Reprinted from: https://www.cnblogs.com/chaosimple/p/3182157.html
Variance and standard deviation is generally used to describe one-dimensional data
It is used to describe two-dimensional data covariance
Covariance matrix used to describe the two-dimensional data and above
Covariance for the correlation between the data
Mathematical Expectation
Why mention expect it, there is definitely a relationship of le. Come, come, first a brief review of the mathematical expectation under the relevant knowledge.
- Mathematical expectation of
all discrete random variable with possible values xi corresponding probability Pi (= xi) the product of the mathematical expectation and called the discrete random variables (set series absolute convergence), denoted by E (x) . One of the most basic mathematical characteristics of random variables. It reflects the average value of the random variable size. Also known as expected or mean.
If the distribution function of the random variable X F (x) can be expressed as a non-negative integrable function f (x) is the integral, then X is a continuous random variable, f (x) is called the probability density function of X (the distribution density function). - Variance
Variance is the average squared difference from the mean of each data. In probability theory and statistics, the variance (English Variance) is used to measure the random variables and its mathematical expectation (ie mean) between the degree of deviation. In many practical problems, the degree of deviation between research and mean random variables has a very important significance.
Variance characterizes the value of the random variable discrete degree for its mathematical expectation.
Covariance
Standard deviation and variance are generally used to describe the one-dimensional data, but in real life we often encounter data sets containing multidimensional data, the simplest is inevitably subject to multiple statistical test scores when we go to school. Faced with this data set, we can follow an independent course of calculating the variance of each dimension, but usually we want to know more, for example, a degree of wretched boy with his degree welcomed by the girls if there is some connection. Covariance is such a statistic used to measure the relationship between two random variables, we can define modeled variance:
To measure the extent of the respective dimensions deviate from its mean, covariance can be defined so that:
The results of covariance what is it? If the result is positive, then the two are positively correlated (from covariance can lead to the definition of "correlation coefficient" a), that is to say a person the more wretched the more welcomed by the girls. If the result is negative, it means the two are negatively correlated, the more annoying the more wretched girl. If 0, there is no relationship between the two, and wretched is not wretched girls like it or not is no correlation between, that is to say statistically "independent."
From the definition of the covariance we can see some obvious nature, such as:
Covariance matrix
Wretched and popular issues mentioned above is a typical two-dimensional problem, and covariance can only handle two-dimensional problem, and that dimension more naturally need to calculate multiple covariance, such as n-dimensional data set is required computing a covariance, that we naturally think of using a matrix to organize the data. It gives the covariance matrix is defined:
This definition is very easy to understand, we can give a three-dimensional example, assume that the data set has three dimensions, the covariance matrix:
Seen, the covariance matrix is a symmetric matrix, and the diagonal is the variance of each dimension
Other blog: Links in this: http://blog.csdn.net/itplus/article/details/11452743