Very cool! I'd love to know what the full set of variables were and what the PCA scree plot looked like. Looking at this with a large sample of amateur players would also be neat, especially if you could do some clustering.
Nice work. Since the criteria are here given ad hoc (by hand) I'm wondering whether this study could be extended to a larger machine learning project where a neural network would find the statistical factors (criteria) itself which have the strongest correlations among players. And then explain us what these are! :)
How did you normalize or construct the variables? I've always found that those choiced can have an influence (sometimes far too much influence) on a PCA.
I scaled the data to have mean 0 and variance 1 before using the PCA. The variables are the relative number of times something occurs per move or per game. For example, I use the relative number of captures in a game
Forgot to mention trying 3D for that group that in 2D seems to be disjoint potatoes, if you can adjust the parameters to get 3 contributing there might be some hope.
but it might be essentially non-linear problem. Disjoint groupings, if it were just a 2D problem and wanting a smooth partition of all the classes, would suggest using some non-linear transformations of the input space to get better class separation. My intuition here. I am thinking the donut or XOR exemplar problem. But this is about topology of the parts in a classification partition over the input space.
I'll look into more dimensions in the future, as this was just a first test I wanted to keep it simple with two dimensions, especially since I felt that the third dimension didn't contribute too much, at least from what I saw
"my views of the players". Do you mean your hypothesis of classification of players according to your hypothesis or detectable styles finite set?
I have read once. I have made comments. but deleted them. I will comment again later.
but I find that I am hungry for more of the full data set characteristics. How may game, etc..
I gues I am curious if this can be turn into a classification prediction problem.
In which case one coudl try given the full set problem to use "non" parametric methods (PCA might not be it, but NN are). NN would be able to detect both most dispersed and most important to your classification problem/hypothesis.
the hypothesis being in part that your have 3 classes that act as labels for the player ID groups of games all combined into a single point on the PCA 2D plot.
see we might need more visuals about the full set problem. I am not sure to have it in mind riht now. I coudl induce, I guess. what does a data point represent. back to chess games.
PCA here is unaware of the label data it was a reduction based only of maximal dispersion.
But there is another "angle" maximal "information" about the reality of styles.
You could do no label clustering on one hand. To see if there might not be emerging classes that you did not consider. That could be another theory of style. what do those give.
There is also the prediction problem where the full set data understanding might help, in assessing if you have enough data to make crossvalidation testing or even a prediction problem itself.
I guess those are my main line of commenting. curious about knowing more of the full set as the other commenter. clustering withiout labels (might not make good graphs but might stil help you in the direction of most clustering like you want).
I guess the elephant problem is what is "style". well. you have one hypothesis. what is the supporting clues for that specific one? Chess culture literature or knowledge? It does not have to, just curious.
For the prediciton problem, it would be about trainging with all players, and omitting one. and then testing on that one. and then doing that many times, changing the test one.
Then you could try amputation in the feature space, if you have some hierarchical groupings of the features themselves, like some clues about wihich ones might be redundant with other or have nothing at all with each other. you could amputate a hole group of similar dimeanions and see if the same training and testing method (using same non-parametric model like NN), and then compare the predicitno metrics tables.
You might not even have any of those to have graet results individually, but find comparative chenages in the amputations. I think I would need again more understanding of the full set data.
Very cool! I'd love to know what the full set of variables were and what the PCA scree plot looked like. Looking at this with a large sample of amateur players would also be neat, especially if you could do some clustering.
Nice work. Since the criteria are here given ad hoc (by hand) I'm wondering whether this study could be extended to a larger machine learning project where a neural network would find the statistical factors (criteria) itself which have the strongest correlations among players. And then explain us what these are! :)
So cool! Each for different reasons I’d love to see where Lasker, Alekhine, Reshevsky, Larsen, Korchnoi wind up
One fascinating player whose style is often misunderstood is Najdorf. I would be really curious to see where your model places him.
I haven't seen many games by Najdorf, how would you describe his style?
I'd say he was aggressive and dynamic, but relying on strong intuition and positional sacrifices instead of heavy calculation
One fascinating player whose style is often misunderstood is Najdorf. I would be really curious to see where your model places him
How did you normalize or construct the variables? I've always found that those choiced can have an influence (sometimes far too much influence) on a PCA.
I scaled the data to have mean 0 and variance 1 before using the PCA. The variables are the relative number of times something occurs per move or per game. For example, I use the relative number of captures in a game
Forgot to mention trying 3D for that group that in 2D seems to be disjoint potatoes, if you can adjust the parameters to get 3 contributing there might be some hope.
but it might be essentially non-linear problem. Disjoint groupings, if it were just a 2D problem and wanting a smooth partition of all the classes, would suggest using some non-linear transformations of the input space to get better class separation. My intuition here. I am thinking the donut or XOR exemplar problem. But this is about topology of the parts in a classification partition over the input space.
I'll look into more dimensions in the future, as this was just a first test I wanted to keep it simple with two dimensions, especially since I felt that the third dimension didn't contribute too much, at least from what I saw
"my views of the players". Do you mean your hypothesis of classification of players according to your hypothesis or detectable styles finite set?
I have read once. I have made comments. but deleted them. I will comment again later.
but I find that I am hungry for more of the full data set characteristics. How may game, etc..
I gues I am curious if this can be turn into a classification prediction problem.
In which case one coudl try given the full set problem to use "non" parametric methods (PCA might not be it, but NN are). NN would be able to detect both most dispersed and most important to your classification problem/hypothesis.
the hypothesis being in part that your have 3 classes that act as labels for the player ID groups of games all combined into a single point on the PCA 2D plot.
see we might need more visuals about the full set problem. I am not sure to have it in mind riht now. I coudl induce, I guess. what does a data point represent. back to chess games.
PCA here is unaware of the label data it was a reduction based only of maximal dispersion.
But there is another "angle" maximal "information" about the reality of styles.
You could do no label clustering on one hand. To see if there might not be emerging classes that you did not consider. That could be another theory of style. what do those give.
There is also the prediction problem where the full set data understanding might help, in assessing if you have enough data to make crossvalidation testing or even a prediction problem itself.
I guess those are my main line of commenting. curious about knowing more of the full set as the other commenter. clustering withiout labels (might not make good graphs but might stil help you in the direction of most clustering like you want).
I guess the elephant problem is what is "style". well. you have one hypothesis. what is the supporting clues for that specific one? Chess culture literature or knowledge? It does not have to, just curious.
For the prediciton problem, it would be about trainging with all players, and omitting one. and then testing on that one. and then doing that many times, changing the test one.
Then you could try amputation in the feature space, if you have some hierarchical groupings of the features themselves, like some clues about wihich ones might be redundant with other or have nothing at all with each other. you could amputate a hole group of similar dimeanions and see if the same training and testing method (using same non-parametric model like NN), and then compare the predicitno metrics tables.
You might not even have any of those to have graet results individually, but find comparative chenages in the amputations. I think I would need again more understanding of the full set data.