每日一练 | Data Scientist & Business Analyst 面试题 161

With very high dimensions, if speed is an issue, then consider that on a matrix of size n×k, PCA takes O(k^2×n+k^3) time, whereas a random projection takes O(nkd), where you're projecting on a subspace of size d.

With a sparse matrix its even faster.

The data may well be low-dimensional, but not in a linear subspace. PCA assumes this.

Random projection are also quite fast for reducing the dimension of a mixture of Gaussians.

If the data is very large, you don't need to hold it in memory for a random projections, whereas for PCA you do.

In general PCA works well on relatively low dimensional data. Of course, PCA maintains the best possible projection.

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