# The Ultimate Comparison Between PCA and t-SNE Algorithm

### Comparing both algorithms on six parameters.

In earlier newsletter issues, we discussed PCA and t-SNE individually.

Yet, a formal comparison between the two approaches is still left to be covered.

Let’s do it today.

The visual below neatly summarizes the major differences between the two algorithms:

**First and foremost, let’s understand their purpose:**

While many interpret PCA as a data visualization algorithm, it is primarily a dimensionality reduction algorithm.

t-SNE, however, is a data visualization algorithm. We use it to project high-dimensional data to low dimensions (primarily 2D).

**Moving on:**

PCA is a deterministic algorithm. Thus, if we run the algorithm twice on the same dataset, we will ALWAYS get the same result.

t-SNE, however, is a stochastic algorithm. Thus, rerunning the algorithm can lead to entirely different results.

*Can you explain why? Share your answers*:)

**As far as uniqueness and interpretation of results is concerned:**

PCA always has a unique solution for the projection of data points. Simply put, PCA is just a rotation of axes such that the new features we get are uncorrelated.

t-SNE, as discussed above, can provide entirely different results, and its interpretation is subjective in nature.

**Next, how do they project data?**

PCA is a linear dimensionality reduction approach. Thus, it is not well-suited if we have a non-linear dataset (which is often true), as shown below:

t-SNE is a non-linear approach. It can handle non-linear datasets.

**During dimensionality reduction:**

PCA only aims to retain the global variance of the data. Thus, local relationships (such as clusters) are often lost after projection, as shown below:

t-SNE preserves local relationships. Thus, data points in a cluster in the high-dimensional space are much more likely to lie together in the low-dimensional space.

In t-SNE, we do not explicitly specify global structure preservation. But it typically does create well-separated clusters.

Nonetheless, it is important to note that the distance between two clusters in low-dimensional space is

**NEVER**an indicator of cluster separation in high-dimensional space.

If you are interested in learning more about their motivation, mathematics, custom implementations, limitations, etc., feel free to read these two in-depth articles:

**👉 **Over to you: What other differences between t-SNE and PCA did I miss?

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It would be nice to see some comparison with UMAP

Yes please do more on comparison