Research Group Thomas Seidl

Allocation tasks represent a class of problems where a limited amount of resources must be allocated to a set of entities at each time step. Prominent examples of this task include portfolio optimization or distributing computational workloads across servers. Allocation tasks are typically bound by linear constraints describing practical requirements that have to be strictly fulfilled at all times. In portfolio optimization, for example, investors may be obligated to allocate less than 30% of the funds into a certain industrial sector in any investment period. Such constraints restrict the action space of allowed allocations in intricate ways, which makes learning a policy that avoids constraint violations difficult. In this paper, we propose a new method for constrained allocation tasks based on an autoregressive process to sequentially sample allocations for each entity. In addition, we introduce a novel de-biasing mechanism to counter the initial bias caused by sequential sampling. We demonstrate the superior performance of our approach compared to a variety of Constrained Reinforcement Learning (CRL) methods on three distinct constrained allocation tasks: portfolio optimization, computational workload distribution, and a synthetic allocation benchmark.

Reliable process information, especially regarding trace du- rations, is crucial for smooth execution. Without it, maintaining a process becomes costly. While many predictive systems aim to identify inefficien- cies, they often focus on individual process instances, missing the global perspective. It is essential not only to detect where delays occur but also to pinpoint specific activity transitions causing them. To address this, we propose CC-HIT (Creating Counterfactuals from High-Impact Transitions), which identifies temporal dependencies across the entire process. By focusing on activity transitions, we provide deeper insights into relational impacts, enabling faster resolution of inefficiencies. CC- HIT highlights the most influential transitions on process performance, offering actionable insights for optimization. We validate this method using the BPIC 2020 dataset, demonstrating its effectiveness compared to existing approaches.

Recommender Systems are a popular and common means to extract relevant information for users. Small and medium-sized enterprises make up a large share of the overall amount of business but need to be more frequently considered regarding the demand for recommender systems. Different conditions, such as the small amount of data, lower computational capabilities, and users frequently not possessing an account, require a different and potentially a more small-scale recommender system. The requirements regarding quality are similar: High accuracy and high diversity are certainly an advantage. We provide multiple solutions with different variants solely based on information contained in event-based sequences and temporal information. Our code is available at GitHub. We conduct experiments on four different datasets with an increasing set of items to show a possible range for scalability. The promising results show the applicability of these grammar-based recommender system variants and leave the final decision on which recommender to choose to the user and its ultimate goals.

Financial portfolio managers typically face multi-period optimization tasks such as short-selling or investing at least a particular portion of the portfolio in a specific industry sector. A common approach to tackle these problems is to use constrained Markov decision process (CMDP) methods, which may suffer from sample inefficiency, hyperparameter tuning, and lack of guarantees for constraint violations. In this paper, we propose Action Space Decomposition Based Optimization (ADBO) for optimizing a more straightforward surrogate task that allows actions to be mapped back to the original task. We examine our method on two real-world data portfolio construction tasks. The results show that our new approach consistently outperforms state-of-the-art benchmark approaches for general CMDPs.

Selecting diverse instances for annotation is one of the key factors of successful active learning strategies. To this end, existing methods often operate on high-dimensional latent representations. In this work, we propose to use the low-dimensional vector of predicted probabilities instead, which can be seamlessly integrated into existing methods. We empirically demonstrate that this considerably decreases the query time, i.e., time to select an instance for annotation, while at the same time improving results. Low query times are relevant for active learning researchers, which use a (fast) oracle for simulated annotation and thus are often constrained by query time. It is also practically relevant when dealing with complex annotation tasks for which only a small pool of skilled domain experts is available for annotation with a limited time budget.

When researchers publish new cluster algorithms, they usually demonstrate the strengths of their novel approaches by comparing the algorithms’ performance with existing competitors. However, such studies are likely to be optimistically biased towards the new algorithms, as the authors have a vested interest in presenting their method as favorably as possible in order to increase their chances of getting published. Therefore, the superior performance of newly introduced cluster algorithms is over-optimistic and might not be confirmed in independent benchmark studies performed by neutral and unbiased authors. This problem is known among many researchers, but so far, the different mechanisms leading to over-optimism in cluster algorithm evaluation have never been systematically studied and discussed. Researchers are thus often not aware of the full extent of the problem. We present an illustrative study to illuminate the mechanisms by which authors—consciously or unconsciously—paint their cluster algorithm’s performance in an over-optimistic light. Using the recently published cluster algorithm Rock as an example, we demonstrate how optimization of the used datasets or data characteristics, of the algorithm’s parameters and of the choice of the competing cluster algorithms leads to Rock’s performance appearing better than it actually is. Our study is thus a cautionary tale that illustrates how easy it can be for researchers to claim apparent 'superiority' of a new cluster algorithm. This illuminates the vital importance of strategies for avoiding the problems of over-optimism (such as, e.g., neutral benchmark studies), which we also discuss in the article.

LUCKe allows any purely distance-based 'classic' clustering algorithm to reliably find linear correlation clusters. An elaborated distance matrix based on the points’ local PCA extracts all necessary information from high dimensional data to declare points of the same arbitrary dimensional linear correlation cluster as 'similar'. For that, the points’ eigensystems as well as only the relevant information about their position in space, are put together. LUCKe allows transferring known benefits from the large field of basic clustering to correlation clustering. Its applicability is shown in extensive experiments with simple representatives of diverse basic clustering approaches.

High-quality arguments are an essential part of decision-making. Automatically predicting the quality of an argument is a complex task that recently got much attention in argument mining. However, the annotation effort for this task is exceptionally high. Therefore, we test uncertainty-based active learning (AL) methods on two popular argument-strength data sets to estimate whether sample-efficient learning can be enabled. Our extensive empirical evaluation shows that uncertainty-based acquisition functions can not surpass the accuracy reached with the random acquisition on these data sets.

During different steps in the process of discovering drug candidates for diseases, it can be supportive to identify groups of molecules that share similar properties, i.e. common overall structural similarity. The existing methods for computing (dis)similarities between chemical structures rely on a priori domain knowledge. Here we investigate the clustering of compounds that are applied on embeddings generated from a recently published Mol2Vec technique which enables an entirely unsupervised vector representation of compounds. A research question we address in this work is: do existent well-known clustering algorithms such as k-means or hierarchical clustering methods yield meaningful clusters on the Mol2Vec embeddings? Further, we investigate how far subspace clustering can be utilized to compress the data by reducing the dimensionality of the compounds vector representation. Our first conducted experiments on a set of COVID-19 drug candidates reveal that well-established methods yield meaningful clusters. Preliminary results from subspace clusterings indicate that a compression of the vector representations seems viable.

Even though most clustering algorithms serve knowledge discovery in fields other than computer science, most of them still require users to be familiar with programming or data mining to some extent. As that often prevents efficient research, we developed an easy to use, highly explainable clustering method accompanied by an interactive tool for clustering. It is based on intuitively understandable kNN graphs and the subsequent application of adaptable filters, which can be combined ensemble-like and iteratively and prune unnecessary or misleading edges. For a first overview of the data, fully automatic predefined filter cascades deliver robust results. A selection of simple filters and combination methods that can be chosen interactively yield very good results on benchmark datasets compared to various algorithms.

We introduce AnyCORE (Anytime Cluster Outlier REmoval), an algorithm that enables users to detect and remove outliers at anytime. The algorithm is based on the idea of MORe++, an approach for outlier detection and removal that iteratively scores and removes 1d-cluster-outliers in n-dimensional data sets. In contrast to MORe++, AnyCORE provides continuous responses for its users and converges independent of cluster centers. This allows AnyCORE to perform outlier detection in combination with an arbitrary clustering method that is most suitable for a given data set. We conducted our AnyCORE experiments on synthetic and real-world data sets by benchmarking its variant with k-Means as the underlying clustering method versus the traditional batch algorithm version of MORe++. In extensive experiments we show that AnyCORE is able to compete with the related batch algorithm version.

In this work, we focus on the problem of retrieving relevant arguments for a query claim covering diverse aspects. State-of-the-art methods rely on explicit mappings between claims and premises, and thus are unable to utilize large available collections of premises without laborious and costly manual annotation. Their diversity approach relies on removing duplicates via clustering which does not directly ensure that the selected premises cover all aspects. This work introduces a new multi-step approach for the argument retrieval problem. Rather than relying on ground-truth assignments, our approach employs a machine learning model to capture semantic relationships between arguments. Beyond that, it aims to cover diverse facets of the query, instead of trying to identify duplicates explicitly. Our empirical evaluation demonstrates that our approach leads to a significant improvement in the argument retrieval task even though it requires less data.

In high-dimensional datasets some dimensions or attributes can be more important than others. Whereas most algorithms neglect one or more dimensions for all points of a dataset or at least for all points of a certain cluster together, our method KISS (textbf{k}NN-based textbf{I}mportance textbf{S}core of textbf{S}ubspaces) detects the most important dimensions for each point individually. It is fully unsupervised and does not depend on distorted multidimensional distance measures. Instead, the $k$ nearest neighbors ($k$NN) in one-dimensional projections of the data points are used to calculate the score for every dimension's importance. Experiments across a variety of settings show that those scores reflect well the structure of the data. KISS can be used for subspace clustering. What sets it apart from other methods for this task is its runtime, which is linear in the number of dimensions and $O(n log(n))$ in the number of points, as opposed to quadratic or even exponential runtimes for previous algorithms.

Peer reviewing is a central process in modern research and essential for ensuring high quality and reliability of published work. At the same time, it is a time-consuming process and increasing interest in emerging fields often results in a high review workload, especially for senior researchers in this area. How to cope with this problem is an open question and it is vividly discussed across all major conferences. In this work, we propose an Argument Mining based approach for the assistance of editors, meta-reviewers, and reviewers. We demonstrate that the decision process in the field of scientific publications is driven by arguments and automatic argument identification is helpful in various use-cases. One of our findings is that arguments used in the peer-review process differ from arguments in other domains making the transfer of pre-trained models difficult. Therefore, we provide the community with a new peer-review dataset from different computer science conferences with annotated arguments. In our extensive empirical evaluation, we show that Argument Mining can be used to efficiently extract the most relevant parts from reviews, which are paramount for the publication decision. The process remains interpretable since the extracted arguments can be highlighted in a review without detaching them from their context.

Subspace clustering has established itself as a state-of-the-art approach to clustering high-dimensional data. In particular, methods relying on the self-expressiveness property have recently proved especially successful. However, they suffer from two major shortcomings: First, a quadratic-size coefficient matrix is learned directly, preventing these methods from scaling beyond small datasets. Secondly, the trained models are transductive and thus cannot be used to cluster out-of-sample data unseen during training. Instead of learning self-expression coefficients directly, we propose a novel metric learning approach to learn instead a subspace affinity function using a siamese neural network architecture. Consequently, our model benefits from a constant number of parameters and a constant-size memory footprint, allowing it to scale to considerably larger datasets. In addition, we can formally show that out model is still able to exactly recover subspace clusters given an independence assumption. The siamese architecture in combination with a novel geometric classifier further makes our model inductive, allowing it to cluster out-of-sample data. Additionally, non-linear clusters can be detected by simply adding an auto-encoder module to the architecture. The whole model can then be trained end-to-end in a self-supervised manner. This work in progress reports promising preliminary results on the MNIST dataset. In the spirit of reproducible research, me make all code publicly available. In future work we plan to investigate several extensions of our model and to expand experimental evaluation.

In this work we propose SRE, the first internal evaluation measure for arbitrary oriented subspace clustering results. For this purpose we present a new perspective on the subspace clustering task: the goal we formalize is to compute a clustering which represents the original dataset by minimizing the reconstruction loss from the obtained subspaces, while at the same time minimizing the dimensionality as well as the number of clusters. A fundamental feature of our approach is that it is model-agnostic, i.e., it is independent of the characteristics of any specific subspace clustering method. It is scale invariant and mathematically founded. The experiments show that the SRE scoring better assesses the quality of an arbitrarily oriented sub-space clustering compared to commonly used external evaluation measures.

In the setting of unsupervised machine learning, especially in clustering tasks, the evaluation of either novel algorithms or the assessment of a clustering of novel data is challenging. While mostly in the literature the evaluation of new methods is performed on labelled data, there are cases where no labels are at our disposal. In other cases we may not want to trust the “ground truth” labels. In general there exists a spectrum of so called internal evaluation measures in the literature. Each of the measures is mostly specialized towards a specific clustering model. The model of arbitrarily oriented subspace clusters is a more recent one. To the best of our knowledge there exist at the current time no internal evaluation measures tailored at assessing this particular type of clusterings. In this work we present the first internal quality measures for arbitrarily oriented subspace clusterings namely the normalized projected energy (NPE) and subspace compactness score (SCS). The results from the experiments show that especially NPE is capable of assessing clusterings by considering archetypical properties of arbitrarily oriented subspace clustering.

Having data with a high number of features raises the need to detect clusters which exhibit within subspaces of features a high similarity. These subspaces can be arbitrarily oriented which gave rise to arbitrarily-oriented subspace clustering (AOSC) algorithms. In the diversity of such algorithms some are specialized at detecting clusters which are global, across the entire dataset regardless of any distances, while others are tailored at detecting local clusters. Both of these views (local and global) are obtained separately by each of the algorithms. While from an algebraic point of view, none of both representations can claim to be the true one, it is vital that domain scientists are presented both views, enabling them to inspect and decide which of the representations is closest to the domain specific reality. We propose in this work a framework which is capable to detect locally dense arbitrarily oriented subspace clusters which are embedded within a global one. We also first introduce definitions of locally and globally arbitrarily oriented subspace clusters. Our experiments illustrate that this approach has no significant impact on the cluster quality nor on the runtime performance, and enables scientists to be no longer limited exclusively to either of the local or global views.

Data Mining and Process Mining -- is one just a variant of the other, or do worlds separate the two areas from each other? The notions sound so similar but the contents sometimes look differently, so respective researchers may get confused in their mutual perception, be it authors or reviewers. The talk recalls commonalities like model-based supervised and unsupervised learning approaches, and it also sheds light to peculiarities in process data and process mining tasks as seen from a data mining perspective. When considering trace data from event log files as time series, as sequences, or as activity sets, quite different data mining techniques apply and may be extended and improved. A particular example is rare pattern mining, which fills a gap between frequent patterns and outlier detection. The task aims at identifying patterns that occur with low frequency but above single outliers. Structural deficiences may cause malfunctions or other undesired behavior which get discarded as outliers in event logs, since they are observed infrequently only. Rare pattern mining may identify these situations, and recent approaches include clustering or ordering non-conformant traces. The talk concludes with some remarks on how to sell process mining papers to the data mining community, and vice versa, in order to improve mutual acceptance, and to increase synergies in the fields.

Using grid-based clustering algorithms on high-dimensionaldata has the advantage of being able to summarize datapoints into cells, but usually produces an exponential number of grid cells. In this paper we introduce Grace (using textit{Gr}id which is textit{a}daptive for textit{c}lusttextit{e}ring), a clustering algorithm which limits the number of cells produced depending on the number of points in the dataset. A non-equidistant grid is constructed based on the distribution of points in one-dimensional projections of the data. A density threshold is automatically deduced from the data and used to detect dense cells, which are later combined to clusters. The adaptive grid structure makes an efficient but still accurate clustering of multidimensional data possible. Experiments with synthetic as well as real-world data sets of various size and dimensionality confirm these properties.

As data processing techniques get more and more sophisticated every day, many of us researchers often get lost in the details and subtleties of the algorithms we are developing and far too easily seem to forget to look also at the very first steps of every algorithm: the input of the data. Since there are plenty of library functions for this task, we indeed do not have to think about this part of the pipeline anymore. But maybe we should. All data is stored and loaded into a program in some order. In this vision paper we study how ignoring this order can (1) lead to performance issues and (2) make research results unreproducible. We furthermore examine desirable properties of a data ordering and why current approaches are often not suited to tackle the two mentioned problems.

When facing high-dimensional data streams, clustering algorithms quickly reach the boundaries of their usefulness as most of these methods are not designed to deal with the curse of dimensionality. Due to inherent sparsity in high-dimensional data, distances between objects tend to become meaningless since the distances between any two objects measured in the full dimensional space tend to become the same for all pairs of objects. In this work, we present a novel oriented subspace clustering algorithm that is able to deal with such issues and detects arbitrarily oriented subspace clusters in high-dimensional data streams. Data streams generally implicate the challenge that the data cannot be stored entirely and hence there is a general demand for suitable data handling strategies for clustering algorithms such that the data can be processed within a single scan. We therefore propose the CASHSTREAM algorithm that unites state-of-the-art stream processing techniques and additionally relies on the Hough transform to detect arbitrarily oriented subspace clusters. Our experiments compare CASHSTREAM to its static counterpart and show that the amount of consumed memory is significantly decreased while there is no loss in terms of runtime.

In this work, we focus on the problem of entity alignment in Knowledge Graphs (KG) and we report on our experiences when applying a Graph Convolutional Network (GCN) based model for this task. Variants of GCN are used in multiple state-of-the-art approaches and therefore it is important to understand the specifics and limitations of GCN-based models. Despite serious efforts, we were not able to fully reproduce the results from the original paper and after a thorough audit of the code provided by authors, we concluded, that their implementation is different from the architecture described in the paper. In addition, several tricks are required to make the model work and some of them are not very intuitive.We provide an extensive ablation study to quantify the effects these tricks and changes of architecture have on final performance. Furthermore, we examine current evaluation approaches and systematize available benchmark datasets.We believe that people interested in KG matching might profit from our work, as well as novices entering the field.

MORe++ is a k-Means based Outlier Removal method working on high dimensional data. It is simple, efficient and scalable. The core idea is to find local outliers by examining the points of different k-Means clusters separately. Like that, one-dimensional projections of the data become meaningful and allow to find one-dimensional outliers easily, which else would be hidden by points of other clusters. MORe++ does not need any additional input parameters than the number of clusters k used for k-Means, and delivers an intuitively accessible degree of outlierness. In extensive experiments it performed well compared to k-Means-- and ORC.

Principal Component Analysis (PCA) is a popular method for linear dimensionality reduction. It is often used to discover hidden correlations or to facilitate the interpretation and visualization of data. However, it is liable to suffer from outliers. Strong outliers can skew the principal components and as a consequence lead to a higher reconstruction loss. While there exist several sophisticated approaches to make the PCA more robust, we present an approach which is intriguingly simple: we replace the covariance matrix by a so-called coMAD matrix. The first experiments show that PCA based on the coMAD matrix is more robust towards outliers.

We introduce a generator for data containing subspace clus- ters which is accurately tunable and adjustable to the needs of developers. It is online available and allows to give a plethora of characteristics the data should contain, while it is simultaneously able to generate mean- ingful data containing subspace clusters with a minimum of input data.

When it comes to the task of dimensionality reduction, the Principal Component Analysis (PCA) is among the most well known methods. Despite its popularity, PCA is prone to outliers which can be traced back to the fact that this method relies on a covariance matrix. Even with the variety of sophisticated methods to enhance the robust- ness of the PCA, we provide here in this work-in-progress an approach which is intriguingly simple: the covariance matrix is replaced by a so- called comode matrix. Through this minor modification the experiments show that the reconstruction loss is significantly reduced. In this work we introduce the comode and its relation to the MeanShift algorithm, including its bandwidth parameter, compare it in an experiment against the classic covariance matrix and evaluate the impact of the bandwidth hyperparameter on the reconstruction error.

Chains connecting two or more different clusters are a well known problem of clustering algorithms like DBSCAN or Single Linkage Clustering. Since already a small number of points resulting from, e.g., noise can form such a chain and build a bridge between different clusters, it can happen that the results of the clustering algorithm are distorted: several disparate clusters get merged into one. This single-link effect is rather known but to the best of our knowledge there are no satisfying solutions which extract those chains, yet. We present a new algorithm detecting not only straight chains between clusters, but also bent and noisy ones. Users are able to choose between eliminating one dimensional and higher dimensional chains connecting clusters to receive the underlying cluster structure. Also, the desired straightness can be set by the user. As this paper is an extension of 'Chain-detection for DBSCAN', we apply our technique not only in combination with DBSCAN but also with single link hierarchical clustering. On a real world dataset containing traffic accidents in Great Britain we were able to detect chains emerging from streets between cities and villages, which led to clusters composed of diverse villages. Additionally, we analyzed the robustness regarding the variance of chains in synthetic experiments.

As machine learning becomes a more and more important area in Data Science, bringing with it a rise of abstractness and complexity, the desire for explainability rises, too. With our work we aim to gain explainability focussing on correlation clustering and try to pursue the original goals of different Data Science tasks,: Extracting knowledge from data. As well-known tools like Fold-It or GeoTime show, gamification is a very mighty approach, but not only to solve tasks which prove more difficult for machines than for humans. We could also gain knowledge from how players proceed trying to solve those difficult tasks. That is why we developed Straighten it up!, a game in which users try to find the best linear correlations in high dimensional datasets. Finding arbitrarily oriented subspaces in high dimensional data is an exponentially complex task due to the number of potential subspaces in regards to the number of dimensions. Nevertheless, linearly correlated points are as a simple pattern easy to track by the human eye. Straighten it up! gives users an overview over two-dimensional projections of a self-chosen dataset. Users decide which subspace they want to examine first, and can draw in arbitrarily many lines fitting the data. An offset inside of which points are assigned to the corresponding line can easily be chosen for every line independently, and users can switch between different projections at any time. We developed a scoring system not only as incentive, but first of all for further examination, based on the density of each cluster, its minimum spanning tree, size of offset, and coverage. By tracking every step of a user we are able to detect common mechanisms and examine differences to state-of-the-art correlation and subspace clustering algorithms, resulting in more comprehensibility.

Artificially generated data sets are present in many data mining and machine learning publications in the experimental section. One of the reasons to use synthetic data is, that scientists can express their understanding of a “ground truth”, having labels and thus an expectation of what an algorithm should be able to detect. This permits also a degree of control to create data sets which either emphasize the strengths of a method or reveal its weaknesses and thus potential targets for improvement. In order to develop methods which detect linear correlated clusters, the necessity of generating such artificial clusters is indispensable. This is mostly done by command-line based scripts which may be tedious since they demand from users to ‘visualize’ in their minds how the correlated clusters have to look like and be positioned within the data space. We present in this work RAIL, a generator for Reproducible Artificial Interactive Linear correlated data. With RAIL, users can add multiple planes into a data space and arbitrarily change orientation and position of those planes in an interactive fashion. This is achieved by manipulating the parameters describing each of the planes, giving users immediate feedback in real-time. With this approach scientists no longer need to imagine their data but can interactively explore and design their own artificial data sets containing linear correlated clusters. Another convenient feature in this context is that the data is only generated when the users decide that their design phase is completed. If researchers want to share data, a small file is exchanged containing the parameters which describe the clusters through information such as e.g. their Hessian-Normal-Form or number of points per cluster, instead of sharing several large csv files.

LUCK allows to use any distance-based clustering algorithm to find linear correlated data. For that a novel distance function is introduced, which takes the distribution of the kNN of points into account and corresponds to the probability of two points being part of the same linear correlation. In this work in progress we tested the distance measure with DBSCAN and k-Means comparing it to the well-known linear correlation clustering algorithms ORCLUS, 4C, COPAC, LMCLUS, and CASH, receiving good results for difficult synthetic data sets containing crossing or non-continuous correlations.

As the ordering of data, particularly of graphs, can influence the result of diverse Data Mining tasks performed on it heavily, we introduce the Circle-Index, the first internal quality measurement for orderings of graphs. It is based on a circular arrangement of nodes, but takes in contrast to similar arrangements from the field of, e.g., visual analytics, the edge lengths in this arrangement into account. The minimization of the Circle-Index leads to an arrangement which not only offers a simple way to cluster the data using a constrained texttt{MinCut} in only linear time, but is also visually convincing. We developed the clustering algorithm CirClu which implements this minimization and texttt{MinCut}, and compared it with several established clustering algorithms achieving very good results. Simultaneously we compared the Circle-Index with several internal quality measures for clusterings. We observed a strong coherence between the Circle-Index and the matching of achieved clusterings to the respective ground truths in diverse real world datasets.

Periodicities are omnipresent: In nature in the cycles of predator and prey populations, reoccurring patterns regarding our power consumption over the days, or the presence of flu diseases over the year. With regards to the importance of periodicities we ask: Is there a way to detect periodic correlated clusters which are hidden in event series? We propose as a work in progress a method for detecting sinusoidal periodic correlated clusters on event series which relies on parameter space transformation. Our contributions are: Providing the first non-linear correlation clustering algorithm for detecting periodic correlated clusters. Further our method provides an explicit model giving domain experts information on parameters such as amplitude, frequency, phase-shift and vertical-shift of the detected clusters. Beyond that we approach the issue of determining an adequate frequency and phase-shift of the detected correlations given a frequency and phase-shift boundary.

In publications where a clustering method is described, the chosen hyperparameters are in many cases to our current observation empirically determined. In this work in progress we discuss and propose one approach on how hyperparameters can be systematically explored and their effects regarding the data set analyzed. We further introduce in the context of hyperparameter analysis a modified definition of the resilience term, which refers here to a subset of data points which persists to be in the same cluster over different hyperparameter settings. In order to analyze relations among different hyperparameters we further introduce the concept of dynamic intersection computing.

In this work we present Rock, a method where the points roam to their clusters using k-NN. Rock is a draft for an algorithm which is capable of detecting non-convex clusters of arbitrary dimension while delivering representatives for each cluster similar to, e.g., Mean Shift or k-Means. Applying Rock, points roam to the mean of their k-NN while k increments in every step. Like that, rather outlying points and noise move to their nearest cluster while the clusters themselves contract first to their skeletons and further to a representative point each. Our empirical results on synthetic and real data demonstrate that Rock is able to detect clusters on datasets where either mode seeking or density-based approaches do not succeed.

In different research domains conducted experiments aim for the detection of (hyper)linear correlations among multiple features within a given data set. For this purpose methods exist where one among them is highly robust against noise and detects linear correlated clusters regardless of any locality assumption. This method is based on parameter space transformation. The cur- rently available parameter transform based algorithms detect the clusters scanning explicitly for intersections of functions in pa- rameter space. This approach comes with drawbacks. It is difficult to analyze aspects going beyond the sole intersection of func- tions, such as e.g. the area around the intersections and further it is computationally expensive. The work in progress method we provide here overcomes the mentioned drawbacks by sampling d-dimensional tuples in data space, generating a (hyper)plane and representing this plane as a single point in parameter space. By this approach we no longer scan for intersection points of functions in parameter space but for dense regions of such pa- rameter vectors. By this approach in future work well established clustering algorithms can be applied in parameter space to detect e.g. dense regions, modes or hierarchies of linear correlations in parameter space.

In recent years the demand for having algorithms which provide not only their results, but also add explainability up to a certain extent increased. In this paper we envision a class of clustering algorithms where the users can interact not only with the input or output but also intercept within the very clustering process itself, which we coin with the term process-aware clustering. Further we aspire to sketch the challenges emerging with such type of algorithms, such as the need of adequate measures which evaluate the progression through the computation process of a clustering method. Beyond the explainability on how the results are generated, we propose methods tailored at systematically analyzing the hyperparameter space of an algorithm, determining in a more ordered fashion suitable hyperparameters rather then applying a trial-and-error schema.

Clustering algorithms are mostly following the pipeline to provide input data, and hyperparameter values. Then the algorithms are executed and the output files are generated or visualized. We provide in our work an early prototype of an interactive density-based clustering tool named DICE in which the users can change the hyperparameter settings and immediately observe the resulting clusters. Further the users can browse through each of the single detected clusters and get statistics regarding as well as a convex hull profile for each cluster. Further DICE keeps track of the chosen settings, enabling the user to review which hyperparameter values have been previously chosen. DICE can not only be used in scientific context of analyzing data, but also in didactic settings in which students can learn in an exploratory fashion how a density-based clustering algorithm like e.g. DBSCAN behaves.