ProDis-ContSHC: learning protein dissimilarity measures and hierarchical context coherently for protein-protein comparison in protein database retrieval

<p>Abstract</p> <p>Background</p> <p>The need to retrieve or classify protein molecules using structure or sequence-based similarity measures underlies a wide range of biomedical applications. Traditional protein search methods rely on a pairwise dissimilarity/similarity measure for comparing a pair of proteins. This kind of pairwise measures suffer from the limitation of neglecting the distribution of other proteins and thus cannot satisfy the need for high accuracy of the retrieval systems. Recent work in the machine learning community has shown that exploiting the global structure of the database and learning the contextual dissimilarity/similarity measures can improve the retrieval performance significantly. However, most existing contextual dissimilarity/similarity learning algorithms work in an unsupervised manner, which does not utilize the information of the known class labels of proteins in the database.</p> <p>Results</p> <p>In this paper, we propose a novel protein-protein dissimilarity learning algorithm, ProDis-ContSHC. ProDis-ContSHC regularizes an existing dissimilarity measure <it>d_ij</it>by considering the contextual information of the proteins. The context of a protein is defined by its neighboring proteins. The basic idea is, for a pair of proteins (<it>i</it>, <it>j</it>), if their context <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1471-2105-13-S7-S2-i1"><m:mi mathvariant="script">N</m:mi><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>i</m:mi></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow></m:math></inline-formula> and <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1471-2105-13-S7-S2-i2"><m:mi mathvariant="script">N</m:mi><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>j</m:mi></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow></m:math></inline-formula> is similar to each other, the two proteins should also have a high similarity. We implement this idea by regularizing <it>d_ij</it>by a factor learned from the context <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1471-2105-13-S7-S2-i3"><m:mi mathvariant="script">N</m:mi><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>i</m:mi></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow></m:math></inline-formula> and <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1471-2105-13-S7-S2-i4"><m:mi mathvariant="script">N</m:mi><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>j</m:mi></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow></m:math></inline-formula>.</p> <p>Moreover, we divide the context to hierarchial sub-context and get the contextual dissimilarity vector for each protein pair. Using the class label information of the proteins, we select the relevant (a pair of proteins that has the same class labels) and irrelevant (with different labels) protein pairs, and train an SVM model to distinguish between their contextual dissimilarity vectors. The SVM model is further used to learn a supervised regularizing factor. Finally, with the new <b>S</b>upervised learned <b>Dis</b>similarity measure, we update the <b>Pro</b>tein <b>H</b>ierarchial <b>Cont</b>ext <b>C</b>oherently in an iterative algorithm--<b>ProDis-ContSHC</b>.</p> <p>We test the performance of ProDis-ContSHC on two benchmark sets, i.e., the ASTRAL 1.73 database and the FSSP/DALI database. Experimental results demonstrate that plugging our supervised contextual dissimilarity measures into the retrieval systems significantly outperforms the context-free dissimilarity/similarity measures and other unsupervised contextual dissimilarity measures that do not use the class label information.</p> <p>Conclusions</p> <p>Using the contextual proteins with their class labels in the database, we can improve the accuracy of the pairwise dissimilarity/similarity measures dramatically for the protein retrieval tasks. In this work, for the first time, we propose the idea of supervised contextual dissimilarity learning, resulting in the ProDis-ContSHC algorithm. Among different contextual dissimilarity learning approaches that can be used to compare a pair of proteins, ProDis-ContSHC provides the highest accuracy. Finally, ProDis-ContSHC compares favorably with other methods reported in the recent literature.</p

Estimating Bounds for Quadratic Assignment Problems Associated with Hamming and Manhattan Distance Matrices based on Semidefinite Programming

Quadratic assignment problems (QAPs) with a Hamming distance matrix for a hypercube or a Manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the issue of how to obtain lower bounds for those two classes of QAPs based on semidefinite programming (SDP). By exploiting the data structure of the distance matrix B, we first show that for any permutation matrix X, the matrix Y = αE − XBX T is positive semi-definite, where α is a properly chosen parameter depending only on the associated graph in the underlying QAP and E = ee T is a rank one matrix whose elements have value 1. This results in a natural way to approximate the original QAPs via SDP relaxation based on the matrix splitting technique. Our new SDP relaxations have a smaller size compared with other SDP relaxations in the literature and can be solved efficiently by most open source SDP solvers. Experimental results show that for the underlying QAPs of size up to n=200, strong bounds can be obtained effectively