Yes, your suggestion is viable, but I have not seen any algorithms in
sklearn that use y like that in fit method.
> I would have thought in the case of Mahalanobis distances that transform
> would transform each feature such that the resulting feature space was
> Euclidean.
Exactly. Thus, methods that use usual L2 distance (like KMeans) will be
effectively using those custom metrics.
Also, one can do the kernel trick to get a metric for a non-linear
transformation.
On Thu, Mar 19, 2015 at 5:35 AM, Joel Nothman <joel.noth...@gmail.com>
wrote:
> I don't know a lot about metric learning either, but it sounded like from
> your initial statement that fit(X, D) where D is the target/known distance
> between each point in X might be appropriate. I have no idea if this is how
> it is formulated in the literature (your mention of asymmetric metrics
> means it might be), but it seems an intuitive representation of the problem.
>
> Your suggestion of "similar" and "dissimilar" groups could be represented
> by D being a symmetric matrix with some distances 1 (dissimilar) and others
> 0 (similar), but you imply that some or the majority of cells would be
> unknown (in which case a sparse D interpreting all non-explicit values as
> unknown may be appropriate).
>
> I would have thought in the case of Mahalanobis distances that transform
> would transform each feature such that the resulting feature space was
> Euclidean.
>
> On 19 March 2015 at 08:47, Andreas Mueller <t3k...@gmail.com> wrote:
>
>> In summary, I think this does look like a good basis for a proposal :)
>>
>>
>>
>> On 03/18/2015 05:14 PM, Artem wrote:
>>
>>
>>> Do you think this interface would be useful enough?
>>
>> One of mentioned methods (LMNN) actually uses prior knowledge in exactly
>> the same way, by comparing labels' equality. Though, it was designed to
>> facilitate KNN.
>>
>> Authors of the other one (ITML) explicitly mention in the paper that one
>> can construct those sets S and D from labels.
>>
>> Do you think it would make sense to use such a transformer in a pipeline
>>> with a KNN classifier?
>>> I feel that training both on the same labels might be a bit of an issue
>>> with overfitting
>>
>> Pipelining looks like a good way to combine these methods, but
>> overfitting could be a problem, indeed.
>> Not sure how severe it can be.
>>
>> On Wed, Mar 18, 2015 at 10:07 PM, Andreas Mueller <t3k...@gmail.com>
>> wrote:
>>
>>>
>>> On 03/18/2015 02:53 PM, Artem wrote:
>>>
>>> I mean that if we were solving classification, we would have y that
>>> tells us which class each example belongs to. So if we pass this
>>> classification's ground truth vector y to metric learning's fit, we can
>>> form S and D inside by saying that observations from the same class should
>>> be similar.
>>>
>>> Ah, I got it now.
>>>
>>>
>>>
>>>> Only being able to "transform" to a distance to the training set is a
>>>> bit limiting
>>>
>>> Sorry, I don't understand what you mean by this. Can you elaborate?
>>>
>>>
>>> The metric does not memorize training samples, it finds a (linear
>>> unless kernelized) transformation that makes similar examples cluster
>>> together. Moreover, since the metric is completely determined by a PSD
>>> matrix, we can compute its square root, and use to transform new data
>>> without any supervision.
>>>
>>> Ah, I think I misunderstood your proposal for the transformer
>>> interface. Never mind.
>>>
>>>
>>> Do you think this interface would be useful enough? I can think of a
>>> couple of applications.
>>> It would definitely fit well into the current scikit-learn framework.
>>>
>>> Do you think it would make sense to use such a transformer in a pipeline
>>> with a KNN classifier?
>>> I feel that training both on the same labels might be a bit of an issue
>>> with overfitting.
>>>
>>>
>>>
>>>
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