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I saw many people using 'J(θ)' to represent cost function, what does the capital letter 'J' exactly mean?
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'J' stands for Jacobian matrix where we are trying to find a scalar valued function in several variables which generalises in all dimensions of the vector. In general terms we are trying to find the best function that could fit our features data.
The “J” in J-Cost refers to the word Jikan, “time” in Japanese. The innovation of the J-Cost theory is that it applies a time element to the determination of a company's profit. Rather than the traditional “profit rate = profit/cost”, it uses the formula “profit rate = profit/cost x time”.
What is cost function: The cost function “J( θ0,θ1)” is used to measure how good a fit (measure the accuracy of hypothesis function) a line is to the data. If the line is a good fit, then your predictions will be far better. The idea is to minimize the value of J by calculating it from given values of θ0 and θ1.
The term alpha means — with how much magnitude you are reducing your value. Theta-j here represents each individual theta you have in your solution, so you run this equation for all the thetas, which in our case are two, but can also be three, four or ten depending upon problem at hand.
But in machine learning J(theta) is not a matrix, it is a multidimensionnal real function that we want to minimize.
So the letter J may well be a reference to Jacobi, but why it is used to name a cost function still remains a mystery, that no MOOC nor blog has revealed.
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