Detecting hierarchical structure in molecular characteristics of disease using transitive approximations of directed graphs

نویسندگان

  • Juby Jacob
  • Marcel Jentsch
  • Dennis Kostka
  • Stefan Bentink
  • Rainer Spang
چکیده

MOTIVATION Molecular diagnostics aims at classifying diseases into clinically relevant sub-entities based on molecular characteristics. Typically, the entities are split into subgroups, which might contain several variants yielding a hierarchical model of the disease. Recent years have introduced a plethora of new molecular screening technologies to molecular diagnostics. As a result molecular profiles of patients became complex and the classification task more difficult. RESULTS We present a novel tool for detecting hierarchical structure in binary datasets. We aim for identifying molecular characteristics, which are stochastically implying other characteristics. The final hierarchical structure is encoded in a directed transitive graph where nodes represent molecular characteristics and a directed edge from a node A to a node B denotes that almost all cases with characteristic B also display characteristic A. Naturally, these graphs need to be transitive. In the core of our modeling approach lies the problem of calculating good transitive approximations of given directed but not necessarily transitive graphs. By good transitive approximation we understand transitive graphs, which differ from the reference graph in only a small number of edges. It is known that the problem of finding optimal transitive approximation is NP-complete. Here we develop an efficient heuristic for generating good transitive approximations. We evaluate the computational efficiency of the algorithm in simulations, and demonstrate its use in the context of a large genome-wide study on mature aggressive lymphomas. AVAILABILITY The software used in our analysis is freely available from http://compdiag.uni-regensburg.de/software/transApproxs.shtml.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Two-geodesic transitive graphs of prime power order

In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be   $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...

متن کامل

On Making Directed Graphs Transitive

We present the first thorough theoretical analysis of the Transitivity Editing problem on digraphs. Herein, the task is to perform a minimum number of arc insertions or deletions in order to make a given digraph transitive. This problem has recently been identified as important for the detection of hierarchical structure in molecular characteristics of disease. Mixing up Transitivity Editing wi...

متن کامل

Perfect Matchings in Edge-Transitive Graphs

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

متن کامل

On the eigenvalues of normal edge-transitive Cayley graphs

A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. ‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, ‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. ‎In this paper‎, ‎the eigenvalues of normal edge-tra...

متن کامل

Product of normal edge-transitive Cayley graphs

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Bioinformatics

دوره 24 7  شماره 

صفحات  -

تاریخ انتشار 2008