Pascal Held

Multi-Layer Perceptrons

Having described the structure, the operation and the training of (artificial) neural networks in a general fashion in the preceding chapter, we turn in this and the subsequent chapters to specific forms of (artificial) neural networks. We start with the best-known and most widely used form, the so-called multi-layer perceptron (MLP), which is closely related to the networks of threshold logic units we studied in a previous chapter. They exhibit a strictly layered structure and may employ other activation functions than a step at a crisp threshold.

On Merging and Dividing Social Graphs

Abstract Modeling social interaction can be based on graphs. However most models lack the flexibility of including larger changes over time. The Barabási-Albert-model is a generative model which already offers mechanisms for adding nodes. We will extent this by presenting four methods for merging and five for dividing graphs based on the Barabási- Albert-model. Our algorithms were motivated by different real world scenarios and focus on preserving graph properties derived from these scenarios. With little alterations in the parameter estimation those algorithms can be used for other graph models as well. All algorithms were tested in multiple experiments using graphs based on the Barabási- Albert-model, an extended version of the Barabási-Albert-model by Holme and Kim, the Watts-Strogatz-model and the Erdős-Rényi-model. Furthermore we concluded that our algorithms are able to preserve different properties of graphs independently from the used model. To support the choice of algorithm, we created a guideline which highlights advantages and disadvantages of discussed methods and their possible use-cases.

Analysis and Visualization of Dynamic Clusterings

Clusterings in dynamic networks are also dynamic. This means that they change over time. In this paper we present a visualization to show these changing behavior. For this purpose we used and modified the MONIC framework to track the clusters over time. Possible transactions during the lifetime of a cluster are birth, death, growth, contraction, splitting, and merging. We extend this list by rebirth, for clusters which were reactivated after death. In our evolution diagram we used lines to represent the lifetime of a cluster. Splitting and merging clusters have connecting lines. For the line adjustment we used a bandwidth reduction on connected components.

The Extension Principle

We have already discussed how set theoretic operations like intersection, union and complement can be generalized to fuzzy sets. This chapter is devoted to the issue of extending the concept of mappings or functions to fuzzy sets. These ideas allow us to define operations like addition, subtraction, multiplication, division or taking squares as well as set theoretic concepts like the composition of relations for fuzzy sets.

Advanced Analysis of Dynamic Graphs in Social and Neural Networks

Dynamic graphs are ubiquitous in real world applications. They can be found, e.g. in biology, neuroscience, computer science, medicine, social networks, the World Wide Web. There is a great necessity and interest in analyzing these dynamic graphs efficiently. Typically, analysis methods from classical data mining and network theory have been studied separately in different fields of research. Dealing with complex networks in real world applications, there is a need to perform interdisciplinary research by combining techniques of different fields. In this paper, we analyze dynamic graphs from two different applications, i.e. social science and neuroscience. We exploit the edge weights in both types of networks to answer distinct questions in the respective fields of science. First, for the representation of edge weights in a social network graph we propose a method to efficiently represent the strength of a relation between two entities based on events involving both entities. Second, we correlate graph measures of electroencephalographic activity networks with clinical variables to find good predictors for patients with visual field damages.

Generating Events for Dynamic Social Network Simulations

Social Network Analysis in the last decade has gained remarkable attention. The current analysis focuses more and more on the dynamic behavior of them. The underlying structure from Social Networks, like facebook, or twitter, can change over time. Groups can be merged or single nodes can move from one group to another. But these phenomenas do not only occur in social networks but also in human brains. The research in neural spike trains also focuses on finding functional communities. These communities can change over time by switching the stimuli presented to the subject. In this paper we introduce a data generator to create such dynamic behavior, with effects in the interactions between nodes. We generate time stamps for events for one-to-one, one-to-many, and many-to-all relations. This data could be used to demonstrate the functionality of algorithms on such data, e.g. clustering or visualization algorithms. We demonstrated that the generated data fulfills common properties of social networks.

Online Fuzzy Community Detection by Using Nearest Hubs

Community and cluster detection is a popular field of social network analysis. Most algorithms focus on static graphs or series of snapshots.

Detecting overlapping community hierarchies in dynamic graphs

Community and cluster detection is a popular field of social network analysis. Most algorithms focus on static graphs or series of snapshots. In this paper we present an hierarchical algorithm, which detects communities in dynamic graphs. The method is based on the shortest paths to high-connected nodes, so called hubs. Due to local message passing, we can update the clustering results with low computational effort. The used hierarchy allows to process the community detection without setting any parameters before. After processing it provides different cluster levels based on the selected threshold. The presented algorithm is compared with the Louvain method on large-scale real-world datasets with given community structure. The detected community structure is compared to the given with NMI scores. The advantage of the algorithm is the good performance in dynamic scenarios.

Clustering on Dynamic Social Network Data

This paper presents a reference data set along with a labeling for graph clustering algorithms, especially for those handling dynamic graph data. We implemented a modification of Iterative Conductance Cutting and a spectral clustering. As base data set we used a filtered part of the Enron corpus. Different cluster measurements, as intra-cluster density, inter-cluster sparseness, and Q-Modularity were calculated on the results of the clustering to be able to compare results from other algorithms.

Learning Graphical Models

In this chapter we will address how graphical models can be learned from given data. So far we were given the graphical structure. Now, we will introduce heuristics that allow us to induce these structures.