There are many ways to project data into higher-dimensional spaces. For our purposes, such projections come with two major concerns. One has to do with Vapnik’s original algorithm, which requires taking mutual dot products of data samples. Let’s say the original dataset was in ten dimensions. That would require taking dot products of ten-dimensional vectors. If this data is linearly inseparable in 10D space, and if it were to be projected into 1,000 dimensions, where the data cleanly clumped into two separable categories, then each data point would be represented by a 1,000-dimensional vector.
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