Of the many operations that I didn't understand, this one stands out in the material I've been going over to learn about Machine Learning. Yes, there are other symbols I don't understand completely yet, but I'm going to focus entirely on understanding the summation operator in this post. While I kind of understood the phrase "summation operator" to mean adding a bunch of numbers together, I did not understand the exact steps of the process. Also, why is there a number or variable at the top and to the right of the sigma, and what is under the Capital-sigma.
Before I get started, my source of information is the Wikipedia article on Summation. If you find my explanations lacking, you are more than welcome to go straight to the source. My aim is to explain briefly the summation operator, so that the notations can be understood by someone looking into machine learning without a deep math background to allow them to get a quick grasp of the meaning of the notation.
Before I get started, my source of information is the Wikipedia article on Summation. If you find my explanations lacking, you are more than welcome to go straight to the source. My aim is to explain briefly the summation operator, so that the notations can be understood by someone looking into machine learning without a deep math background to allow them to get a quick grasp of the meaning of the notation.
Breaking it down:
What does the k in k=0 mean? k in k=0 is the index of summation. If you've done any coding and used arrays, then you know exactly what an index is. It is just the position in the array.
The 0 in k=0 is the lower bound of summation. In other words, the beginning of your index. If there is a beginning, is there an end? Yes, the upper bound of summation, and in this case it's the 5 above sigma.
Now, why is there another k on the right side of Capital-sigma? This k tells you what, if anything, to do to the value of k before including in the summed value. So for example if it was 2k that would indicate that you multiply the value of k by the value of 2 before adding it to the other values. It could be k^2, sqrt(k), or any number of functions before adding to the sum.
This is a massive summarization of the summation operator, but there are plenty of sources of information. I've included some C# code that shows how you might implement a simple version of summation. There are more complex summation operations, but this should give you a good base understanding on which to build as you learn about machine learning.
What does the k in k=0 mean? k in k=0 is the index of summation. If you've done any coding and used arrays, then you know exactly what an index is. It is just the position in the array.
The 0 in k=0 is the lower bound of summation. In other words, the beginning of your index. If there is a beginning, is there an end? Yes, the upper bound of summation, and in this case it's the 5 above sigma.
Now, why is there another k on the right side of Capital-sigma? This k tells you what, if anything, to do to the value of k before including in the summed value. So for example if it was 2k that would indicate that you multiply the value of k by the value of 2 before adding it to the other values. It could be k^2, sqrt(k), or any number of functions before adding to the sum.
This is a massive summarization of the summation operator, but there are plenty of sources of information. I've included some C# code that shows how you might implement a simple version of summation. There are more complex summation operations, but this should give you a good base understanding on which to build as you learn about machine learning.
Summation Only Example