Which aspect of mathematics does the Mahalanobis distance method belong to?

Here's what I'm looking for: the description is statistical, just look at the books on statistics (I studied statistics at Tongji University, which is not bad).

The Mahalanobis distance was developed by Indian statistician P. Maharanobis c.mahalanobis), which represents the covariance distance of the data.

It is an effective way to calculate the similarity of two sets of unknown samples. Unlike Euclidean distance, it takes into account the connection between various properties (e.g., a piece of information about height leads to a piece of information about weight, because the two are related) and is scale-invariant, i.e. independent of the scale of measurement.

For a multivariate vector with a mean of covariance matrix of , the Mahalanobis distance is .

The Mahalanobis distance can also be defined as the degree of difference between two random variables that obey the same distribution and whose covariance matrix is

If the covariance matrix is an identity matrix, then the Mahalanobis distance is simplified to a Euclidean distance, and if the covariance matrix is a diagonal matrix, it can also be called a normalized Euclidean distance'.

where i is the standard deviation of xi.

What is the Marhalanobis distance discriminant method.

The Mahalanobis distance was proposed by the Indian statistician Maharanobis () and represents the covariance distance of the data. It is an effective way to calculate the similarity of two sets of unknown samples. Unlike Euclidean distance, it takes into account the connections between various properties (e.g.

A piece of information about height leads to a piece of information about weight, because the two are related) and is scale-invariant, i.e. independent of the scale of measurement. For a multivariate vector with a mean of covariance and a matrix of covariance, the Mahalanobis distance can also be defined as the degree of difference between two random variables that obey the same distribution and whose covariance matrix is'.

where i is the standard deviation of xi.

You don't need to know which distance it is here... After you make it, find the coefficients and multiply them with the corresponding independent variables to get the discriminant discriminant and know the critical value y0. Y0 can be obtained by adding all the y-values of a known grouping and dividing by the number.

Taking the two groups as an example, when the mean value of the first group is greater than the mean value of the second group, then when the sample is substituted into the discriminant formula, if y is greater than y0, it is judged to be the first group. Otherwise, it will be judged as the second group.

If you don't understand, you can hi me.

After completing the Fisher discriminant analysis, SPSS will give the canonical discriminant function coefficients and the Mahalanobis distance of the function at each type of centroid.

Euclidean, the most common, geometric math mostly uses this, which is the true distance between two points in an m-dimensional space. The same 2 points A and B, regardless of how the spatial coordinate system is defined, the distance is the same. The Mahalanobis distance is the covariance distance of the data, and the calculation is related to the population sample, the same two samples A and B, put into two different populations, and the final calculated Mahalanobis distance between the two samples is generally not the same, unless the covariance matrix of the two populations is the same;

Matrices are a common tool in advanced algebra and are also commonly found in applied mathematics disciplines such as statistical analysis. In physics, matrices have applications in circuits, mechanics, optics, and quantum physics; In computer science, 3D animation also requires the use of matrices. The operation of matrices is an important problem in the field of numerical analysis.

Decomposing matrices into combinations of simple matrices can simplify the operation of matrices in theory and practical applications. For some matrices with wide applications and special forms, such as sparse matrices and quasi-diagonal matrices, there are specific fast operation algorithms. For the development and application of matrix-related theory, please refer to Matrix Theory.

In the fields of astrophysics, quantum mechanics, etc., infinite-dimensional matrices will also appear, which is a kind of generalization of matrices.