![]() (This helps compute the covariance matrix, a measure of self-similarity in the data.) Putting The Intuition To Use It's the "function x" working on the "vector x". Here, we've mixed the data with itself in every possible permutation. The result is a grid where we've applied each function to each data point. When we see x * x' we mean x (as a set of functions) is working on x' (a set of individual data points). In other words, we've applied the data to itself. The result is the dot product ( read more). When we see x' * x we mean: x' (as a single function) is working on x (a single vector). f' is separated into three functions (each taking a single input).A single data vector, in a vertical column.Similarly, if f = is our row vector, then f' can mean: x' can still remain a data vector, but as three separate entries.If x was a column vector with 3 entries ( ), then x' is: The matrix transpose swaps rows and columns. This is getting neat: depending on the desired outcome, we can combine data and code in a different order. The vertical column of data could really be three distinct functions, each taking a single parameter.Īh. The row containing a horizontal function could really be three data points (each with a single element). This is a function taking three inputs and returning a single result.Īnd the aha! moment: data is code, code is data! ![]() Here, x is a vector of data (I'm using to separate each row). We take raw information like "3 4 5" treat it as a vector or function, depending on how it's written:īy convention, a vertical column is usually a vector, and a horizontal row is typically a function: (Compilers treat a program as text, modify it, and eventually output "instructions" - which could be text for another layer.) The result is a new recipe, which can be further tweaked, or executed as instructions to make a different pie, muffin, cake, etc.
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