Understanding how genes are regulated is fundamental to many biological research questions. While experimental and computational methods allow us to identify which genes can interact with each other, finding the polarity of these interactions (whether activation or repression) is a non-trivial problem. We introduce sc-GRIP (Single-cell Gene Regulation Interaction Polarity), a graph convolutional framework that infers the directionality of transcription factor gene interactions directly from single-cell RNA data. By combining gene expression profiles with gene interaction graphs, sc-GRIP learns latent representations of genes and predicts regulatory polarity using a bilinear decoder. Our method enables scalable, cell-type-specific inference without relying on prior species-specific annotations or extensive biological validation. We demonstrate sc-GRIP's effectiveness on curated datasets from human and mouse, and show the advantages over other methods. sc-GRIP particularly excels in the usage on non-model organisms, and we provide a case study on a morphologically simple animal, Suberites domuncula, where sc-GRIP manages to expand our understanding of gene regulations. sc-GRIP offers a novel computational approach for reconstructing biologically interpretable regulatory networks, not only in well-studied organisms but especially in emerging organisms, where large-scale experimental setups are often unfeasible.

Ordered data arises in many areas, e.g., in molec-ular dynamics and other spatial-temporal trajectories. While data points that are close in this order are related, common dimensionality reduction techniques cannot capture this relation or order. Thus, the information is lost in the low-dimensional representations. We introduce DROPP, which incorporates order into dimensionality reduction by adapting a Gaussian kernel function across the ordered covariances between data points. We find underlying principal components that are characteristic of the process that generated the data. In extensive experiments, we show DROPP's advantages over other dimensionality re-duction techniques on synthetic as well as real-world data sets from molecular dynamics and climate research: The principal components of different data sets that were generated by the same underlying mechanism are very similar to each other. They can, thus, be used for dimensionality reduction with low reconstruction errors along a set of data sets, allowing an explainable visual comparison of different data sets as well as good compression even for unseen data.

Detecting arbitrarily shaped clusters in high-dimensional noisy data is challenging for current clustering methods. We introduce SHADE, the first deep clustering algorithm that incorporates density-connectivity into its loss function. Similar to existing deep clustering algorithms, SHADE supports high-dimensional and large data sets with the expressive power of a deep autoencoder. In contrast to most existing deep clustering methods that rely on a centroid-based clustering objective, SHADE incorporates a novel loss function that captures density-connectivity. It thereby learns a representation that enhances the separation of density-connected clusters. SHADE detects a stable clustering and noise points fully automatically without any user input. It outperforms existing methods in clustering quality, especially on data that contain non-Gaussian clusters, such as video data. Moreover, the embedded space of SHADE is suitable for visualization and interpretation of the clustering results as the individual shapes of the clusters are preserved.

Despite the popularity of density-based clustering, its procedural definition makes it difficult to analyze compared to clustering methods that minimize a loss function. In this paper, we reformulate DBSCAN through a clean objective function by introducing the density-connectivity distance (dc-dist), which captures the essence of density-based clusters by endowing the minimax distance with the concept of density. This novel ultrametric allows us to show that DBSCAN, k-center, and spectral clustering are equivalent in the space given by the dc-dist, despite these algorithms being perceived as fundamentally different in their respective literatures. We also verify that finding the pairwise dc-dists gives DBSCAN clusterings across all epsilon-values, simplifying the problem of parameterizing density-based clustering. We conclude by thoroughly analyzing density-connectivity and its properties -- a task that has been elusive thus far in the literature due to the lack of formal tools. Our code recreates every experiment below: https://github.com/Andrew-Draganov/dc_dist

Spectral clustering is one of the most advantageous clustering approaches. However, standard Spectral Clustering is sensitive to noisy input data and has a high runtime complexity. Tackling one of these problems often exacerbates the other. As real-world datasets are often large and compromised by noise, we need to improve both robustness and runtime at once. Thus, we propose Spectral Clustering - Accelerated and Robust (SCAR), an accelerated, robustified spectral clustering method. In an iterative approach, we achieve robustness by separating the data into two latent components: cleansed and noisy data. We accelerate the eigendecomposition - the most time-consuming step - based on the Nyström method. We compare SCAR to related recent state-of-the-art algorithms in extensive experiments. SCAR surpasses its competitors in terms of speed and clustering quality on highly noisy data.

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.

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 MinCut in only linear time, but is also visually convincing. We developed the clustering algorithm CirClu, which implements this minimization and 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.

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.

Many algorithms have been developed for detecting clusters of various kinds over the past decades. However, just few attempts have been made to provide an interactive setting for the clustering algorithms. In this paper, we present PARADISO, an interactive Mean Shift method. It enables the user to get back to any arbitrary iteration point of the run observing the evolution of the clusters after each iteration and to set different bandwidth parameters. The user gets a clustering result with this method which emerged through multiple bandwidths while the user can see the full chain of effects of the chosen bandwidths over all iterations. Further, our method provides so-called Points-Shifted-Distance plots (PSD plots) for the Mean Shift algorithm which aim to facilitate the choice of a different bandwidth for the user. Beyond the mentioned features, PARADISO provides a visualization method which lets the user see the different bandwidth choices made in form of pathways.