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K Nearest Neighbour with different distance matrix to each datapoint

0

$begingroup$

I'm wondering if there is library support in python (such as sklearn) for doing KNN on a data set that has a custom distance matrix (positive definite) for each data point (x is a query point, $x_i$ is a data set point):
$$
d(x,x_i) = (x-x_i)^TQ_i(x-x_i)
$$

I know that for a fixed positive definite matrix for all data points, this is a metric that I can transform into
$$
Q = A^TA

d(x,x_i) = (Ax - Ax_i)^T(Ax - Ax_i)
$$
Which I can compute via normal KNN by first transforming the input space via multiplying $A$.

My problem of having a separate matrix for each data point came up because I have a covariance around the neighbourhood of each point. KNN can then be interpreted as what are the most likely neighbourhoods this query point lies in. If a neighbourhood doesn't vary along a dimension then we should penalize difference along that dimension highly in terms of increasing distance.

machine-learning scikit-learn distance k-nn

share|improve this question

asked 16 mins ago

LemonPiLemonPi

101

New contributor

LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

0

$begingroup$

I'm wondering if there is library support in python (such as sklearn) for doing KNN on a data set that has a custom distance matrix (positive definite) for each data point (x is a query point, $x_i$ is a data set point):
$$
d(x,x_i) = (x-x_i)^TQ_i(x-x_i)
$$

I know that for a fixed positive definite matrix for all data points, this is a metric that I can transform into
$$
Q = A^TA

d(x,x_i) = (Ax - Ax_i)^T(Ax - Ax_i)
$$
Which I can compute via normal KNN by first transforming the input space via multiplying $A$.

My problem of having a separate matrix for each data point came up because I have a covariance around the neighbourhood of each point. KNN can then be interpreted as what are the most likely neighbourhoods this query point lies in. If a neighbourhood doesn't vary along a dimension then we should penalize difference along that dimension highly in terms of increasing distance.

machine-learning scikit-learn distance k-nn

share|improve this question

asked 16 mins ago

LemonPiLemonPi

101

New contributor

LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

I'm wondering if there is library support in python (such as sklearn) for doing KNN on a data set that has a custom distance matrix (positive definite) for each data point (x is a query point, $x_i$ is a data set point):
$$
d(x,x_i) = (x-x_i)^TQ_i(x-x_i)
$$

I know that for a fixed positive definite matrix for all data points, this is a metric that I can transform into
$$
Q = A^TA

d(x,x_i) = (Ax - Ax_i)^T(Ax - Ax_i)
$$
Which I can compute via normal KNN by first transforming the input space via multiplying $A$.

My problem of having a separate matrix for each data point came up because I have a covariance around the neighbourhood of each point. KNN can then be interpreted as what are the most likely neighbourhoods this query point lies in. If a neighbourhood doesn't vary along a dimension then we should penalize difference along that dimension highly in terms of increasing distance.

machine-learning scikit-learn distance k-nn

share|improve this question

asked 16 mins ago

LemonPiLemonPi

101

New contributor

LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

asked 16 mins ago

LemonPiLemonPi

101

New contributor

LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 16 mins ago

LemonPiLemonPi

101

New contributor

LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 16 mins ago

LemonPiLemonPi

101

New contributor

LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 16 mins ago

LemonPiLemonPi

101