Lecture 65:- ML TSNE

t-SNE (t-Distributed Stochastic Neighbor Embedding) is a dimensionality reduction and visualization technique used in machine learning and data analysis. It's particularly useful for visualizing high-dimensional data in a lower-dimensional space while preserving the local structure and relationships between data points. t-SNE is often used for exploratory data analysis, clustering visualization, and identifying patterns in complex datasets.

Here's the intuition behind t-SNE:

1. Local and Global Relationships: t-SNE focuses on preserving both local and global relationships in the data. Local relationships involve nearby data points that are similar to each other, while global relationships involve data points that have similar properties across the entire dataset.

2. Probability Distribution: t-SNE constructs two probability distributions for each data point: a Gaussian distribution that represents the pairwise similarities of data points in the original high-dimensional space, and a Student's t-distribution that represents the pairwise similarities in the lower-dimensional space.

3. Mapping Data Points: The algorithm iteratively adjusts the positions of data points in the lower-dimensional space to minimize the difference between the two probability distributions. It does so by minimizing the Kullback-Leibler divergence, which measures the difference between the two distributions.

4. Perplexity: A hyperparameter called "perplexity" determines the balance between focusing on local vs. global relationships. A higher perplexity value emphasizes preserving global structure, while a lower value emphasizes local structure.

5. Gradient Descent: t-SNE uses gradient descent optimization to find the optimal positions for data points in the lower-dimensional space. It adjusts the positions based on the difference in pairwise similarities between the high-dimensional and low-dimensional spaces.

6. Applications: t-SNE is often used for visualizing clusters in high-dimensional data, identifying outliers or anomalies, and gaining insights into the underlying structure of complex datasets.

Here's a simplified example of how you can apply t-SNE using Python and the sklearn.manifold module:

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import numpy as np from sklearn.datasets import load_iris from sklearn.manifold import TSNE import matplotlib.pyplot as plt # Load the Iris dataset (you can replace this with your own data) iris = load_iris() X = iris.data y = iris.target # Apply t-SNE with the desired number of components num_components = 2 tsne = TSNE(n_components=num_components, random_state=42) X_tsne = tsne.fit_transform(X) # Plot the t-SNE-transformed data plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y, cmap='viridis') plt.xlabel('t-SNE Dimension 1') plt.ylabel('t-SNE Dimension 2') plt.title('t-SNE - Iris Dataset') plt.colorbar(label='Species') plt.show()

In this example, we load the Iris dataset, apply t-SNE with the desired number of components (2), and visualize the data in the reduced-dimensional space. The plot shows the data points projected onto the t-SNE dimensions, where the color represents the target class.

Keep in mind that t-SNE is a stochastic algorithm, meaning it can produce different results on different runs due to its random initialization. It's also important to choose an appropriate perplexity value for your dataset to achieve meaningful visualizations.