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Ptolemy: A Semantic Map of Exploratory Data Analysis

Dylan Wootton, Denny Bromley, Vidya Setlur

arXiv:2609.16539v1cs.HC

TL;DR

EDA tools often expose execution order without showing how current and prior analyses relate across the broader space of possible views. Ptolemy builds a semantic map from normalized data-view descriptions, and its mixed-methods evaluation finds that maps improve orientation and local comparison while ordered layouts reduce decision cost. The findings identify a trade-off between orientation and actionability for strategic EDA exploration.

  • Problem

    Most EDA tools expose linear analysis histories rather than relationships among analysis states, leaving analysts without an overview of explored and nearby alternatives.

  • Method

    Ptolemy represents notebook analyses as analets, normalizes their effective data views with CellQL, and embeds them into a similarity-based 2D semantic map.

  • Results

    Maps improve global orientation and local comparison, whereas visible ordering makes the next action easier to choose.

  • Takeaways & Limitations

    Strategic EDA interfaces should balance semantically grounded spatial overviews with route cues that support actionable next-step selection.

  • Takeaways & Limitations

    CellQL sacrifices Python’s full expressivity, the fixed 100-seed framing set may under-represent user intents, and Fixes may lose coherence in sparse regions.

Abstract

from arXiv · show

A central challenge in exploratory data analysis (EDA) is keeping track of what has already been examined in order to decide what to analyze next. In practice, analysts often run dozens of analyses while building an understanding of a dataset. However, most tools provide little support for maintaining an overview of this evolving process, instead exposing only a linear history of analysis steps. These tools show sequence, what came before, but not position, how a current analysis relates to the broader space of possible analyses. As a result, analysts must mentally reconstruct which parts of the space they have explored and where gaps remain, increasing the risk of redundant work or overlooked patterns. We present Ptolemy, a navigational interface that externalizes analysis history as a semantic map. Each analytic step is represented as a point positioned by embeddings derived from a structured description of its effective data view (e.g., columns, filters, transformations), allowing spatial distance to reflect analytic similarity. In a mixed-methods study comparing map, canvas, and tree representations, we find that maps improve global orientation and local comparison, while ordered layouts reduce decision cost. These findings surface a trade-off between orientation and actionability, and highlight design principles for supporting strategic exploration in EDA.

1 Introduction

Ptolemy addresses EDA’s navigation problem by mapping analysis states according to semantic similarity rather than execution order. Its study shows a trade-off: maps support orientation and comparison, while ordered layouts make next actions easier to choose.

  • Motivation: Existing notebook aids mainly expose ordinal structure, helping analysts retrace sequence but not compare similar views or assess unexplored alternatives.This leaves analysts to mentally reconstruct coverage and whether they are circling the same questions.
  • Design: Ptolemy uses a sparse, semantically grounded scaffold rather than an exhaustive map, supporting orientation, nearby comparison, diversification, and deliberate pivots.The system coordinates semantic spatialization with ordinal provenance and interaction techniques for navigating the analysis space.
  • Contribution: Ptolemy maps analytic steps by semantic similarity, using CellQL to normalize effective data-view signatures across heterogeneous notebook code.Map points represent analets, and proximity encodes similarity in columns, filters, transformations, aggregations, and other data-view properties.
  • Findings: The Semantic Map makes investigations easier to read as a space, while visible ordering makes the next action easier to choose.These findings motivate hybrid interfaces that combine semantically grounded maps with lightweight route cues.

2 Related Work

Related systems support analytical wayfinding through landmarks, routes, spatial overviews, recommendations, or structured analytical artifacts. Ptolemy extends this work by making operation-level semantics and trajectory-level navigation explicit in a similarity-based analysis space.

  • Interfaces for Analytical Wayfinding: Prior wayfinding systems distinguish landmark, route, and survey knowledge, but landmark-oriented tools provide local anchors with limited global structure.These categories frame recognition of salient states, provenance reasoning, and global reasoning about coverage and remaining possibilities.
  • Spatial Semantic Systems: Policy Maps and Amplio make semantic spaces navigable, whereas Ptolemy maps executable analysis states rather than model behaviors or unstructured-text instances.The systems share spatial overview but differ in the objects they spatialize.
  • Interfaces for Analytical Wayfinding: Ptolemy spatializes operation-level semantics, representing analysis queries through normalized effective data views rather than only variable coverage.This makes survey knowledge reflect both which variables were touched and which analytic operations were performed.
  • EDA Recommendation Systems: EDA recommendation and mixed-initiative systems provide local suggestions but are typically agnostic to session-level structure and unexplored regions.Ptolemy instead reframes recommendation as trajectory-level navigation through neighborhoods and deliberate pivots.
  • Data-Fact Extraction: Unlike Erato’s editorial convergence between fixed endpoints, Ptolemy supports navigational divergence across an open-ended space of analysis steps.Both systems use embeddings, but their interaction goals differ.

3 System Design

Ptolemy represents notebook analyses as a structured space combining spatial similarity with provenance and hierarchy. Its navigation techniques help analysts compare nearby views, pursue alternative regions, record findings, and reflect on major shifts in exploration.

  • Usage Scenario: In the usage scenario, analysts refine analyses while preserving visible relationships: filtered and unfiltered views remain neighbors, and findings stay linked within the Tree.The scenario also uses the map to inspect alternative analyses and the Tree to organize a bearing, finding, and related analyses.
  • Analysis Space: Ptolemy combines nodes with ordinal and interval relations, letting analysts reconstruct how steps unfold while also reasoning about similarity, nearby alternatives, and pivots.Ordinal relations encode sequence and hierarchy; interval relations define spatial neighborhoods grounded in analytic semantics.
  • Analysis Space: The Semantic Map positions analyses using semantic distances, while the Tree presents the same session as an ordered and nested hierarchy.The two views expose complementary spatial and ordinal structures for the same analytical states.
  • Navigation: Ptolemy uses bearings, fixes, and the Gazetteer to support orientation, exploration of sparse regions, and accumulation of reusable semantic documentation.These techniques are enabled by representing notebook history as an embedding and linking notes, definitions, and derived variables to associated nodes.
  • Navigation: Fixes generate analyses from relative neighbors or targeted regions, adapting CellQL patterns from nearby analets to turn exploratory gaps into concrete next steps.Sparse regions far from any seed may produce less coherent suggestions, so the system uses diverse seeding and warns outside the convex hull.
  • Reading the Map: Empty map regions are only weak contextual cues because they may indicate unexplored areas or projection artifacts, and seeded structure may remain hidden.Each session seeds approximately 100 framing analets while surfacing roughly 20, and maps often stabilize around 40 analets.

4 Interface Evaluation

The evaluation shows that semantic maps improve global orientation, similarity recall, and strategic reasoning, while ordered layouts make immediate next-step decisions clearer. Behavioral breadth and subjective wayfinding diverged, revealing a trade-off between exploration coverage, interpretability, and actionability.

  • Global Wayfinding: 12/12 participants ranked the Map first for seeing covered versus uncovered analysis regions, with the highest rating for perceiving possible analyses (M=5.13).The Map also led for identifying the current analysis state (M=5.65) and situating oneself in the broader process (M=5.47; 11/12 ranked it first).
  • Interpretability and Mental Models: Interpretability varied: the Map helped some participants organize progress and coverage, but others found its distances and empty regions difficult to interpret.Tree’s persistent textual labels offered immediate readability and reduced hovering, while interface fit also depended on whether participants preferred hierarchical or spatial mental models.
  • History and Similarity Recall: Map ratings for recognizing previously run similar analyses reached M=5.49, exceeding Canvas (M=4.12) and Tree (M=4.10).Participants attributed this advantage to clustered near-duplicates that appeared close together, while Tree supported recall of specifically named steps.
  • Actionability and Planning: The Map best supported reasoning about subsequent steps (M=4.85), whereas Tree narrowly led clarity of what to do next (M=4.52 versus Map M=4.47).The Map encouraged strategic navigation through the analysis space, while Tree and Canvas supplied stronger ordinal cues for linear progression.
  • Behavioral Breadth: Canvas achieved the widest analytical breadth despite low subjective wayfinding ratings, with convex-hull areas of 0.42 versus Map 0.27 and Tree 0.24.Its minimal interpretive friction encouraged rapid sampling, whereas Map users often deepened exploration within one cluster before moving elsewhere.
  • Study Boundary: The short-form study may have favored analytical fixation in the Map, although the authors hypothesize that longer sessions could encourage broader dispersion through cues for unvisited space.This remains a hypothesis rather than an observed long-session result.

5 Discussion

Ptolemy’s findings expose a trade-off between semantic maps that support global orientation and ordered layouts that reduce immediate decision cost. The discussion therefore advocates combining spatial overview with lightweight routes, richer manipulation, and broader evaluation.

  • 5.1 Discussion: The Semantic Map revealed global structure and near-duplicate analyses, while tree and grid layouts made next steps more obvious through natural reading order.Spatial encodings supporting survey knowledge aid coverage and strategic reasoning; route-oriented layouts lower planning friction but can encourage shallow, enumerative interaction.
  • 5.1 Discussion: The Static Canvas produced the largest behavioral breadth despite the lowest subjective wayfinding, because enumerative sampling encouraged participants to explore broadly.The tree showed a milder version of this effect through sequential movement down a branch.
  • 5.1 Discussion: The map prompted deeper local comparison and strategic reconnaissance, but its global awareness imposed decision costs that reduced short-term dispersion.The authors caution that breadth in the grid does not disprove semantic maps; it highlights the need for lower-friction next steps.
  • 5.1 Discussion: A productive design goal is to blend survey power with optional routes such as touring clusters, contrasting nearest neighbors, and jumping to distant relevant regions.These operators would serialize immediate actions without abandoning the map’s broader spatial overview.
  • 5.2 Design Implications: Participants wanted to steer similarity, label regions, and treat neighborhoods as composable interaction units, motivating metric steering and region-level operators.They also sought to pin anchors and adjust dimensions of relevance so the analytic space could reflect their hypotheses.
  • 5.2 Design Implications: EDA tools should expose both ordinal and interval structure, while retaining simple trees or grids when low decision overhead matters, especially early in a session.The broader design argument treats analytic space as a manipulable substrate for mixed-initiative interaction and collaboration.
  • 5.3 Limitations: The interface study used a fixed set of candidate analets, so its results concern navigational affordances rather than history construction, recommendation quality, or Bearings.The evaluation also emphasizes thematic findings because short conditions and code artifacts can confound breadth and depth; longitudinal deployment remains an open direction.
  • 5.3 Limitations: CellQL captures most typical data semantics but cannot represent highly expressive Python operations such as machine-learning model fitting.The fixed 100-seed framing may under-represent user intents, and generative features may lose coherence in sparse regions.

6 Conclusion

Ptolemy frames EDA as navigation through a conceptual analysis space rather than merely generation of visualizations. Its semantic layout makes landmarks, routes, survey knowledge, neighborhoods, coverage, and trajectories visible, while the findings support combining strategic spatial exploration with deliberate focus.

  • 6 Conclusion: Ptolemy models EDA as navigation through a similarity-based analysis space, making analytic neighborhoods, coverage, and trajectories visible alongside individual outputs.The conclusion describes analytic space as a manipulable substrate for adaptive recommendation, semantic interaction, and collaboration.

A Appendix A: CellQL Formalism and Preliminary Evaluation

CellQL provides a syntax-invariant representation of effective data views and is evaluated for semantic consistency and differentiation across controlled variants and modalities.

  • A.1 Formal Language: CellQL: CellQL represents each analet’s effective data view through columns, filters, transformations, and aggregations rather than surface syntax.Its goal is to preserve analytic structure across heterogeneous notebook code.
  • A.1 Formal Language: CellQL: REPEAT, BRANCH, and CONCAT preserve recurring EDA structures, schema-dependent choices, and grouped parallel views in a compact representation.REPEAT captures iteration across dimensions, BRANCH selects templates from schema facts, and CONCAT bundles independent queries.
  • A.2 CellQL Preliminary Evaluation: The evaluation compares Python, natural language, and CellQL embeddings for invariance to syntactic changes and separation under functional changes.Controlled variants are generated from notebook cells, transpiled into three modalities, and evaluated through an end-to-end pipeline.
  • A.2.3 Transpilation to CellQL.: CellQL translations pass an LLM-based semantic fidelity check in 86.6% of 1300 Python–CellQL pairs.The judges assess whether columns, aggregations, derived calculations, and row filters are captured comparably.
  • A.2.3 Transpilation to CellQL.: Translation failures concentrate where procedural Python exceeds CellQL’s declarative scope, including model fitting, hypothesis testing, visualization nuances, and metadata operations.The authors identify expanded function libraries or improved transpilation prompts as possible remedies.
  • A.2.6 Semantic consistency (syntax invariance).: CellQL shows higher syntax invariance than natural language and Python across syntax buckets, with scores around 0.395–0.417 versus 0.223–0.243 and 0.087–0.098.The intervals do not overlap across modalities, while some bucket ordering is not perfectly monotonic.
  • A.2.7 Functional distance (ordered separation).: Distances increase with functional change for CellQL and natural language, especially for structural or task shifts, while Python is more affected by refactoring.CellQL therefore preserves neighborhoods for functionally similar analyses while separating more distinct ones.

A.2.5 Results.

Cosine distance is computed in each modality’s embedding space to support the evaluation’s comparison of representations.

  • A.2.5 Results.: Cosine distance d_m(·, ·) is defined separately for Python, CellQL, and natural-language modalities.The modality index m ranges over the three representations.
  • A.2.5 Results.: The distance definition provides the basis for comparing how representations organize syntax-preserving and function-changing variants.The supplied passage defines the measure but does not report results.
  • A.2.5 Results.: The modality-specific distance is used as the comparison quantity across Python, CellQL, and Natural Language.No additional numerical outcome is stated in the supplied passage.

A.2.8 Limitations of the CellQL Evaluation.

The CellQL evaluation is deliberately preliminary, using generated controlled examples and LLM-based semantic judgments rather than organically evolved notebooks or human annotations.

  • A.2.8 Limitations of the CellQL Evaluation.: The evaluation uses LLM-generated seed cells and controlled variants instead of organically evolved notebooks.Its scope is local adequacy for common EDA operations and robustness to surface-level refactoring, not arbitrary notebook transpilation.
  • A.2.8 Limitations of the CellQL Evaluation.: Semantic equivalence is assessed with multiple LLM judges rather than human annotation.The reported 86.6% pass rate should therefore be interpreted within this evaluation design.
  • A.2.8 Limitations of the CellQL Evaluation.: Figure 6 compares a semantic map, a labeled tree, and a fixed canvas as distinct interface conditions.The figure establishes the study’s organizational comparison rather than a limitation of CellQL transpilation itself.

B Appendix B: Extended Interface Study Protocol

Appendix B consolidates the protocol and supplemental details for the main interface evaluation, including its session procedure and survey-related materials.

  • B Appendix B: Extended Interface Study Protocol: The appendix consolidates protocol and supplemental quantitative details referenced by the main Interface Evaluation section.It serves as supporting documentation for the study.
  • B Appendix B: Extended Interface Study Protocol: The session procedure is presented before instrument development, assignment strategy, and non-wayfinding survey outcomes.These components are organized as successive parts of the appendix.
  • B Appendix B: Extended Interface Study Protocol: The appendix covers both study operations and survey outcomes from adapted CSI domains.The supplied passages identify the scope but do not report specific survey values.

B.1 Session Procedure

Each session used three condition blocks with standardized orientation, think-aloud analysis, and post-block surveys.

  • B.1 Session Procedure: Each session comprised three blocks, one for each interface condition.Blocks lasted 25–40 minutes and included at least 17 minutes of analysis.
  • B.1 Session Procedure: Participants received a short orientation before each block and followed a think-aloud protocol throughout.
  • B.1 Session Procedure: Researchers captured screen and audio recordings, field notes, interaction logs, and brief post-block surveys.

B.2 Interface Condition Overview

The study compared three interfaces exposing identical analets and interactions but differing in how they organized analytical relationships.

  • B.2 Interface Condition Overview: All conditions exposed the same candidate analets and supported the same preview and materialization interactions.
  • B.2 Interface Condition Overview: The Semantic Map used local semantic similarity, the Tree used labeled user-organized hierarchy, and the Static Canvas used a semantically arbitrary fixed grid.
  • B.2 Interface Condition Overview: Experts reviewed survey-item relevance, clarity, and coverage, prompting wording revisions for five of twenty items before deployment.
  • B.2 Interface Condition Overview: A Williams balanced Latin-square design counterbalanced the three interface orders across 12 participants.
  • B.2 Interface Condition Overview: A balanced permutation schedule distributed Vehicles, Diamonds, and Listings across session positions and condition pairings.

B.5 Supplementary Interface Survey Results (Non-Wayfinding)

The supplementary section reports adapted CSI domains outside the paper’s central wayfinding analysis and preserves their complete reporting in Figure 7.

  • B.5 Supplementary Interface Survey Results (Non-Wayfinding): The reported domains include Exploration, Expressiveness, Immersion, Enjoyment, Results Worth Effort, and Collaboration.
  • B.5 Supplementary Interface Survey Results (Non-Wayfinding): Figure 7 summarizes supplementary adapted CSI outcomes for non-wayfinding domains.
  • B.5 Supplementary Interface Survey Results (Non-Wayfinding): Main-text wayfinding claims are reported in Figure 4, while Figure 7 preserves completeness of supplementary reporting.
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