Christian Braune

Introduction to Neural Networks

(Artificial) neural networks are information processing systems, whose structure and operation principles are inspired by the nervous system and the brain of animals and humans. They consist of a large number of fairly simple units, the so-called neurons, which are working in parallel. These neurons communicate by sending information in the form of activation signals, along directed connections, to each other.

New algorithms for finding approximate frequent item sets

In standard frequent item set mining a transaction supports an item set only if all items in the set are present. However, in many cases this is too strict a requirement that can render it impossible to find certain relevant groups of items. By relaxing the support definition, allowing for some items of a given set to be missing from a transaction, this drawback can be amended. The resulting item sets have been called approximate, fault-tolerant or fuzzy item sets. In this paper we present two new algorithms to find such item sets: the first is an extension of item set mining based on cover similarities and computes and evaluates the subset size occurrence distribution with a scheme that is related to the Eclat algorithm. The second employs a clustering-like approach, in which the distances are derived from the item covers with distance measures for sets or binary vectors and which is initialized with a one-dimensional Sammon projection of the distance matrix. We demonstrate the benefits of our algorithms by applying them to a concept detection task on the 2008/2009 Wikipedia Selection for schools and to the neurobiological task of detecting neuron ensembles in (simulated) parallel spike trains.

Density Based Clustering: Alternatives to DBSCAN

Clustering data has been an important task in data analysis for years as it is now. The de facto standard algorithm for density-based clustering today is DBSCAN. The main drawback of this algorithm is the need to tune its two parameters e and minPts. In this paper we explore the possibilities and limits of two novel different clustering algorithms. Both require just one DBSCAN-like parameter. Still they perform well on benchmark data sets. Our first approach just uses a parameter similar to DBSCAN’s minPts parameter that is used to incrementally find protoclusters which are eventually merged while discarding those that are too sparse. Our second approach only uses a local density without any minimum number of points to be specified. It estimates clusters by seeing them from spectators watching the data points at different angles. Both algorithms lead to results comparable to DBSCAN. Our first approach yields similar results to DBSCAN while being able to assign multiple cluster labels to a points while the second approach works significantly faster than DBSCAN.

Behavioral Clustering for Point Processes

Groups of parallel point processes may be analyzed with a variety of different goals. Here we consider the case in which one has a special interest in finding subgroups of processes showing a behavior that differs significantly from the other processes. In particular, we are interested in finding subgroups that exhibit an increased synchrony. Finding such groups of processes poses a difficult problem as its naive solution requires enumerating the power set of all processes involved, which is a costly procedure. In this paper we propose a method that allows us to efficiently filter the process set for candidate subgroups. We pay special attention to the possibilities of temporal imprecision, meaning that the synchrony is not exact, and selective participation, meaning that only a subset of the related processes participates in each synchronous event.

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.

Assembly detection in continuous neural spike train data

Since Hebbs work on the organization of the brain [16] finding cell assemblies in neural spike trains has become a vivid field of research. As modern multi-electrode techniques allow to record the electrical potentials of many neurons in parallel, there is an increasing need for efficient and reliable algorithms to identify assemblies as expressed by synchronous spiking activity. We present a method that is able to cope with two core challenges of this complex task: temporal imprecision (spikes are not perfectly aligned across the spike trains) and selective participation (neurons in an ensemble do not all contribute a spike to all synchronous spiking events). Our approach is based on modeling spikes by influence regions of a user-specified width around the exact spike times and a clustering-like grouping of similar spike trains.

Finding ensembles of neurons in spike trains by non-linear mapping and statistical testing

Finding ensembles in neural spike trains has been a vital task in neurobiology ever since D.O. Hebbs work on synaptic plasticity [15]. However, with recent advancements in multi-electrode technology, which provides means to record 100 and more spike trains simultaneously, classical ensemble detection methods became infeasible due to a combinatorial explosion and a lack of reliable statistics. To overcome this problem we developed an approach that reorders the spike trains (neurons) based on pairwise distances and Sammons mapping to one dimension. Thus, potential ensemble neurons are placed close to each other. As a consequence we can reduce the number of statistical tests considerably over enumeration-based approaches (like e.g. [1]), since linear traversals of the neurons suffice, and thus can achieve much lower rates of falsepositives. This approach is superior to classical frequent item set mining algorithms, especially if the data itself is imperfect, e.g. if only a fraction of the items in a considered set is part of a transaction.

Obtaining Shape Descriptors from a Concave Hull-Based Clustering Algorithm

In data analysis clustering is one of the core processes to find groups in otherwise unstructured data. Determining the number of clusters or finding clusters of arbitrary shape whose convex hulls overlap is in general a hard problem. In this paper we present a method for clustering data points by iteratively shrinking the convex hull of the data set. Subdividing the created hulls leads to shape descriptors of the individual clusters. We tested our algorithm on several data sets and achieved high degrees of accuracy. The cluster definition employed uses a notion of spatial separation. We also compare our algorithm against a similar algorithm that automatically detects the boundaries and the number of clusters. The experiments show that our algorithm yields the better results.

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.

Prototype Construction for Clustering of Point Processes based on Imprecise Synchrony

We consider the task to cluster realizations of point processes, that is, lists of points in time. Our guiding principle is that two such lists are the more similar, the more (approximately) synchronous points they contain. This task occurs in the analysis of parallel spike trains in neurobiology, where it arises from the desire to detect assemblies of neurons, which are characterized by the synchronous spiking activity they exhibit. While earlier approaches along similar lines employed mainly hierarchical agglomerative clustering, based on distance measures for spike trains, we try to make prototype-based clustering approaches (like (fuzzy-)c-means clustering) applicable by proposing a method to construct cluster prototypes. For this we draw on an idea that is inspired by mountain clustering. In addition, we adapt a method that was originally developed for outlier detection in order to actually single out relevant groups of related realizations of point processes in front of a background of noise, and thus to identify neuron assemblies in parallel spike train data.