned} $$(4)Density of subgraph is defined as:$$ \begin{aligned} densitynbhdsubgraph(v)&= \frac {deg(v)} {nbhdsubgraph(v)}\\ densitynbhdsubgraph[\!v]&= \frac {deg(v)} {nbhdsubgraph[\!v]} \end{aligned} $$(5)
Note that the formal density of a graph is defined differently, however, the aim of this feature and all other features used in the paper is to be as straight forward and simple as possible. Therefore, we used a somewhat different density that is more related to a vertex v.

CommonNeighbors (CN): The common neighbors (CN) of u and v refers to the number of common neighbors of u and v. Two vertices u and v are more likely to connect if they have bigger number of common neighbors. It is defined as Newman (2001):$$ CN(u,v)=N(u) \cap N(v) $$(6)

TotalNeighbors (TN): The total neighbors (TN) of u and v measure the number of distinct neighbors of u and v. which refers to the total number of neighbors u and v have together. The formal definition of TN is:$$ TN(u,v)=N(u) \cup N(v) $$(7)

Jaccard’s Coefficient (JC): Jaccard’s coefficient (JC) normalizes the size of common neighbors by total neighbors. This gives higher weight to those pairs of nodes which share a higher proportion of common neighbors relative to the total number of neighbors they have. The formal definition of JC is (Jaccard 1912):$$ JC(u,v)=\frac{N(u) \cap N(v)}{N(u) \cup N(v)} $$(8)

AdamicAdar Coefficient (AA): This metric refines the simple counting of common neighbors by assigning higher likelihood scores to neighbors that are not shared with many others. It is defined as (Adamic and Adar 2003):$$ AA(u,v)=\sum_{z \in N(u) \cap N(v)} \frac{1}{log(N(z))} $$(9)

Resource allocation Coefficient (RA): The RA coefficient and AA coefficient have very similar forms the only difference being that the RA coefficient punishes the high degree common neighbors more heavily than the AA coefficient. It is defined as (Ou et al. 2007):$$ RA(u,v)=\sum_{z \in N(u) \cap N(v)} \frac{1}{N(z)} $$(10)

Preferential Attachment (PA): This measure assigns higher likelihood scores to those pairs of nodes for which one or both nodes have a high degree. The formal definition of PA is (Newman 2001):$$ PA(u,v)=N(u).N(v) $$(11)

LCPbased measures and Cannistraci variants: The local community paradigm suggests that two nodes are more likely to link together if their commonfirstneighbors are members of a strongly innerlinked cohort or localcommunity. The Cannistraci (LCPbased) variants of classical neighborhood methods (CN, PA, AA, RA, JC) are defined as (Cannistraci et al. 2013b):$$\begin{array}{@{}rcl@{}} CAR(u,v)= CN(u,v).LCL(u,v) =CN(u,v).\sum_{z \in N(u) \cap N(v)}\frac{\gamma(z)}{2} \end{array} $$(12)$$\begin{array}{@{}rcl@{}} CPA(u,v)= e_{u}.e_{v} + e_{u}.CAR(u,v) + e_{v}.CAR(u,v) + CAR(u,v)^{2} \end{array} $$(13)$$\begin{array}{@{}rcl@{}} CAA(u,v)=\sum_{z \in N(u) \cap N(v)}\frac{\gamma(z)}{{log}_{2}(N(z))} \end{array} $$(14)$$\begin{array}{@{}rcl@{}} CRA(u,v)=\sum_{z \in N(u) \cap N(v)}\frac{\gamma(z)}{N(z)}\!\!\qquad\qquad\qquad\qquad\qquad\quad \end{array} $$(15)$$\begin{array}{@{}rcl@{}} CJC(u,v)=\frac{CAR(u,v)}{N(u) \cup N(v)}\!\!\qquad\qquad\qquad\qquad\qquad\quad \end{array} $$(16)
Where γ(z) refers to the subset of nodes in the neighborhood of z that are also common neighbors of of u and v, thus γ(z) is the local community degree of z; e _{ u } refers to the external degree of u, and is computed considering the nodes in the neighborhood of u that are not common neighbors of u and v.

Friends Measure (FM): Friend Measure (FM) of u and v measures the total number of links between the neighborhoods of u and v. Here we assume that two nodes have higher chance to get connected if their neighborhoods have more links with each other. The formal definition of FM is (Fire et al. 2011):$$ FM(u,v)=\sum_{x \in N(u)} \sum_{y \in N(v)} \delta(x,y) $$(17)Where$$ \delta(x,y)= \left\{\begin{array}{cl} 1 & if\ x=y \;or\; (x,y) \in E \;or\; (y,x) \in E\\ 0 & otherwise \end{array}\right. $$(18)

Edge Subgraphs Edges Number: This measure counts the number of links in the above subgraphs:
$$ \begin{aligned} nbhdsubgraph(u,v)\\ nbhdsubgraph[\!u,v]\\ innersubgraph(u,v) \end{aligned} $$(21)
In this study, we extracted a total of 25 features for each PPI network.
Anomaly detection
We attempt to apply multiple anomaly detection techniques such as Parzen Windows, Principal Component Analysis (PCA), Nearest Neighbor (a distancebased method) and a oneclass Gaussian process for removing anomalous negative links from the training data. The details of these methods can be found in (Clifton 2007; 2009; Pimentel et al. 2014). We utilize the link prediction feature set for training the anomaly detector, described in an earlier subsection. Note that all the methods presented below require only normal data for training, however abnormal data is used for validating the models. In that sense the methods below may be considered unsupervised. as these methods do not require anomalous data for training. After experimentation, we found that the Gaussian Process based anomaly detection gave the most reliable results. Hence, we chose the Gaussian Process model as our anomaly detector for our classification experiments. Next, we present a brief introduction to all of the methods considered.
 1.
Locate a hyperspherical Gaussian window, or kernel, with width σ, on each of the Ddimensional feature vectors in the training dataset, x _{ i }, where i = 1, …, N.
 2.
Evaluate the sum of the Gaussian distributions using the squared Euclidean distances between the test feature vector x and the training vectors x _{ i }, normalized by a factor that ensures p(x) integrates to 1.
By placing a Gaussian kernel over each feature vector x _{ i } in our training dataset, we construct a probability density estimate of p(x) that will have a higher value of p where the concentration of training data is greatest. Points in the test set with values of p(x) are classified as anomalies.
PCA method: PCA is an orthogonal transformation for transforming the raw data into a space such that the new basis vectors (principal components) are linear combinations of the original basis vectors, are linearly uncorrelated and correspond to the directions of maximal variance of the data, where the first principal component is in the direction of the highest variance, the second in the direction of the highest remaining variance and so on. Anomaly detection is performed with PCA under the assumption that normal data would be best explained by looking at the first few principal components whereas abnormal data would be captured by the remaining principal components (Bishop 2006; Chiang et al. 2001; Marsland 2003). Thus points in the data that have high coefficients for the last few principal components would correspond to anomalous data.
Gaussian process: Given a training set \(D =\{(x_{i},y_{i})\}_{i=1}^{n} =(X,y)\) where x _{ i }∈X⊂R ^{ d } denotes feature vector and y denotes a scalar output or target. We are interested in identifying the target y _{∗} for a new sample x _{∗}. The objective of regression is to find the association between inputs x and target y. To identify the association between the input and target, we modelled the mapping in terms of y=f(x)+ε, where f is an unknown function, and ε denotes a noise term. To do this, one approach is to assume that f is a parametric function f(x;θ) where the parameters θ are tuned based on the training data. But, the major pitfall of this kind of approach is that, if in case, a wrong form of the function is chosen, it can lead to poor predictions. Another approach, based on Gaussian process takes care of this problem by assigning a priori probability to all possible functions, which are more likely to be sampled. The process is based on the assumption that these functions are drawn from a specified probability distribution. This method requires a training set and may be considered supervised.
Where moments μ _{∗} and \(\sigma _{*}^{2}\) can be given in closed form expressions. More details about GP framework, can be found in (Williams and Rasmussen 2006).
Where K=κ(X,X) denotes the kernel matrix of the training set, k _{∗}=κ(X,x _{∗}) represents the vector of kernel values between training set and test input and k _{∗∗}=κ(x _{∗},x _{∗}) is the kernel values of the test input. The correlation of function values using the similarity of input samples are calculated by the radial basis function (rbf): \(\kappa (x,x')=exp\left (\frac { x  x^{'}^{2}} {2.\sigma ^{2}}\right)\).
Experimental setup
Since the number of known links are few, we oversample the positive links in the datasets to generate sufficient positive links from each network when required. The set of negative links is much larger and it has been shown that the subset sampling method used to generate the negative training links impacts the performance of the resulting classifier (Yu et al. 2010). Two predominant sampling methods have been proposed for the negative set sampling in PPI networks, namely balanced random sampling and simple random sampling. In simple random sampling care is taken to ensure the proteins in the positive set must also appear in the negative set. In balanced random sampling the proteins must occur with the same frequency in both sets. It has further been shown that protein pairs with higher number of common neighbours are more likely to interact (AlanisLobato 2015), therefore by choosing non interacting pairs within 2 hops of each other we are in effect constructing a negative set that is harder to classify. To ensure no bias is introduced due to the sampling method we experimented with both balanced random and simple random sampling for choosing our negative set.
 1.
We extract positive links from the network, and divided them into a validation and test set in the ratio 50:50. Note that positive links are not used for training the anomaly detector but only for validation.
 2.
We extract negative links from the network, such that the vertices are within two hops of each other. These are divided into training, validation and test set in the ratio 60:20:20.
 3.
Topological features are extracted for the above training, validation and test sets.
 4.
We train and evaluate different anomaly detection methods and select the best performing anomaly detection method from these methods. We use this trained anomaly detector model in phaseII.
 1.
We extract positive links from the network, and divided them into a training set, validation set and a test set in the ratio 60:20:20.
 2.
In order to introduce synthetic noise we mislabel a fraction of the positive links and assign them labels corresponding to negative links.
 3.
We extract negative links from the network using simple random sampling, such that the vertices are within two hops of each other.
 4.
The mislabelled negative links generated in step 2 are merged with the negative links in the training set from step 3 to allow for creation of a noisy dataset with synthetic ground truth. This is divided into a training, validation and test set in the ratio 60:20:20 such that the positive and negative datasets are balanced.
 5.
Topological features are extracted for the above training and test sets. We call this the unfiltered training dataset.
 6.
Next we generate a filtered version of the dataset using anomaly detection to filter out the noisy negative links we had generated in step 4.
 7.
We evaluate different machine learning classifiers on both the filtered and unfiltered training datasets.
 8.
Prediction accuracy is compared across classifiers trained on the filtered vs. the unfiltered dataset.
Results
Performance evaluation of different anomaly detector
Anomaly detection techniques comparison under different metrics
Network  Anomaly Method  Accuracy  Fmeasure  Sensitivity  Specificity  FP rate  FN rate 

Arabidopsis  gpoc  96.69  96.77  99.19  94.19  5.81  0.81 
thaliana  parzen  85.75  85.12  81.50  90.00  10.00  18.50 
pca  69.25  76.48  1  38.50  61.50  0  
nn  77.50  81.63  1  55.00  45.00  0  
Caenorhabditis  gpoc  90.98  91.59  98.23  83.73  16.27  1.77 
elegans  parzen  69.63  76.61  99.50  39.75  60.25  0.50 
pca  56.13  69.50  1  12.25  87.75  0  
nn  56.37  69.63  1  12.75  87.25  0  
Mus musculus  gpoc  94.90  95.13  99.56  90.24  9.76  0.44 
parzen  90.62  91.39  99.50  81.75  18.25  0.50  
pca  70.37  77.15  1  40.75  59.25  0  
nn  76.50  80.97  1  53.00  47.00  0  
Rattus  gpoc  98.10  98.13  99.68  96.52  3.48  0.32 
norvegicus  parzen  96.13  96.25  99.50  92.75  7.25  0.50 
pca  77.25  81.47  1  54.50  45.50  0  
nn  91.37  92.06  1  82.75  17.25  0 
Anomaly detector performance measure
Network  TPR  TNR 

Arabidopsis thaliana  99.62  93.23 
Caenorhabditis elegans  99.22  82.33 
Mus musculus  99.70  91.50 
Rattus norvegicus  99.65  95.58 
Gene Ontology (GO) validation of anomaly detection
We also elucidated the biological significance of anomaly detection using the Gene Ontology (GO) scores of protein pairs in different PPI networks. Since proteins which are involved in the same biological function or share the same biological pathway are more likely to interact with each other compared to proteins which belong to other pathways, hence this statistics is a better measure to test the quality of our prediction. We calculated the GO score corresponding to each of the gene ontology classes i.e. biological process, cellular components and molecular functions of protein pairs using the Protein Interaction Network Analysis Platform (PINA) ^{2}. As we saw in Table 3 TNR is lower than the TPR this is because our anomaly detector extracts some non interacting protein pairs as anomalies. These may be undiscovered interactions and to validate this hypothesis we look at the GO scores of these anomalous protein pairs. In Mus musculus, the anomaly detection extracts 1360 proteins pairs as anomalies out of which 612 protein pairs have a GO score greater than 0.5, and out of these 268 protein pairs were found to interact with different public databases. In Rattus norvegicus, 707 protein pairs were extracted out of which 543 protein pairs had GO scores greater than 0.5. In Caenorhabditis elegans, 2826 protein pairs were extracted as anomalies out of which 1254 protein pairs had GO scores greater than 0.5. Thus, a high proportion of the protein pairs filtered by the anomaly detection technique outlined in this paper appear to have significant GO scores and may potentially have undiscovered interactions. We further validated the discovered anomalies against the Negatome Database which contains experimentally supported noninteracting protein pairs. On matching the resuts not a single anomalous negative link discovered by the anomaly detector was found to lie in the Negatome database, further validating the fact that the interactions discovered by the anomaly detector.
Performance evaluation of different classifiers
Classification comparison Under different metrics using simple random sampling
Network  Classifier  Without anomaly detection  With anomaly detection  

Accuracy  Fmeasure  AUC  Accuracy  Fmeasure  AUC  
Arabidopsis  SVM  93.07  92.80  93.07  96.85  96.94  96.85 
thaliana  C5.0*  99.35  99.35  99.35  99.34  99.34  99.34 
KNN  94.24  93.97  94.24  98.42  98.44  98.42  
NB  62.29  40.54  62.29  84.22  82.24  84.22  
Caenorhabditis  SVM  87.67  86.02  87.67  94.02  94.34  94.02 
elegans  C5.0  97.81  97.78  97.81  98.30  98.32  98.30 
KNN  92.99  92.73  92.99  96.07  96.20  96.07  
NB  59.18  36.39  59.18  67.23  57.46  67.23  
Mus musculus  SVM  93.30  93.03  93.31  96.83  96.93  96.84 
C5.0  98.06  98.04  98.06  99.32  99.33  98.32  
KNN  94.12  93.84  94.12  98.47  98.49  98.47  
NB  60.38  35.23  60.38  79.32  75.55  79.32  
Rattus  SVM  91.65  90.79  91.65  98.79  98.81  98.79 
norvegicus  C5.0  91.34  90.54  91.34  99.46  99.45  99.45 
KNN  88.15  86.57  88.15  99.35  99.35  99.35  
NB  66.29  49.32  66.29  84.25  82.00  84.25 
Classification comparison Under different metrics using balanced random sampling
Network  Classifier  Without anomaly detection  With anomaly detection  

Accuracy  Fmeasure  AUC  Accuracy  Fmeasure  AUC  
Arabidopsis  SVM  92.99  92.70  92.99  97.01  97.09  97.01 
thaliana  C5.0*  99.41  99.76  99.41  99.41  99.41  99.41 
KNN  94.81  94.60  94.81  98.43  98.45  98.43  
NB  62.55  41.18  62.55  86.77  85.53  86.77  
Caenorhabditis  SVM  87.02  85.18  87.02  93.60  93.97  93.60 
elegans  C5.0*  97.77  97.74  97.77  97.95  97.97  97.95 
KNN  92.63  92.33  92.63  96.20  96.32  96.20  
NB  60.32  41.53  60.32  66.90  56.98  66.90  
Mus musculus  SVM  93.71  93.49  93.71  96.64  96.75  96.64 
C5.0  98.63  98.62  98.63  99.37  99.37  99.37  
KNN  93.14  92.74  93.14  98.38  98.41  98.38  
NB  59.67  33.26  59.67  78.60  74.78  78.60  
Rattus  SVM  94.61  94.35  94.61  98.56  98.57  98.56 
norvegicus  C5.0  90.75  89.84  90.75  99.40  99.40  99.40 
KNN  86.20  84.04  86.20  99.37  99.37  99.37  
NB  67.42  51.85  67.42  82.73  80.13  82.73 
Feature importance
In order to understand the contribution from each feature for link prediction in the PPI network, we comparatively analyzed the predictive power of the features. To measure the relative importance of different features, we analysed the information gain with respect to each feature. Information gain is based on the decrease in entropy after a dataset is split on an attribute. An attribute with highest information gain is selected for the split. We obtained the information gain of an attribute as follows: Information gain=(Entropy of distribution before the split)  (entropy of distribution after the split)
InfoGain values of different features for all PPI networks
Networks  

Arabidopsis  Caenorhabditis  Mus  Rattus  Average  Standard  
thaliana  elegans  musculus  norvegicus  deviation  
deg(u)  0.32  0.10  0.24  0.260  0.23  0.09  
deg(v)  0.24  0.093  0.17  0.17  0.17  0.06  
subgraphedgeno(u)  0.23  0.07  0.19  0.20  0.17  0.07  
subgraphedgeno(v)  0.18  0.07  0.13  0.14  0.13  0.05  
subgraphedgeno[u]  0.32  0.11  0.23  0.25  0.23  0.09  
subgraphedgeno[v]  0.24  0.09  0.16  0.17  0.17  0.06  
densitynbhdsubgraph(u)  0.27  0.11  0.23  0.23  0.21  0.07  
densitynbhdsubgraph(v)  0.23  0.10  0.17  0.17  0.17  0.05  
densitynbhdsubgraph[u]  0.28  0.11  0.23  0.23  0.21  0.07  
densitynbhdsubgraph[v]  0.23  0.10  0.17  0.17  0.17  0.05  
CN(u,v)  0.56  0.60  0.54  0.58  0.57  0.03  
TN(u,v)  0.52  0.20  0.41  0.49  0.40  0.15  
JC(u,v)  0.08  0.03  0.037  0.12  0.06  0.04  
AA(u,v)  0.82  0.73  0.79  0.80  0.79  0.04  
RA(u,v)  0.82  0.71  0.79  0.80  0.78  0.05  
PA(u,v)  0.54  0.23  0.42  0.51  0.42  0.14  
CAR(u,v)  0.08  0.06  0.11  0.09  0.08  0.02  
CPA(u,v)  0.67  0.40  0.59  0.76  0.60  0.15  
CAA(u,v)  0.10  0.07  0.11  0.09  0.09  0.02  
CRA(u,v)  0.11  0.08  0.12  0.10  0.10  0.02  
CJC(u,v)  0.08  0.06  0.10  0.09  0.08  0.02  
FM(u,v)  0.82  0.58  0.69  0.66  0.69  0.10  
nbhdsubgraph(u,v)   0.71  0.40  0.55  0.61  0.57  0.13  
nbhdsubgraph[u,v]   0.50  0.19  0.36  0.44  0.37  0.14  
innersubgraph(u,v)   0.86  0.61  0.72  0.71  0.72  0.10 
Performance evaluation across datasets
Results for Classifier trained on Arabidopsis thaliana and tested on remaining datasets
Classifier  Networks  Without anomaly detection  With anomaly detection  

Accuracy  Fmeasure  AUC  Accuracy  Fmeasure  AUC  
SVM  Rattus norvegicus  96.71  96.64  96.71  98.98  98.99  98.98 
MusMusculus  93.78  93.68  93.78  95.79  95.96  95.79  
C.elegans  85.03  86.03  85.03  81.63  84.48  81.63  
C5.0  Rattus norvegicus  99.46  99.46  99.46  99.45  99.45  99.45 
MusMusculus  99.34  99.34  99.34  99.22  99.22  99.22  
C.elegans  96.92  97.00  96.92  95.72  95.89  95.72  
KNN  Rattus norvegicus  96.66  96.56  96.67  99.58  99.58  99.58 
MusMusculus  95.45  95.31  95.45  98.18  98.20  98.18  
C.elegans  91.38  91.45  91.37  90.52  91.34  90.52  
NB  Rattus norvegicus  64.42  44.95  64.42  77.33  71.09  77.33 
MusMusculus  60.78  36.47  60.78  76.14  70.10  76.15  
C.elegans  57.96  35.03  57.96  70.69  68.43  70.69 
Results for Classifier trained on Caenorhabditis elegans and tested on remaining datasets
Classifier  Networks  Without anomaly detection  With anomaly detection  

Accuracy  Fmeasure  AUC  Accuracy  Fmeasure  AUC  
SVM  Rattus norvegicus  81.24  76.99  81.24  99.05  99.05  99.05 
MusMusculus  82.57  78.98  82.57  98.23  98.25  98.23  
A.thaliana  81.28  77.04  81.28  97.93  97.95  97.93  
C5.0  Rattus norvegicus  95.56  95.37  95.56  97.87  97.83  97.87 
MusMusculus  95.07  94.82  95.07  98.48  98.46  98.48  
A.thaliana  94.77  94.49  94.77  98.68  98.66  98.68  
KNN  Rattus norvegicus  93.94  93.56  93.94  99.08  99.08  99.08 
MusMusculus  93.45  93.02  93.45  98.53  98.52  98.53  
A.thaliana  93.29  92.87  93.29  98.29  98.29  98.29  
NB  Rattus norvegicus  65.38  47.24  65.38  74.37  65.78  74.37 
MusMusculus  62.56  40.95  62.56  71.66  61.22  71.66  
A.thaliana  62.62  40.82  62.62  72.99  64.02  72.99 
Results for Classifier trained on Mus musculus and tested on remaining datasets
Classifier  Networks  Without anomaly detection  With anomaly detection  

Accuracy  Fmeasure  AUC  Accuracy  Fmeasure  AUC  
SVM  Rattus norvegicus  96.93  96.86  96.93  99.02  99.02  99.02 
C.elegans  83.96  84.87  83.96  81.52  84.40  81.52  
A.thaliana  92.83  92.67  92.83  95.66  95.84  95.66  
C5.0  Rattus norvegicus  97.93  97.89  97.93  99.68  99.68  99.68 
C.elegans  94.64  94.69  94.64  95.80  95.96  95.80  
A.thaliana  97.13  97.06  97.13  99.37  99.37  99.37  
KNN  Rattus norvegicus  94.64  94.36  94.64  99.72  99.43  99.72 
C.elegans  91.50  91.63  91.50  91.68  92.31  91.68  
A.thaliana  93.43  93.12  93.43  98.26  98.29  98.26  
NB  Rattus norvegicus  65.63  47.83  65.63  79.26  74.37  79.26 
C.elegans  57.06  33.21  57.06  69.10  67.95  69.10  
A.thaliana  62.28  40.61  62.28  81.72  79.44  81.72 
Results for Classifier trained on Rattus norvegicus and tested on remaining datasets
Classifier  Networks  Without anomaly detection  With anomaly detection  

Accuracy  Fmeasure  AUC  Accuracy  Fmeasure  AUC  
SVM  MusMusculus  90.89  90.68  90.89  92.81  93.29  92.81 
C.elegans  77.71  80.01  77.71  74.33  79.57  74.33  
A.thaliana  90.91  90.76  90.91  92.57  93.07  92.57  
C5.0  MusMusculus  84.24  81.46  84.24  98.61  98.62  98.61 
C.elegans  82.43  79.73  82.43  94.31  94.59  94.31  
A.thaliana  82.03  78.25  82.03  98.75  98.75  98.75  
KNN  MusMusculus  84.38  81.85  84.38  96.63  96.72  96.63 
C.elegans  81.45  79.86  81.45  85.88  87.57  85.88  
A.thaliana  83.11  80.19  83.11  96.57  96.66  96.57  
NB  MusMusculus  65.93  50.25  65.93  85.73  84.82  85.73 
C.elegans  60.12  48.44  60.12  71.98  74.68  71.98  
A.thaliana  68.10  56.24  68.10  87.29  87.10  87.29 
Discussion
This paper presents a technique for filtering graphical link training data by using anomaly detection for the purpose of link prediction in PPI networks. The performance of the resulting predictor compares favourably with the classifier trained on unfiltered data. The central idea is to have a filtering step before the classification step where suspicious links are removed from the training data. One issue that needs emphasis here is that the choice of anomaly detection technique plays a critical role in the success of the resulting classifier. If the anomaly detector is inaccurate, then the classifier may not yield optimum performance. One way to ascertain the efficacy of the anomaly detection is by deliberately mislabeling the positive links and checking if the anomaly detection algorithm can detect them, which is how we have selected our Gaussian Process algorithm. Additionally, this technique shows most improvement in performance when the link prediction accuracy is not particularly high before filtering, as this allows for greater room for classification improvement. Additionally, this technique needs to be extended to link prediction in networks with directed edges (metabolic networks), weighted edges (neural networks). While the given technique is useful for detecting missing links more efficiently, it may have to adapt to work for evolving networks where the links are constantly changing. These ideas are the focus of our future work.
Endnotes
^{1} Downloaded from: http://cbg.garvan.unsw.edu.au/pina/interactome.stat.doon February 10, 2015.
^{2} http://cbg.garvan.unsw.edu.au/pina/interactome.goSimForm.do
Declarations
Acknowledgments
The authors would like to thank J.N.U. and U.G.C., India for providing the research fellowship to K.V.S.
Authors’ contributions
L.V. and K.V.S. conceived and designed the algorithm. K.V.S. implemented the algorithm and prepared the figures of the numerical results. K.V.S. and L.V. analyzed and interpreted the results, and wrote the manuscript. Both the authors have read and approved the final manuscript.
Competing interests
We declare that there is no competing of interests for this work.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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