# Dimensionality Reduction: t-Distributed Stochastic Neighbor Embedding (t-SNE)

Dimensionality reduction is a fundamental technique in machine learning and data visualization that is used to simplify the complexity of high-dimensional data by transforming it into a lower-dimensional space while preserving the intrinsic structure of the original data. One popular dimensionality reduction algorithm is t-Distributed Stochastic Neighbor Embedding (t-SNE).

##### What is t-SNE?

t-SNE, short forΒ t-Distributed Stochastic Neighbor Embedding, is a non-linear dimensionality reduction technique introduced by Laurens van der Maaten and Geoffrey Hinton in 2008. It aims to map high-dimensional data points into a low-dimensional representation, typically 2D or 3D, by modeling each high-dimensional object with their similarities as pairwise probabilities.

##### How does t-SNE work?
1. Similarity Calculation: In t-SNE, the first step involves calculating pairwise similarities between points in high-dimensional space using a Gaussian kernel function.

2. Constructing Probability Distributions: Next, these similarities are converted into conditional probability distributions using a Student's t-distribution with one degree of freedom.

3. Defining Low-Dimensional Mapping: The goal is to find a mapping from high to low dimensions that minimizes the Kullback-Leibler divergence between the joint probabilities in both spaces.

4. Optimization: The optimization process minimizes this divergence through gradient descent techniques such as stochastic gradient descent.

5. Visualization: By reducing dimensionality and preserving local neighbor relationships, t-SNE creates visualizations that reveal clusters and patterns within complex datasets.

##### Key Features of t-SNE:
• Non-linear: Captures complex structures present in high-dimensional data.
• Retains Local Information: Preserves local similarity relationships during the embedding process.
• Visualization Tool: Commonly used for visualizing high-dimensional datasets for exploratory analysis.
• Sensitivity to Perplexity Parameter: Perplexity controls balance between local vs global aspects; tuning required.

Overall, t-Distributed Stochastic Neighbor Embedding (t-SNE) provides an effective way to visualize and explore complex datasets by projecting them into lower dimensions while maintaining important structural information inherent in the original data distribution.

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