To my knowledge, there does not exist a mathematical fefinition of Big Data in the world. I have paid attention to it since 2012 see, my “a Mathematical foundation of big data”.
No mathematicians nor computer scientists have introduced a Mathematical Definition of Big Data. This is the reason why I raises this question here.
At the moment, I like to use 10 Bigs (see Big data with ten big characteristics) as data elements to propose a Mathematical Definition of Big Data. This definition is based on integration of calculus, logic and alegbra. For example, partly, a Mathematical Definition of Big Data is based on the definition of group in algebra, and definition of limit in calculus. Only in such a way is it a real a Mathematical Definition of Big Data.
Prof Zhaohao Sun
2018-10-30
I doubt that a mathematical definition of the term "big data" makes sense as long as it does not account for the relativity of the term.
During my diploma theses in the mid of the 80's I worked on a mainframe. Each account had by default 1MB of RAM. During the programming I run into trouble with the stack size of my Prolog program, so I needed to ask for an extension of my account to 4MB. During that period 4 MB was big already.
So how can a mathematical definition be given with accounting for the current available memory sizes and processor speeds? Big is always relative to something. A strawberry is big for an ant, but small for an elephant.
Dear Thomas,
you are right, a mathematical definition of the term "big data" is based on the relativity of the term. For example, a fuzzy logic based definition of big data is certainly based on the fuzzy relativity, taking into account 10 bigs of big data. I will provide this definition soon.
"Big Data" is born out of the explosion of unstructured data (video, images, sounds, and texts as in social media posts and comments) facilitated by the internet and the proliferation of mobile devices, like smart phones, that are able to capture and share these data.
Thus, in the same way that there is no "mathematical definition" for the ubiquitously term "data," we can not assign a similar definition to "Big Data," except that Big Data has a loy of zerores attached to it. While data as we know now is limited to bytes, megabytes, gigabytes and terabytes, Big Data is represented by "monstrous bytes" in the zone of exa-, peta-, and other stratospheric prefixes.
While your common data processing applications like Excel and Access may be able to handle "data," big data requires far more robust applications and platforms for processing.
The mathematical distinction between data science and statistics is of practical relevance to your question: data science works by Gaussian distribution, while statistics works into probability.
https://www.datasciencecentral.com/profile/StephenITernyik
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