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"To deal with hyper-planes in a 14-dimensional space, visualize a 3D space and say 'fourteen' to yourself very loudly. Everyone does it." - Geoffrey Hinton In many domains, ranging from computational imaging to finance, data comes in the form of high-dimensional signals that are challenging for humans to directly reason about, as our intuition is generally confined to two or three dimensions. Thankfully, while data may often lay in very high-dimensional spaces, it is often the case that the intrinsic dimensionality of the data is much lower. This is a concept known as the manifold hypothesis, and is a core assumption for many machine learning techniques. The goal of dimensionality reduction is to compress high-dimensional data into lower-dimensional forms that preserve their relevant structure while being much easier for people to interpret. A simple dataset to start our investigation of dimensionality reduction is a one dimensional spiral embedded in a two dimensional space (see Figur

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• Ali Ahmad
• Markus Strasser