arXiv subjects

Marius Huber

Publications and source records attributed to Marius Huber.

7 recordsLinked to original sources

arXiv2026

Exploring Dowker Homology for Sentence Similarity

Dowker homology is a topological tool that may be used to analyze the relative position of two point clouds living in a common space. We investigate whether Dowker homology captures sentence similarity information by treating the embeddings of the tokens that constitute a sentence pair as a pair of point clouds in the latent space of a transformer model, using both models that have and have not been fine-tuned for sentence similarity. We find that Dowker homology captures sentence similarity information, as measured by regressing Dowker homology features onto ground-truth similarity scores, and that it can be used for visual inspection of similarity data and models. In an attempt to make Dowker homology readily applicable, we derive from it single-number summaries that we expect to capture sentence similarity directly. These turn out to work reasonably well, but without outperforming standard sentence similarity measures based on established pooling methods.

cs.CL↗

arXiv2026

Fixation Sequences as Time Series: A Topological Approach to Dyslexia Detection

Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a \textit{filtration}). We develop novel filtrations for time series and introduce topological methods for the analysis of eye-tracking data, by interpreting fixation sequences as time series, and constructing ``hybrid models'' that combine topological features with traditional statistical features. We empirically evaluate our method by applying it to the task of dyslexia detection from eye-tracking-while-reading data using the Copenhagen Corpus, which contains scanpaths from dyslexic and non-dyslexic L1 and L2 readers. Our hybrid models outperform existing approaches that rely solely on traditional features, showing that persistent homology captures complementary information encoded in fixation sequences. The strength of these topological features is further underscored by their achieving performance comparable to established baseline methods. Importantly, our proposed filtrations outperform existing ones.

cs.CL↗

arXiv2025

Flagifying the Dowker Complex

The Dowker complex $\mathrm{D}_{R}(X,Y)$ is a simplicial complex capturing the topological interplay between two finite sets $X$ and $Y$ under some relation $R\subseteq X\times Y$. While its definition is asymmetric, the famous Dowker duality states that $\mathrm{D}_{R}(X,Y)$ and $\mathrm{D}_{R}(Y,X)$ have homotopy equivalent geometric realizations. We introduce the Dowker-Rips complex $\mathrm{DR}_{R}(X,Y)$, defined as the flagification of the Dowker complex or, equivalently, as the maximal simplicial complex whose $1$-skeleton coincides with that of $\mathrm{D}_{R}(X,Y)$. This is motivated by applications in topological data analysis, since as a flag complex, the Dowker-Rips complex is less expensive to compute than the Dowker complex. While the Dowker duality does not hold for Dowker-Rips complexes in general, we show that one still has that $\mathrm{H}_{i}(\mathrm{DR}_{R}(X,Y))\cong\mathrm{H}_{i}(\mathrm{DR}_{R}(Y,X))$ for $i=0,1$. We further show that this weakened duality extends to the setting of persistent homology, and quantify the ``failure" of the Dowker duality in homological dimensions higher than $1$ by means of interleavings. This makes the Dowker-Rips complex a less expensive, approximate version of the Dowker complex that is usable in topological data analysis. Indeed, we provide a Python implementation of the Dowker-Rips complex and, as an application, we show that it can be used as a drop-in replacement for the Dowker complex in a tumor microenvironment classification pipeline. In that pipeline, using the Dowker-Rips complex leads to increase in speed while retaining classification performance.

math.AT↗

arXiv2024

AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm

We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make it into an out-of-the-box clustering algorithm that performs well across the board. AuToMATo combines the existing ToMATo clustering algorithm with a bootstrapping procedure in order to separate significant peaks of an estimated density function from non-significant ones. We perform a thorough comparison of AuToMATo (with its parameters fixed to their defaults) against many other state-of-the-art clustering algorithms. We find not only that AuToMATo compares favorably against parameter-free clustering algorithms, but in many instances also significantly outperforms even the best selection of parameters for other algorithms. AuToMATo is motivated by applications in topological data analysis, in particular the Mapper algorithm, where it is desirable to work with a clustering algorithm that does not need tuning of its parameters. Indeed, we provide evidence that AuToMATo performs well when used with Mapper. Finally, we provide an open-source implementation of AuToMATo in Python that is fully compatible with the standard scikit-learn architecture.

cs.LG↗

arXiv2022

Ribbon cobordisms as a partial order

We show that the notion of ribbon rational homology cobordism yields a partial order on the set of aspherical $3$-manifolds, thus supporting a conjecture formulated by Daemi, Lidman, Vela-Vick and Wong. Our proof is built on Agol's recent proof of the fact that ribbon concordance yields a partial order on the set of knots in the 3-sphere.

math.GT↗

arXiv2020

Ribbon cobordisms between lens spaces

We determine when there exists a ribbon rational homology cobordism between two connected sums of lens spaces, i.e. one without $3$-handles. In particular, we show that if a lens space $L$ admits a ribbon rational homology cobordism to a different lens space, then $L$ must be homeomorphic to $L(n,1)$, up to orientation-reversal. As an application, we classify ribbon $\chi$-concordances between connected sums of $2$-bridge links. Our work builds on Lisca's work on embeddings of linear lattices.

math.GT↗

arXiv2018

Cubic Range Error Model for Stereo Vision with Illuminators

Use of low-cost depth sensors, such as a stereo camera setup with illuminators, is of particular interest for numerous applications ranging from robotics and transportation to mixed and augmented reality. The ability to quantify noise is crucial for these applications, e.g., when the sensor is used for map generation or to develop a sensor scheduling policy in a multi-sensor setup. Range error models provide uncertainty estimates and help weigh the data correctly in instances where range measurements are taken from different vantage points or with different sensors. The weighing is important to fuse range data into a map in a meaningful way, i.e., the high confidence data is relied on most heavily. Such a model is derived in this work. We show that the range error for stereo systems with integrated illuminators is cubic and validate the proposed model experimentally with an off-the-shelf structured light stereo system. The experiments confirm the validity of the model and simplify the application of this type of sensor in robotics. The proposed error model is relevant to any stereo system with low ambient light where the main light source is located at the camera system. Among others, this is the case for structured light stereo systems and night stereo systems with headlights. In this work, we propose that the range error is cubic in range for stereo systems with integrated illuminators. Experimental validation with an off-the-shelf structured light stereo system shows that the exponent is between 2.4 and 2.6. The deviation is attributed to our model considering only shot noise.

cs.CV↗