Coursera Machine Learning Notes (vii)

Mainly for the ninth week content: Anomaly detection, recommendation system

(i) Anomaly detection (DENSITY estimation)

kernel density estimation ( Kernel density estimation X (1) , X (2) ,.., x (m) If the data set is normal, we want to know the new data X (test) p (x)

After density estimation, it is a common method to select a probability threshold to determine whether it is an anomaly, which is often used in anomaly detection. Such as:

1. Gaussian distribution

   The Gaussian kernel function is the kernel function commonly used in kernel density estimation. The one-element Gaussian probability density function is:

   You can use the data you already have to predict the overall μ and the σ2 The calculation method is as follows:

   The probability density function of the multivariate Gaussian distribution is:

   Note: For variance in machine learning we usually divide by m rather than statistically ( m-1 ).

2. Anomaly Detection

   in a general Gaussian distribution model, for a given data set x (1), X (2),..., x (m) , we want to calculate for each feature μ and the σ2 estimates, based on the model calculation p (x) :

   As shown in the following:

   for the multivariate Gaussian distribution model, First we calculate the average of all the features, then we calculate the covariance matrix, and finally we calculate the p (x)of the multivariate Gaussian distribution:

(b) Referral system

Based on content

Based on user

Http://www.ccf.org.cn/resources/1190201776262/2010/05/12/h049617016.pdf

Coursera Machine Learning Notes (vii)