# 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 Fuzzy Possibilistic C-Medians (sgFPCMed).

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

The sgFPCMed algorithm enhances the sgFCMed [3] algorithm that incorporates possibilistic theory to reduce the effects of outliers. The typicality value (as in [4]) of a string in a cluster is utilized here. This algorithm still uses the Levenshtein distance to compute distance between two strings, and the fuzzy median is utilized to calculate a cluster prototype, similar to sgFCMed.

**Key Features:**

- Incorporates possibilistic theory by introducing typicality values of a data point to a cluster.
- Utilizes both fuzzy membership and typicality to improve clustering robustness in noisy and overlapping string data.
- Measures string dissimilarity using the Levenshtein distance.
- Employs a fuzzy median string to represent cluster prototypes.
- Suitable for clustering unlabeled string data with varying lengths.

**\*\*Please be noted that this sgFPCMed 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, “A String Grammar Fuzzy-Possibilistic C-Medians”, Applied Soft Computing, 57, pp. 684 – 695, August 2017.

[3] Atcharin Klomsae, Sansanee Auephanwiriyakul, and Nipon Theera-Umpon, “A Novel String Grammar Fuzzy C-Medians,” Proceedings of the 2015 IEEE International Conference on Fuzzy Systems, Istanbul, Turkey, August 2015.

[4] R. Pal, K. Pal, and J. C. Bezdek, A mixed c-means clustering model, in IEEE Int. Conf. Fuzzy Systems, Spain, 1997, pp. 11–21.

# Installation

You can install the library using pip:

```bash
pip install sgFPCMed
```

# USAGE

## Example Code

```python
import random
from sgFPCMed import SGFPCMed # 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 = SGFPCMed(C=2, m=2.0, 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}")
```
