# [SciPy-user] KDE question

David Cournapeau david@ar.media.kyoto-u.ac...
Thu Nov 15 22:13:58 CST 2007

Robert Kern wrote:
> David Cournapeau wrote:
>
>
>> For kernel estimators, you assume each component is the same 'shape', (I
>> mean same covariance matrix) right ?
>>
>
> This is the only form that has been implemented, yes. Fancier implementations
> can adapt the covariance matrix (in KDE jargon, "bandwidth") of the kernels to
> take into account the properties of the local neighborhood. However, this is
> usually only done in 1-D because N-D sorting is hard.
>
>
>> Maybe this make the computation
>> feasible (find all the points such as sum_i{a_i f(x - \mu_i)} = cst) ?
>>
>
> That boils down to evaluating on the grid again, I think.
>
Yes, sorry, I was stupid. That's the different locations which matters,
having the same shape for each Gaussian does not help that much. For one
component case, the thing which makes it easy it that pdf = cst boils
down to a "quadratic form involving the samples = constant". For
multiple components, this does not seem feasible anymore.

cheers,

David