多元高斯分布公式的实现 [英] Multivariate Gaussian distribution formula implementation

问题描述

在实现用于检测异常的多元高斯分布时，我遇到了一个问题.

I have a certain problem while implementing multivariate Gaussian distribution for anomaly detection.

我已经参考了吴国栋笔记中的公式

I have referred the formula from Andrew Ng notes

http://www.holehouse.org/mlclass/15_Anomaly_Detection.html

以下是我面临的问题

假设我有一个具有2个特征和m个训练集的数据集，即n = 2，并且想确定我的多元高斯概率p(x; mu; sigma)，它应该是[m * 1]矩阵，因为通过特征相关产生估计的高斯值.

Suppose I have a data set with 2 features and m number of training set i.e n=2 and wants to determine my multivariate Gaussian probability p(x;mu;sigma) which should be a [m*1] matrix because it produces estimated Gaussian value by feature correlation.

我面临的问题是我无法使用公式来生成矩阵[m * 1].

The problem I face is I am unable to use the formula to produce the matrix [m*1].

我正在使用Octave作为IDE来开发算法.

I am using Octave as IDE to develop the algorithm.

下面是展示我的问题的快照

Below is a snapshot showcasing my problem

考虑红色边界方程的乘法，因为红色边界的LHS只是一个实数

Considering the multiplication of the Red boundary equation because the LHS of the red boundary is just a real number

请帮助我理解我错误的地方

PLEASE HELP ME UNDERSTAND WHERE AM I GOING WRONG

谢谢

推荐答案

我认为尺寸不正确.

让我们假设您有一个 m 个实例的二维( n = 2 )数据.我们可以在MATLAB中将这些数据存储为 n-by-m 矩阵(列是数据实例，行代表要素/维度).在这种情况下，我们有:

Let's assume you have a 2-dimensional (n=2) data of m instances. We can store this data as a n-by-m matrix in MATLAB (columns are data instances, rows represent features/dimensions). In this case we have:

• X 大小为 nxm 的数据矩阵，每个实例 x = X(:，i)是大小为的向量nx1 (在我们的惯例中为列向量).
• mu 是均值向量( mu = mean(X，2)).这也是与实例 nx1 大小相同的列向量.
• sigma 是协方差矩阵( sigma = cov(X.')).它的大小为 nxn (描述每个维度如何彼此变化).

• X the data matrix of size nxm, each instance x = X(:,i) is a vector of size nx1 (column vector in our convention).
• mu is the mean vector (mu = mean(X,2)). This is also a column vector of same size as an instance nx1.
• sigma is the covariance matrix (sigma = cov(X.')). It has size nxn (it describes how each dimensions co-vary with each other dimension).

因此，以红色突出显示的部分涉及以下尺寸的表达式:

So the part that you highlighted in red involves expressions of the following sizes:

 = ([nx1] - [nx1])' * [nxn] * ([nx1] - [nx1])
 = [1xn] * [nxn] * [nx1]
 = 1x1

这篇关于多元高斯分布公式的实现的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！