t-SNE is a non-linear dimensionality reduction technique primarily used for visualizing high-dimensional data in a lower-dimensional space (typically 2D or 3D). It's particularly effective at revealing the underlying structure of data by preserving local similarities.
How it Works:
High-Dimensional Similarity:
t-SNE first calculates the pairwise similarities between data points in the original high-dimensional space.
It uses a Gaussian distribution to model the probability of points being neighbors.
This step focuses on capturing local relationships – how close points are to each other in the high-dimensional space.
Low-Dimensional Mapping:
It then aims to find a corresponding low-dimensional representation of the data points.
It uses a t-distribution (hence the "t" in t-SNE) to model the pairwise similarities in the low-dimensional space.
The t-distribution has heavier tails than a Gaussian, which helps to spread out dissimilar points in the low-dimensional space, preventing the "crowding problem" where points tend to clump together.
Minimizing Divergence:
t-SNE minimizes the Kullback-Leibler (KL) divergence between the high-dimensional and low-dimensional similarity distributions.
This optimization process iteratively adjusts the positions of the points in the low-dimensional space to best preserve the local similarities from the high-dimensional space.
Characteristics of t-SNE:
Pairwise Similarity:
t-SNE focuses on preserving the pairwise similarities between data points. This is its core mechanism.
Non-Linearity:
It's a non-linear technique, meaning it can capture complex, non-linear relationships in the data.
Local Structure:
It excels at preserving the local structure of the data, meaning that points that are close together in the high-dimensional space will tend to be close together in the low-dimensional space.
Visualization:
It's primarily used for visualization, not for general-purpose dimensionality reduction.
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