Calculating Mahalanobis parameters from x data
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Roughly speaking, the Mahalanobis distance $d(x) = sqrt{(x - mu)^T * Sigma^{-1} * (x - mu)}$ is the distance between a multivariate Gaussian distribution ($mu$, $Sigma$) and a point. If the Gaussian distribution represents a class, we can classify new points by choosing the class with the minimum distance.
I'm giving an N*D trained data as class data, and I need to calculate mu and inverse of Sigma.
Estimates the parameters for the mahalanobis distance for a specific class.
:param x_class: a (n x d) numpy array, containing n samples with d features coresponding to a specific class.
:return: tuple of (mu, inv_Si)
where mu is a (d,) numpy array
inv_Si is a (d, d) numpy array.
linear-algebra python mahalanobis-distance
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
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add a comment |
$begingroup$
Roughly speaking, the Mahalanobis distance $d(x) = sqrt{(x - mu)^T * Sigma^{-1} * (x - mu)}$ is the distance between a multivariate Gaussian distribution ($mu$, $Sigma$) and a point. If the Gaussian distribution represents a class, we can classify new points by choosing the class with the minimum distance.
I'm giving an N*D trained data as class data, and I need to calculate mu and inverse of Sigma.
Estimates the parameters for the mahalanobis distance for a specific class.
:param x_class: a (n x d) numpy array, containing n samples with d features coresponding to a specific class.
:return: tuple of (mu, inv_Si)
where mu is a (d,) numpy array
inv_Si is a (d, d) numpy array.
linear-algebra python mahalanobis-distance
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
$endgroup$
1
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What are your thoughts? What have you tried? You cannot "calculate" these parameters, you can only estimate them from data. Which estimator are you using? MLE?
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– angryavian
Jan 7 at 22:39
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@angryavian I didn't think about any estimator.. didn't even understand the problem. Can you show me how to estimate them using MLE for example ?
$endgroup$
– andre ahmed
Jan 7 at 22:42
$begingroup$
I'm using EmpiricalCovariance, I get correct mu but inverse of covariance is wrong
$endgroup$
– andre ahmed
Jan 7 at 23:46
add a comment |
$begingroup$
Roughly speaking, the Mahalanobis distance $d(x) = sqrt{(x - mu)^T * Sigma^{-1} * (x - mu)}$ is the distance between a multivariate Gaussian distribution ($mu$, $Sigma$) and a point. If the Gaussian distribution represents a class, we can classify new points by choosing the class with the minimum distance.
I'm giving an N*D trained data as class data, and I need to calculate mu and inverse of Sigma.
Estimates the parameters for the mahalanobis distance for a specific class.
:param x_class: a (n x d) numpy array, containing n samples with d features coresponding to a specific class.
:return: tuple of (mu, inv_Si)
where mu is a (d,) numpy array
inv_Si is a (d, d) numpy array.
linear-algebra python mahalanobis-distance
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
$endgroup$
Roughly speaking, the Mahalanobis distance $d(x) = sqrt{(x - mu)^T * Sigma^{-1} * (x - mu)}$ is the distance between a multivariate Gaussian distribution ($mu$, $Sigma$) and a point. If the Gaussian distribution represents a class, we can classify new points by choosing the class with the minimum distance.
I'm giving an N*D trained data as class data, and I need to calculate mu and inverse of Sigma.
Estimates the parameters for the mahalanobis distance for a specific class.
:param x_class: a (n x d) numpy array, containing n samples with d features coresponding to a specific class.
:return: tuple of (mu, inv_Si)
where mu is a (d,) numpy array
inv_Si is a (d, d) numpy array.
linear-algebra python mahalanobis-distance
linear-algebra python mahalanobis-distance
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
asked Jan 7 at 22:31
andre ahmedandre ahmed
61
61
1
$begingroup$
What are your thoughts? What have you tried? You cannot "calculate" these parameters, you can only estimate them from data. Which estimator are you using? MLE?
$endgroup$
– angryavian
Jan 7 at 22:39
$begingroup$
@angryavian I didn't think about any estimator.. didn't even understand the problem. Can you show me how to estimate them using MLE for example ?
$endgroup$
– andre ahmed
Jan 7 at 22:42
$begingroup$
I'm using EmpiricalCovariance, I get correct mu but inverse of covariance is wrong
$endgroup$
– andre ahmed
Jan 7 at 23:46
add a comment |
1
$begingroup$
What are your thoughts? What have you tried? You cannot "calculate" these parameters, you can only estimate them from data. Which estimator are you using? MLE?
$endgroup$
– angryavian
Jan 7 at 22:39
$begingroup$
@angryavian I didn't think about any estimator.. didn't even understand the problem. Can you show me how to estimate them using MLE for example ?
$endgroup$
– andre ahmed
Jan 7 at 22:42
$begingroup$
I'm using EmpiricalCovariance, I get correct mu but inverse of covariance is wrong
$endgroup$
– andre ahmed
Jan 7 at 23:46
1
1
$begingroup$
What are your thoughts? What have you tried? You cannot "calculate" these parameters, you can only estimate them from data. Which estimator are you using? MLE?
$endgroup$
– angryavian
Jan 7 at 22:39
$begingroup$
What are your thoughts? What have you tried? You cannot "calculate" these parameters, you can only estimate them from data. Which estimator are you using? MLE?
$endgroup$
– angryavian
Jan 7 at 22:39
$begingroup$
@angryavian I didn't think about any estimator.. didn't even understand the problem. Can you show me how to estimate them using MLE for example ?
$endgroup$
– andre ahmed
Jan 7 at 22:42
$begingroup$
@angryavian I didn't think about any estimator.. didn't even understand the problem. Can you show me how to estimate them using MLE for example ?
$endgroup$
– andre ahmed
Jan 7 at 22:42
$begingroup$
I'm using EmpiricalCovariance, I get correct mu but inverse of covariance is wrong
$endgroup$
– andre ahmed
Jan 7 at 23:46
$begingroup$
I'm using EmpiricalCovariance, I get correct mu but inverse of covariance is wrong
$endgroup$
– andre ahmed
Jan 7 at 23:46
add a comment |
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$begingroup$
What are your thoughts? What have you tried? You cannot "calculate" these parameters, you can only estimate them from data. Which estimator are you using? MLE?
$endgroup$
– angryavian
Jan 7 at 22:39
$begingroup$
@angryavian I didn't think about any estimator.. didn't even understand the problem. Can you show me how to estimate them using MLE for example ?
$endgroup$
– andre ahmed
Jan 7 at 22:42
$begingroup$
I'm using EmpiricalCovariance, I get correct mu but inverse of covariance is wrong
$endgroup$
– andre ahmed
Jan 7 at 23:46