What is Perplexity value in tSNE

 The perplexity parameter in t-SNE is a crucial setting that influences the algorithm's behavior and the resulting visualization. It essentially controls the balance between preserving local and global structure in the data.   

What Perplexity Represents:

Perplexity can be thought of as a measure of the effective number of local neighbors each point considers.

It's related to the variance (spread) of the Gaussian distribution used to calculate pairwise similarities in the high-dimensional space.

In simpler terms, it determines how many nearby points each point is "concerned" with when trying to preserve its local structure.

How Perplexity Works:

Local Neighborhood Size:

A smaller perplexity value causes t-SNE to focus on very close neighbors. It will prioritize preserving the fine-grained local structure of the data.   

A larger perplexity value makes t-SNE consider a wider range of neighbors. It will attempt to preserve a more global view of the data's structure.

Balancing Local and Global:

The choice of perplexity affects the trade-off between preserving local and global relationships.   

Too low a perplexity can lead to noisy visualizations with many small, disconnected clusters.   

Too high a perplexity can obscure fine-grained local structure and make the visualization appear overly smooth.   

Impact on Visualization:

Low Perplexity:

Reveals fine-grained local patterns.   

Can produce many small, tight clusters.

May be sensitive to noise.   

High Perplexity:

Shows broader global patterns.

Produces smoother, more spread-out visualizations.

Less sensitive to noise.

Practical Considerations:

Typical Range:

Perplexity is typically set between 5 and 50.   

The optimal value depends on the size and density of your dataset.

Experimentation:

It's often necessary to experiment with different perplexity values to find the one that produces the most informative visualization.

Dataset Size:

Larger datasets generally benefit from higher perplexity values.

Smaller datasets might require lower perplexity values.

No Single "Best" Value:

There is no single "best" perplexity value. The optimal value is subjective and depends on the specific dataset and the goals of the visualization.   

In summary:

The perplexity parameter in t-SNE controls the algorithm's focus on local versus global structure. It influences the number of neighbors each point considers, affecting the resulting visualization's appearance and interpretability. Experimentation is often necessary to find a suitable value.