K Nearest Neighbour with different distance matrix to each datapoint
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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
asked 7 mins ago
LemonPiLemonPi
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$begingroup$
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
asked 7 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
asked 7 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.
$endgroup$
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
machine-learning scikit-learn distance k-nn
asked 7 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 7 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 7 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 7 mins ago
LemonPiLemonPi
101
asked 7 mins ago
LemonPiLemonPi
101
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.
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.
LemonPi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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