The Limitation of PCA Which Many Folks Often Ignore

Imagine you have a classification dataset. If you use PCA to reduce dimensions, it is inherently assumed that your data is linearly separable.

But it may not be the case always. Thus, PCA will fail in such cases.

To resolve this, we use the kernel trick (or the KernelPCA). The idea is to:

• Project the data to another space using a kernel function, where the data becomes linearly separable.

• Apply the standard PCA algorithm to the transformed data.

For instance, in the image below, the original data is linearly inseparable. Using PCA directly does not produce any desirable results.

But as mentioned above, KernelPCA first transforms the data to a linearly separable space and then applies PCA, resulting in a linearly separable dataset.

Sklearn provides a KernelPCA wrapper, supporting many popularly used kernel functions. You can find more details here: Sklearn Docs.

Having said that, it is also worth noting that the run-time of PCA is cubic in relation to the number of dimensions of the data.

When we use a KernelPCA, typically, the original data (in n dimensions) is projected to a new higher dimensional space (in m dimensions; m>n). Therefore, it increases the overall run-time of PCA.

Over to you: What are some other limitations of PCA that you know of? Let me know :)

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