By de-correlation, the multi variate distribution can be the product of independent univariate distributions.
Pattern Recognition and Machine Learning (Christopher Bishop) - 2.3 The Gaussian Distribution
By de-correlation, the multi variate distribution can be the product of independent univariate distributions.
Pattern Recognition and Machine Learning (Christopher Bishop) - 2.3 The Gaussian Distribution
Which one, A or B, is closer to the mean inof the distribution, or conversely which is more remote outlier to the distribution.
The eigenvectors $u_i$ tell the directions of the dispersions, and the eigenvalues $\lambda_i$ tell the variances of the dispersions. Higher eigenvalue means larger variance. Then if I scale the space by $\frac {1}{\sqrt{\lambda_A}}$ in the A direction and $\frac {1}{\sqrt{\lambda_B}}$ in the B direction, I can decide which is nearclose to the mean by comparing:
- What is Mahalanobis distance?
- Mahalanobis Distance
- 5 Multivariate Normal Distribution (slides not the transcript)
- Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?
- STAT 505 Applied Multivariate Statistical Analysis - 4.6 - Geometry of the Multivariate Normal Distribution
- (PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)
- Deriving the formula for multivariate Gaussian distribution
- Pattern Recognition and Machine Learning (Christopher Bishop) - 2.3 The Gaussian Distribution
Which one, A or B, is closer to the mean in the distribution, or conversely which is more remote outlier to the distribution.
The eigenvectors $u_i$ tell the directions of the dispersions, and the eigenvalues $\lambda_i$ tell the variances of the dispersions. Higher eigenvalue means larger variance. Then if I scale the space by $\frac {1}{\sqrt{\lambda_A}}$ in the A direction and $\frac {1}{\sqrt{\lambda_B}}$ in the B direction, I can decide which is near to the mean by comparing:
- What is Mahalanobis distance?
- Mahalanobis Distance
- 5 Multivariate Normal Distribution (slides not the transcript)
- Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?
- STAT 505 Applied Multivariate Statistical Analysis - 4.6 - Geometry of the Multivariate Normal Distribution
- Deriving the formula for multivariate Gaussian distribution
- Pattern Recognition and Machine Learning (Christopher Bishop) - 2.3 The Gaussian Distribution
Which one, A or B, is closer to the mean of the distribution, or conversely which is more remote outlier to the distribution.
The eigenvectors $u_i$ tell the directions of the dispersions, and the eigenvalues $\lambda_i$ tell the variances of the dispersions. Higher eigenvalue means larger variance. Then if I scale the space by $\frac {1}{\sqrt{\lambda_A}}$ in the A direction and $\frac {1}{\sqrt{\lambda_B}}$ in the B direction, I can decide which is close to the mean by comparing:
- What is Mahalanobis distance?
- Mahalanobis Distance
- 5 Multivariate Normal Distribution (slides not the transcript)
- Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?
- STAT 505 Applied Multivariate Statistical Analysis - 4.6 - Geometry of the Multivariate Normal Distribution
- (PP 6.7) Geometric intuition for the multivariate Gaussian (part 2)
- Deriving the formula for multivariate Gaussian distribution
- Pattern Recognition and Machine Learning (Christopher Bishop) - 2.3 The Gaussian Distribution