# Functional dependency in Support Vector Machine input

I'm currently training a support vector machine with a second order Markov transition matrix. These probabilities are taken from a computer image, and are the probabilities of adjacent pixels having the difference between them being specific values - so each value can be represented as a fraction $a/b$, where a and b are the cardinality of sets.

Now, I've come across a curious phenomenon, which I'm trying to explain. I can remove a significant part of my input features with no loss in the accuracy of the support vector machine.

My current theory as for why this occurs is because there are functional dependencies between certain statistics. For example, the statistics for one sample might be

$(n_1/d_1, n_1/d_2, n_2/d_2, n_2/d_3, n_3/d_3, n_3/d_4, n_4/d_4, \dots, n_n/d_1)$

Each $d_i$ is used seven times in total, whilst each $n_1$ is used either once (all parameters identical) or twice.

Now, I'm not as familiar with support vector machines as many, so I'd like to ask - is there a theorem or something which would confidently allow me to state that the above feature set is no better a feature set than:

$(n_1/d_1, n_2/d_2, n_3/d_3, n_4/d_4, \dots, n_n, d/n)$ in terms of the constructed hyperplane?

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