arxiv: 2604.21698 · v1 · submitted 2026-04-23 · 💻 cs.CL · cs.LG· math.AT

Recognition: unknown

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

Marius Huber , David R. Reich , Lena A. J\"ager

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:21 UTC · model grok-4.3

classification 💻 cs.CL cs.LGmath.AT

keywords persistent homologytopological data analysiseye-trackingdyslexia detectionfixation sequencestime serieshybrid models

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The pith

Treating eye fixation sequences as time series and applying persistent homology extracts features that improve dyslexia detection when combined with traditional statistics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper treats sequences of eye fixations during reading as time series data to which persistent homology can be applied. It develops new filtration methods that produce stable multi-scale topological features from these sequences. These features are then fused with conventional statistical descriptors to create hybrid classification models for identifying dyslexic readers. On the Copenhagen Corpus the hybrid models outperform purely statistical baselines, and the new filtrations outperform earlier ones, indicating that the topological descriptors capture patterns in fixation timing and order that standard measures overlook. A sympathetic reader would care because this supplies an additional analytical layer for eye-tracking data that could support more accurate, objective identification of reading difficulties.

Core claim

We interpret fixation sequences as time series and develop novel filtrations to compute persistent homology features. These features are combined with traditional statistical features to form hybrid models that outperform existing methods relying solely on statistical features in detecting dyslexia from eye-tracking-while-reading data in the Copenhagen Corpus. Our proposed filtrations also outperform existing filtrations.

What carries the argument

Novel filtrations for persistent homology applied to fixation-sequence time series, which extract robust multi-scale topological invariants that complement statistical summaries.

If this is right

Hybrid models achieve higher classification accuracy than models built from statistical features alone.
Topological features capture information in fixation sequences that is complementary to traditional statistical measures.
The newly proposed filtrations produce stronger performance than previously published filtrations when applied to the same data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same topological pipeline could be applied to eye-movement data collected for other cognitive or neurological conditions to test whether the signal generalizes.
If the features prove stable across languages and age groups, they could be combined with existing statistical pipelines in clinical screening tools.
Ablation studies that isolate individual topological invariants might reveal which scale of fixation pattern most strongly distinguishes dyslexic reading.

Load-bearing premise

The performance gains seen on the Copenhagen Corpus will hold for other eye-tracking datasets and the topological features supply information genuinely distinct from that already present in the statistical features.

What would settle it

Testing the same hybrid models on an independent eye-tracking corpus for dyslexia and finding no accuracy gain over statistical-only models would show that the topological features are not adding complementary information.

Figures

Figures reproduced from arXiv: 2604.21698 by David R. Reich, Lena A. J\"ager, Marius Huber.

**Figure 2.** Figure 2: Persistence diagram corresponding to the time [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Schematic showing the transformation of a persistence diagram [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Two stages of sweeping of the graph corresponding to a time series by a line of slope c ≈ −0.3 moving from left to right (indicated in blue). The number of line segments constituting the portion of the graph lying to the left of the line changes from two to one as the line moves from the left panel to the right one. 4.1 Computation of Topological Features and Non-Horizontal Filtrations To compute the topol… view at source ↗

**Figure 5.** Figure 5: Computation of the topological feature vector [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces new filtrations for persistent homology on fixation sequences and reports that hybrid topo-statistical models beat pure statistical baselines for dyslexia detection on the Copenhagen Corpus, but the gains rest on a single dataset without clear checks for feature complementarity.

read the letter

The main thing to know is that this work develops novel filtrations for turning time series into persistent homology inputs and then combines those topological features with standard statistical summaries of eye movements to classify dyslexia. On the Copenhagen Corpus the hybrid versions show better performance than statistical-only models, and the new filtrations beat prior ones. That is the concrete advance they are claiming. The application itself is straightforward: fixation sequences are treated as time series, filtrations are built around thresholds on durations or positions, and the resulting persistence diagrams are turned into features for a classifier. The empirical result is that adding the topological part helps on this particular data set. That part is new enough to be worth noting, since most prior TDA work on time series uses off-the-shelf filtrations rather than the tailored ones described here. The paper also keeps the hybrid construction explicit, which makes it easier to reproduce the feature pipeline. The soft spots are exactly where the stress-test note flags them. Everything is evaluated on one corpus, so we do not yet know whether the improvement travels to other eye-tracking collections or languages. More importantly, there is no ablation that removes the topological block while keeping total feature count matched, and no correlation matrix showing how much the persistence features overlap with the usual duration and saccade statistics. Without those controls it remains possible that the lift comes from extra capacity rather than genuinely complementary information. The abstract also leaves out the details on cross-validation folds and significance testing, though the full text presumably supplies them. Readers who work on eye-movement diagnostics or on applied topological data analysis will find the methods section useful as a worked example. The central claim is testable and the construction is honest, so the paper is coherent on its own terms. I would send it to peer review. The referees can ask for the missing ablations and an additional corpus test; those are fixable requests rather than fatal problems.

Referee Report

3 major / 2 minor

Summary. The paper interprets fixation sequences from eye-tracking-while-reading as time series and applies persistent homology with novel filtrations to extract topological features. These are combined with traditional statistical features (e.g., durations, saccade amplitudes) into hybrid models for binary dyslexia detection on the Copenhagen Corpus (L1/L2 readers). The central empirical claim is that the hybrid models outperform baselines relying only on traditional features, that the proposed filtrations are superior to existing ones, and that topological features capture complementary information.

Significance. If the performance gains are shown to be robust, statistically significant, and driven by genuinely complementary information rather than model capacity or dataset artifacts, the work would demonstrate a concrete application of topological data analysis to eye-tracking time series. This could open a new feature family for reading-disorder classification and encourage further TDA work on scanpaths. The explicit construction of new filtrations is a positive technical contribution.

major comments (3)

[Experimental Evaluation / Results] The abstract and experimental claims assert that hybrid models outperform traditional-feature baselines and that topological features are complementary, yet the manuscript provides no ablation studies (e.g., performance with topological features removed), no feature-correlation matrices, and no dimensionality-matched controls that add extra statistical summaries instead of topological ones. Without these, the reported gains on the Copenhagen Corpus could be explained by increased feature count alone rather than orthogonality of information.
[Methods and Experimental Setup] Evaluation is reported on a single corpus (Copenhagen) with no mention of cross-validation procedure, statistical significance testing (e.g., McNemar or paired t-tests across folds), or exact definitions of the topological feature vectors (which persistence diagrams or summaries are used, how they are vectorized). These omissions make it impossible to judge whether the outperformance is reproducible or sensitive to post-hoc choices.
[Filtration Design and Results] The claim that the proposed filtrations outperform existing ones is central to the novelty argument, but the manuscript does not provide a direct, controlled comparison table isolating filtration choice while holding all other model components fixed. It is therefore unclear whether the reported superiority is load-bearing or an artifact of the particular hybrid architecture.

minor comments (2)

[Methods] Notation for the new filtrations should be introduced with explicit mathematical definitions (e.g., threshold functions) rather than descriptive prose only, to allow replication.
[Figures] Figure captions and axis labels for persistence diagrams or barcodes should explicitly state the filtration parameter range and the meaning of the plotted points.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments identify key areas where additional controls and clarifications will strengthen the empirical support for our claims regarding complementary information from topological features and the advantages of the proposed filtrations. We address each point below and commit to revisions.

read point-by-point responses

Referee: The abstract and experimental claims assert that hybrid models outperform traditional-feature baselines and that topological features are complementary, yet the manuscript provides no ablation studies (e.g., performance with topological features removed), no feature-correlation matrices, and no dimensionality-matched controls that add extra statistical summaries instead of topological ones. Without these, the reported gains on the Copenhagen Corpus could be explained by increased feature count alone rather than orthogonality of information.

Authors: We agree that these controls are necessary to rule out explanations based solely on feature count. In the revised manuscript we will add: (i) ablation results with topological features removed from the hybrid models, (ii) correlation matrices between the traditional statistical features and the topological feature vectors, and (iii) dimensionality-matched baselines that augment the statistical feature set with additional hand-crafted summaries or random features of equal cardinality. These will be reported in a new subsection of the experimental evaluation to demonstrate that the observed gains arise from complementary information. revision: yes
Referee: Evaluation is reported on a single corpus (Copenhagen) with no mention of cross-validation procedure, statistical significance testing (e.g., McNemar or paired t-tests across folds), or exact definitions of the topological feature vectors (which persistence diagrams or summaries are used, how they are vectorized). These omissions make it impossible to judge whether the outperformance is reproducible or sensitive to post-hoc choices.

Authors: We will expand the Methods and Experimental Setup sections with the missing details. We will specify the cross-validation protocol (subject-independent k-fold splits), include statistical significance testing via paired t-tests and McNemar tests across folds, and provide the precise vectorization procedure for persistence diagrams (including the choice of summary functions such as persistence landscapes or images together with all discretization parameters). The Copenhagen Corpus remains the only large public dataset for this task; we will add an explicit limitations paragraph discussing generalizability. revision: yes
Referee: The claim that the proposed filtrations outperform existing ones is central to the novelty argument, but the manuscript does not provide a direct, controlled comparison table isolating filtration choice while holding all other model components fixed. It is therefore unclear whether the reported superiority is load-bearing or an artifact of the particular hybrid architecture.

Authors: We concur that an isolated comparison is required. The revised manuscript will contain a new table that evaluates all filtrations (proposed and baseline) under identical conditions: the same classifier, the same hybrid feature-combination strategy, and fixed hyper-parameters. This will isolate the contribution of filtration design to the performance differences. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical evaluation of novel filtrations with no derivation chain

full rationale

The paper proposes new filtrations for persistent homology applied to fixation sequences treated as time series, then evaluates hybrid statistical+topological models for dyslexia detection on the Copenhagen Corpus. All claims rest on experimental performance metrics rather than any first-principles derivation, prediction, or uniqueness theorem. No equations reduce to fitted parameters by construction, no self-citations are load-bearing for the core method, and the filtrations are explicitly described as novel constructions. The work is self-contained as an empirical study.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard axioms of persistent homology (stability under small perturbations) and the domain assumption that fixation sequences are meaningfully interpretable as real-valued time series. No new entities are postulated. A small number of free parameters are likely present in the choice of filtration thresholds and in the hybrid classifier.

free parameters (1)

filtration thresholds and hybrid model hyperparameters
Choices of thresholds in the new filtrations and parameters in the machine-learning models are fitted or selected to optimize performance on the corpus.

axioms (1)

domain assumption Persistent homology produces stable, multi-scale representations of time series under varying thresholds
Invoked throughout the method description as the justification for using topological features.

pith-pipeline@v0.9.0 · 5469 in / 1310 out tokens · 33076 ms · 2026-05-09T21:21:13.591175+00:00 · methodology

discussion (0)

Reference graph

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In practice, the parameterc∈R\ {0}is a hyperparameter that can be tuned according to the problem setting

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As a consequence of Corollary C.4, we have that fσc(t, T(t)) =f τc(t, T(t)) =±∞whenevert∈Iis such thatT(t)∈ { ˇT , ˆT}. To avoid infinite filtration values in practice, we “pad” the range of the time seriesTby a percentage of its actual range. This amounts to replacing the values of ˇTand ˆTin Equa- tion (1) by ˇT−ε( ˆT− ˇT) and ˆT+ε( ˆT− ˇT), respectivel...