Alexander Dockhorn

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.

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.

An Alternating Optimization Approach Based on Hierarchical Adaptations of DBSCAN

DBSCAN is one of the most common density-based clustering algorithms. While multiple works tried to present an appropriate estimate for needed parameters we propose an alternating optimization algorithm, which finds a locally optimal parameter combination. The algorithm is based on the combination of two hierarchical versions of DBSCAN, which can be generated by fixing one parameter and iterating through possible values of the second parameter. Due to monotonicity of the neighborhood sets and the core-condition, successive levels of the hierarchy can efficiently be computed. An local optimal parameter combination can be determined using internal cluster validation measures. In this work we are comparing the measures edge-correlation and silhouette coefficient. For the latter we propose a density-based interpretation and show a respective computational efficient estimate to detect non-convex clusters produced by DBSCAN. Our results show, that the algorithm can automatically detect a good DBSCAN clustering on a variety of cluster scenarios.

On merging and dividing of Barabási-Albert-graphs

The Barabási-Albert-model is commonly used to generate scale-free graphs, like social networks. To generate dynamics in these networks, methods for altering such graphs are needed. Growing and shrinking is done simply by doing further generation iterations or undo them. In our paper we present four methods to merge two graphs based on the Barabási-Albert-model, and five strategies to reverse them. First we compared these algorithms by edge preservation, which describes the ratio of the inner structure kept after altering. To check if hubs in the initial graphs are hubs in the resulting graphs as well, we used the node-degree rank correlation. Finally we tested how well the node-degree distribution follows the power-law function from the Barabási-Albert-model.

Predicting Opponent Moves for Improving Hearthstone AI

Games pose many interesting questions for the development of artificial intelligence agents. Especially popular are methods that guide the decision-making process of an autonomous agent, which is tasked to play a certain game. In previous studies, the heuristic search method Monte Carlo Tree Search (MCTS) was successfully applied to a wide range of games. Results showed that this method can often reach playing capabilities on par with humans or even better. However, the characteristics of collectible card games such as the online game Hearthstone make it infeasible to apply MCTS directly. Uncertainty in the opponent’s hand cards, the card draw, and random card effects considerably restrict the simulation depth of MCTS. We show that knowledge gathered from a database of human replays help to overcome this problem by predicting multiple card distributions. Those predictions can be used to increase the simulation depth of MCTS. For this purpose, we calculate bigram-rates of frequently co-occurring cards to predict multiple sets of hand cards for our opponent. Those predictions can be used to create an ensemble of MCTS agents, which work under the assumption of differing card distributions and perform simulations according to their assigned distribution. The proposed ensemble approach outperforms other agents on the game Hearthstone, including various types of MCTS. Our case study shows that uncertainty can be handled effectively using predictions of sufficient accuracy, ultimately, improving the MCTS guided decision-making process. The resulting decision-making based on such an MCTS ensemble proved to be less prone to errors by uncertainty and opens up a new class of MCTS algorithms.

Combining cooperative and adversarial coevolution in the context of pac-man

In this paper we discuss our recent approach for evolving a diverse set of agents for both the Pac-Man and the Ghost Team track of the current Ms. Pac-Man vs. Ghost Team competition. We used genetic programming for generating various agents, which were distributed in multiple populations. The optimization includes cooperative and adversarial subtasks, such that Pac-Man is constantly competing against the Ghost Team, whereas the Ghost Team is formed of four cooperatively evolving populations. For the generation of a Ghost Team and calculation of the associated fitness we took one individual from each population. This strict separation preserves the evolution pressure for each population such that respective Ghost Teams compete against each other in developing an efficient cooperation in catching Pac-Man. This approach not only is useful for developing a versatile set of playing agents, but also for adapting the team to the current behavior of the competing populations. Ultimately, we aim for optimizing both tasks in parallel.

Variable density based clustering

The class of density-based clustering algorithms excels in detecting clusters of arbitrary shape. DBSCAN, the most common representative, has been demonstrated to be useful in a lot of applications. Still the algorithm suffers from two drawbacks, namely a non-trivial parameter estimation for a given dataset and the limitation to data sets with constant cluster density. The first was already addressed in our previous work, where we presented two hierarchical implementations of DBSCAN. In combination with a simple optimization procedure, those proofed to be useful in detecting appropriate parameter estimates based on an objective function. However, our algorithm was not capable of producing clusters of differing density. In this work we will use the hierarchical information to extract variable density clusters and nested cluster structures. Our evaluation shows that the clustering approach based on edge-lengths of the dendrogram or based on area estimates successfully detects clusters of arbitrary shape and density.

Clustering Social Networks Using Competing Ant Hives

Methods for clustering static graphs cannot always be transferred straight forward to dynamic scenarios. A typical approach is to reduce the number of updates by reusing results of previous iterations. But are there natural ways to implement dynamic graph clustering? This paper proposes a method, which was derived by graph based ant colony algorithms. Similar to other clustering algorithms, multiple ant colonies are competing for the available nodes. Each hive creates ants, which will explore nearby graph structures and drop hive-specific pheromones on visited nodes. Over time, hives will collect nodes and will be relocated to the center of all collected nodes. In case of dynamic graph clustering, pheromone values can be reused in consecutive iterations. Our evaluation revealed that the proposed algorithm can lead to results on a par with the k-median algorithm and performs worse than Louvain clustering. However competing ant hives have the advantage of implicit noise detection, which comes at the cost of longer computation times. This can make it a suitable choice for certain clustering tasks.