κ-SNE: Kaniadakis-Gaussian Distributed Stochastic Neighbor Embedding

$\kappa$-SNE is a tool designed for the visualization of high-dimensional data. It operates by converting similarities between data points into joint probabilities and aims to minimize the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data.

Features

• Visualization of high-dimensional data in lower dimensions (usually 2D or 3D).
• Utilizes the Kaniadakis-Gaussian distribution for transforming the data.
• Allows customization through various parameters to suit different data types and preferences.

Installation

Ensure that you have Python 3 and pip installed on your system. You can then install the required packages using the following command:

pip install -r requirements.txt

Compiling Cython Code

To compile the Cython code, run the following command:

python3 setup.py build_ext --inplace

Usage

Here is a simple example to get you started with using $\kappa$-SNE:

Example

import numpy as np
from kSNE import kSNE

# Sample high-dimensional data
X = np.array([[0, 0, 0], [0, 1, 1], [1, 0, 1], [1, 1, 1]])

# Transforming the data using k-SNE
X_embedded = kSNE(n_components=2).fit_transform(X)

# Checking the shape of the transformed data
print(X_embedded.shape)  # Should print: (4, 2)

You can also try to run the exampleCode.py for an example of a visualization.

Parameters

• n_components (int, optional, default: 2): Dimension of the embedded space.
• perplexity (float, optional, default: 30): Related to the number of nearest neighbors, with typical values between 5 and 50.
• k (float, optional, default: 0.5): Hyperparameter of the Kaniadakis-Gaussian distribution, where 0 < k < 1.
• beta (float, optional, default: 1.0): Shape parameter for the Kaniadakis-Gaussian distribution, must be greater than 0.
• early_exaggeration (float, optional, default: 12.0): Controls cluster spacing in the embedded space.
• learning_rate: float or “auto”, default=”auto”: The learning rate for optimization, typically in the range [10.0, 1000.0]. The ‘auto’ option sets the learning_rate to max(N / early_exaggeration / 4, 50), where N is the sample size.
• n_iter (int, optional, default: 1000): Maximum number of iterations for optimization.
• n_iter_without_progress (int, optional, default: 300): Maximum iterations without progress before aborting.
• min_grad_norm (float, optional, default: 1e-7): Minimum gradient norm required to continue optimization.
• metric (string or callable, optional): Metric for calculating distance between data points.
• init (string or numpy array, optional, default: "random"): Method for initialization of embedding.
• verbose (int, optional, default: 0): Verbosity level.
• random_state (int or RandomState instance, optional, default=None): Determines the random number generator.
• n_jobs (int or None, optional, default=None): The number of parallel jobs to run for neighbors search.

Dependencies

• numpy
• scipy
• cython
• scikit-learn

License

This project is licensed under the GNU GENERAL PUBLIC LICENSE - see the LICENSE file for details.

Contact

If you have any questions or feedback, please open an issue in this repository, and we will get back to you as soon as possible.