# What is String Grammar Fuzzy Clustering?

String Grammar Fuzzy Clustering is a clustering framework designed for syntactic or structural pattern recognition, where each data instance is represented not as a numeric vector but as a string that encodes structural information.

Unlike conventional numerical clustering method (e.g., Fuzzy C-Means), which assume that data have a fixed-length feature vector whereas structural clustering method operates directly on string data whose lengths and internal structures may vary.

In this approach, each pattern is described by a sequence of primitives (symbols) defined by grammatical rules. This is similar to how a sentence is formed from characters following syntax rules.

To measure similarity between strings, the method employs the Levenshtein distance[1], which counts the minimum number of edit operations (insertions, deletions, substitutions) required to transform on string into another.

The "fuzzy" aspect of this framework allows each string to belong to multiple clusters, with a membership degree that reflects how strongly it is associated with each cluster. This provides a more flexible and realistic clustering behavior compared to traditional "hard" clustering, which forces each sample to belong to only one group.

# About This Library

This Python library introduces an algorithm belonging to the String Grammar Fuzzy Clustering framework, namely the String Grammar Unsupervised Possibilistic Fuzzy C-Medians (sgUPFCMed).

## String Grammar Unsupervised Possibilistic Fuzzy C-Medians (sgUPFCMed)[2]

The sgUPFCMed algorithm is an unsupervised clustering algorithm for string data. The sgUPFCMed is developed based on the Unsupervised Possibilistic Fuzzy C-Means (UPFCM) [3]. The algorithm jointly utilizes fuzzy membership value and possibilistic typicality value, as defined in the objective function. While fuzzy membership value satisfies a probabilistic constraint among clusters, typicality value is a possibilistic value of a string in a cluster. As a result, string that is far from all cluster prototypes tends to receive low typicality value. Similarly to the sgPFCMed [4]  a modified fuzzy median string is used to calculate each cluster prototype.

**Key Features:**

- Jointly incorporates fuzzy membership and possibilistic typicality to improve clustering robustness.
- Enforces probabilistic constraints through fuzzy membership while allowing independent typicality assignment.
- Reduces the influence of noise and outliers by using possibilistic typicality.
- Uses the Levenshtein distance to measure dissimilarity between strings.
- Represents each cluster prototype using a modified fuzzy median string.
- Suitable for unsupervised clustering of unlabeled string data with varying lengths.


**\*\*Please be noted that this sgUPFCMed can be used for academic and research purposes only. Please also cite this paper [2].\*\***

## Reference

[1] S. K. Fu, Syntactic Pattern Recognition and Applications, 1982, Prentice-Hall, Zbl0521.68091.

[2] Atcharin Klomsae, Sansanee Auephanwiriyakul, and Nipon Theera-Umpon. “String Grammar Unsupervised Possibilistic Fuzzy C-Medians for Gait Pattern Classification in Patients with Neurodegenerative Diseases”, Computational Intelligence and Neuroscience, Vol. 2018, Article ID 1869565, June 2018.

[3] Wu, X., Wu, B., Sun, J., and Fu, H., “Unsupervised Possibilistic Fuzzy Clustering,” Journal of Information & Computational Science, Vol 7, No.5, pp. 1075-1080, 2010.

[4] Atcharin Klomsae, Sansanee Auephanwiriyakul, and Nipon Theera-Umpon, “A string grammar possibilistic-fuzzy C-medians”, Soft Computing , vol. 23, no. 17, pp. 7637 – 7653, 2019: http://doi.org/10.1007/s00500-018-3392-6.

# Installation

You can install the library using pip:

```bash
pip install sgUPFCMed
```

# USAGE

## Example Code

```python
import random
from sgUPFCMed import SGUPFCMed # Import the clustering class

if __name__ == "__main__":
    # Set random seed for reproducibility
    random.seed(42)

    # Define a list of strings to cluster
    data = ["book", "back", "boon", "cook", "look", "cool", "kick", "lack", "rack", "tack"]

    # Create the model with 2 clusters and fuzzifier m=2.0
    model = SGUPFCMed(C=2, m=2.0, a=1, b=4, eta=2.0)

    # Fit the model on the data
    model.fit(data)

    # Print the final prototype strings representing each cluster
    print("Prototypes:", model.prototypes())

    # Print the fuzzy membership matrix for each input string
    print("\nMembership Matrix (U):")
    for s, u in zip(data, model.membership()):
        print(f"{s:>6} → {[val for val in u]}")

    # Print the fuzzy typicality matrix for each input string
    print("\nTypicality Matrix:")
    for s, t in zip(data, model.typicality()):
        print(f"{s:>6} → {[val for val in t]}")

    # Define new strings to classify using the trained model
    new_data = ["hack", "rook", "cook"]

    # Predict the cluster index (0 or 1) for each new string
    preds = model.predict(new_data, model.prototypes())
    print("\nPredictions:")
    for s, c in zip(new_data, preds):
        print(f"{s} → Cluster {c+1}")
```
