Features Maximization Metric

Implementation of Features Maximization Metric, an unbiased metric aimed at estimate the quality of an unsupervised classification.

Quick description

Features Maximization (FMC) is a features selection method described in Lamirel, J.-C., Cuxac, P., & Hajlaoui, K. (2016). A Novel Approach to Feature Selection Based on Quality Estimation Metrics. In Advances in Knowledge Discovery and Management (pp. 121–140). Springer International Publishing. https://doi.org/10.1007/978-3-319-45763-5_7.

This metric is computed by applying the following steps:

1. Compute the Features F-Measure metric (based on Features Recall and Features Predominance metrics).

   (a) The Features Recall FR[f][c] for a given class c and a given feature f is the ratio between the sum of the vectors weights of the feature f for data in class c and the sum of all vectors weights of feature f for all data. It answers the question: "Can the feature f distinguish the class c from other classes c' ?"

   (b) The Features Predominance FP[f][c] for a given class c and a given feature f is the ratio between the sum of the vectors weights of the feature f for data in class c and the sum of all vectors weights of all feature f' for data in class c. It answers the question: "Can the feature f better identify the class c than the other features f' ?"

   (c) The Features F-Measure FM[f][c] for a given class c and a given feature f is the harmonic mean of the Features Recall (a) and the Features Predominance (c). It answers the question: "How much information does the feature f contain about the class c ?"

2. Compute the Features Selection (based on F-Measure Overall Average comparison).

   (d) The F-Measure Overall Average is the average of Features F-Measure (c) for all classes c and for all features f. It answers the question: "What are the mean of information contained by features in all classes ?"

   (e) A feature f is Selected if and only if it exist at least one class c for which the Features F-Measure (c) FM[f][c] is bigger than the F-Measure Overall Average (d). It answers the question: "What are the features which contain more information than the mean of information in the dataset ?"

   (f) A Feature f is Deleted if and only if the Features F-Measure (c) FM[f][c] is always lower than the F-Measure Overall Average (d) for each class c. It answers the question: "What are the features which do not contain more information than the mean of information in the dataset ?"

3. Compute the Features Contrast and Features Activation (based on F-Measure Marginal Averages comparison).

   (g) The F-Measure Marginal Averages for a given feature f is the average of Features F-Measure (c) for all classes c and for the given feature f. It answers the question: "What are the mean of information contained by the feature f in all classes ?"

   (h) The Features Contrast FC[f][c] for a given class c and a given selected feature f is the ratio between the Features F-Measure (c) FM[f][c] and the F-Measure Marginal Averages (g) for selected feature f put to the power of an Amplification Factor. It answers the question: "How relevant is the feature f to distinguish the class c ?"

   (i) A selected Feature f is Active for a given class c if and only if the Features Contrast (h) FC[f][c] is bigger than 1.0. It answers the question : "For which classes a selected feature f is relevant ?"

This metric is an efficient method to:

• identify relevant features of a dataset modelization;
• describe association between vectors features and data classes;
• increase contrast between data classes.

Documentation

• Main documentation

Installation

Features Maximization Metric requires Python 3.8 or above.

To install with pip:

# install package
python3 -m pip install cognitivefactory-features-maximization-metric

To install with pipx:

# install pipx
python3 -m pip install --user pipx

# install package
pipx install --python python3 cognitivefactory-features-maximization-metric

Development

To work on this project or contribute to it, please read:

• the Copier PDM template documentation ;
• the Contributing page for environment setup and development help ;
• the Code of Conduct page for contribution rules.

References

• Features Maximization Metric: Lamirel, J.-C., Cuxac, P., & Hajlaoui, K. (2016). A Novel Approach to Feature Selection Based on Quality Estimation Metrics. In Advances in Knowledge Discovery and Management (pp. 121–140). Springer International Publishing. https://doi.org/10.1007/978-3-319-45763-5_7
• V-Measure: Rosenberg, Andrew & Hirschberg, Julia. (2007). V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure. 410-420.

How to cite

Schild, E. (2023). cognitivefactory/features-maximization-metric. Zenodo. https://doi.org/10.5281/zenodo.7646382.