Exploring high dimensional data with Butterfly: a novel classification algorithm based on discrete dynamical systems
Bibliographic record
Abstract
MOTIVATION: We introduce a novel method for visualizing high dimensional data via a discrete dynamical system. This method provides a 2D representation of the relationship between subjects according to a set of variables without geometric projections, transformed axes or principal components. The algorithm exploits a memory-type mechanism inherent in a certain class of discrete dynamical systems collectively referred to as the chaos game that are closely related to iterative function systems. The goal of the algorithm was to create a human readable representation of high dimensional patient data that was capable of detecting unrevealed subclusters of patients from within anticipated classifications. This provides a mechanism to further pursue a more personalized exploration of pathology when used with medical data. For clustering and classification protocols, the dynamical system portion of the algorithm is designed to come after some feature selection filter and before some model evaluation (e.g. clustering accuracy) protocol. In the version given here, a univariate features selection step is performed (in practice more complex feature selection methods are used), a discrete dynamical system is driven by this reduced set of variables (which results in a set of 2D cluster models), these models are evaluated for their accuracy (according to a user-defined binary classification) and finally a visual representation of the top classification models are returned. Thus, in addition to the visualization component, this methodology can be used for both supervised and unsupervised machine learning as the top performing models are returned in the protocol we describe here. RESULTS: Butterfly, the algorithm we introduce and provide working code for, uses a discrete dynamical system to classify high dimensional data and provide a 2D representation of the relationship between subjects. We report results on three datasets (two in the article; one in the appendix) including a public lung cancer dataset that comes along with the included Butterfly R package. In the included R script, a univariate feature selection method is used for the dimension reduction step, but in the future we wish to use a more powerful multivariate feature reduction method based on neural networks (Kriesel, 2007). AVAILABILITY AND IMPLEMENTATION: A script written in R (designed to run on R studio) accompanies this article that implements this algorithm and is available at http://butterflygeraci.codeplex.com/. For details on the R package or for help installing the software refer to the accompanying document, Supporting Material and Appendix.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".