Automated Network Drawing Using Self-Organizing Map Xiangjun Xu Mladen Kezunovic* Electrical Engineering Department, Texas A&M University College Station, TX 77843-3128, USA (Phone) 979-845-7509, (Fax) 979-845-9887, [email protected] have many old power network data files without graphical ABSTRACT: In this paper, a method for automatically creating representation information. It is meaningful to find a way to circuit schematic diagrams from the topological information automatically create graphical representations of those data contained in network data files has been proposed. This method is files. For example, ATPDraw [8] provides a graphics user based on Self-Organizing Map (SOM) neural network and the basic idea behind the method is to let the network span itself interface to create and edit circuit diagrams. Those ATPDraw according to a given “shape” of the network grid. The topology circuit files (.CIR) contain both the layout information and the of a network is defined by the connections between its nodes. By component parameters. ATPDraw can convert those circuit forming an SOM using the network connection topology and files into ATP files (.ATP) before calling the ATP [9] training it using data grids of desired “shape”, the positions of the program. On the other hand, the ATP files have no layout nodes and their neighbors will be gradually updated until a desired information. So, the process can not be reversed, i.e. the diagram has been created. function to recover an ATPDraw circuit file from an ATP file Keywords: Visualization, Graph Drawing, Layout, Routing, Self- is not available. Since the graphical representation of an Organizing Map, Artificial Neural Network. electric circuit has many benefits when compared to just the data file, it is meaningful to find a method, which can automatically create a graphical representation for a give data I. INTRODUCTION file. Such kind of function of ATPDraw has been demanded Automated graph drawing has been studied many years and for a long time. become relatively mature, especially for directed and layered Guise [10] developed a program that can automatically graphs. R. Tamassa addressed the problem of readability of create schematic diagrams from EMTP data files. Since the automatically created diagrams in [1] and a procedure for problems are “NP-complete”, heuristics are used to create the automatically drawing directed graphs was presented in [2], drawing initially, and then the user can adjust the drawing which was based on the clan-based graph decomposition. In manually. In [11], Kolysh proposed a method to create [3], the author proposed an automatic method for drawing substation scheme graphs from substation data files compound digraphs that contain both inclusion and adjacency automatically. The method utilized the fact that there are only edges. There are also some graph drawing tools available. In a few well-known types of substation configurations, which is [4], an X window based visualization tool for automatic not applicable in general networks. generation of high-quality drawings of directed graphs has In this paper, a method, which uses Self-Organizing Map been introduced. AT&T Bell Laboratory [5] and University (SOM) neural network [12] to generate the graphical of Saarlandes [6] also have automated graph drawing tools. representation of the network data files, will be proposed. The Automated routing plays a important role in VLSI layout [7]. basic idea behind the method is to let the network span itself Due to the hierarchical relationships existing in the directed according to a given shape of the network grid. The paper is graphs, they are not very suitable for power system network organized as follows: Automatic graph drawing is briefly visualization, where all the nodes are at the same level. introduced at first, followed by the introduction of SOM and As a contrast, fewer studies were done about automated the proposed method. Also an example of using this approach graph drawing in the power system realm. The users may in creating the network diagrams from IEEE 30-bus system is given. At last, the selection of training parameters, data grid “shape”, data presentation sequence and stop criteria has been discussed. II. AUTOMATIC GRAPH DRAWING A graph can be defined by G(V,E), where V is a set of vertices (or nodes) and E a set of edges (or connections). The central problem of Automated Graph Drawing is to create a drawing which looks as pleasing as possible from a given set of nodes and their connections. Some commonly used aesthetic criteria are: minimum crossing, minimum bends, maximum of symmetries, optimal usage of layout area, etc. the map. The commonly used two-dimensional topologies are [1]. grid and hex. Every neuron in a map receives the same input k n n Graphs with edges of directions are called digraphs. x ∈ R and has an n-dimensional weight vector wi ∈ R Several automatic graph-drawing algorithms have been associated with it. The competitive learning rule to update the proposed for digraphs [2][3]. For general undirected graphs, weight is: the most commonly used method is the spring embedder k algorithm, which may show poor performance for graphs ∆w = ρφ(ri,ri*)(x – wi)foralli=1,2,…s containing dense subgraphs [1]. * ρ There are usually two steps to create a drawing from a where i is the index of the winner unit, is the learning rate, φ given set of data. First, the nodes must be arranged at their and (ri,ri*) is the neighborhood function. optimal positions. Second, the connections among those Applying all the training data once to the map is called one nodes should be routed in an aesthetic manner to improve the epoch. After the training, the weights of the neurons will be visibility. updated to resemble the input data and similar neurons will be It is possible to arrange the nodes to avoid line crossing for grouped into neighborhoods. SOMs are often applied in planar graphs. Also for un-planar graphs, minimum line categorizing the data or visualizing the patterns in the data of crossing can also be used as a criteria to layout the nodes, high dimensions. although the problem is "NP-complete" and certain heuristic Usually, two phases are involved in the training process. In methods must be used to solve the optimization problem. the ordering phase, the neuron weights are expected to order There may be some other requirements on the node positions. themselves in the input space consistent with the associated For example, it may be required to locate the nodes on a grid. neuron positions. Higher learning rate and larger Routing the connections is very application oriented. For neighborhood are used for this phase. During the tuning example, some applications require that the connection lines phase, the weights are expected to spread out relatively are straight. In VLSI applications, orthogonal routing is used evenly over the input space while retaining their topological [7]. order found during the ordering phase. For a big graph, it is often desirable to divide it into to smaller subgraphs and process each part separately. One B. Proposed Graph Drawing Algorithm heuristic method for graph partitioning has been given in [13]. Automatic graph drawing is still an open problem. No The prime task for automatic circuit diagram drawing of a existing method is suitable for all situations. In this paper, a given electric network is to determine the positions of its new algorithm based on Self-Organizing Map, which can be nodes. The connections among nodes define the topology used for automatically creating electric circuit diagram, is structure, which is the most important property of a network. proposed. Unlike control systems, circuit diagrams are If we use neurons to represent the network nodes and connect undirected graphs and the methods given in [2-4] are not the neurons in the same network topology, a SOM will be applicable. formed. The weights of neurons will be the coordinate In this paper, we will focus only on the node layout positions of the nodes. Actually, in this specific application, problem and simply connect the nodes using straight lines neuron weights, node positions and coordinates are only after the positions of the nodes have been obtained. different views of the same thing. Initially, all the neurons in the SOM will have either III. NETWROK DRAWING USING SELF-ORGANIZING random or the same weights (positions). The weights will be MAP updated using the competitive learning rule. If the training points are equally distributed in the drawing area, the network A method based on Self-Organizing Map (SOM) is will expand and adjust its node positions to occupy the whole described in this section. Compared with the existing area. The overall procedure of the algorithms is as follows: automatic graph drawing methods [1-3,10,11], the new method is more adaptive. For a given network, its nodes are Step 1. Read in the network topology Step 2. Form SOM according to the network topology seen as neurons and the whole network forms a SOM. By Step 3. Create training data grid, which specifies the drawing area presenting training data to the SOM, it will automatically Step 4. Train the SOM and obtain the coordinates of all nodes expand to form a circuit diagram. In the following three sections, step 2, 3, and 4 will be discussed A. Self-Organizing Map in detail. Kohonen's Self-Organizing Maps (SOM) are neural C. Network Connection Topology networks consisting of a single layer of neurons (or nodes) [12]. The neurons in a SOM are usually organized into a one In a SOM, topology is used to determine the neighbors of a or two-dimensional structure, which is called the topology of neuron.