Dfind outliers in high dimension code#

Next, for certain number of points (MinPts) we calculate the reach-distance:Ĥ.Then we calculate the local reachability density of each point using below formula:ĥ. Finally, we calculate LOF Scores using below formula:.For example, for the first point if used K=3 and found the 3 nearest neighbors have distances of 1.2, 2.5 and 6.4 the k-distance for this point will be 6.4. We call the max distance to K-nearest points that we found in previous step K-distance.Selecting the right K has been discussed in the paper First we find the K-nearest neighbors of each point in dataset.The density based approaches and specially LOF approach discussed here are sensitive to densities and those approaches are more appropriate for calculating local outliers.īelow are main steps for calculating outlier score using LOF: Because they only consider the distance between point and centroid of cluster to calculate outlier score. If we chose a large threshold to capture an outlier like O2, many of the points in C1 will be counted as outliers.Ĭluster based approaches have similar problems. Because the points in cluster C1 are less dense compare to cluster C2. Distance based approaches will have problem finding an outlier like point O2. Local Outlier Factor method is discussed here using density based methods. Distance based methods in the other hand are more granular and use the distance between individual points to find outliers. Proximity based methods can be classified in 3 categories: 1) Cluster based methods 2)Distance based methods 3) Density based methodsĬluster based methods classify data to different clusters and count points which are not members of any of known clusters as outliers. In this post we briefly discuss proximity based methods and High-Dimensional Outlier detection methods. High-Dimensional Outlier Detection: Specifc methods to handle high dimensional sparse data.

Dfind outliers in high dimension code#

Information Theoretic Models: The idea of these methods is the fact that outliers increase the minimum code length to describe a data set.Cluster analysis, density based analysis and nearest neighborhood are main approaches of this kind. Proximity-based Models: The idea with these methods is to model outliers as points which are isolated from rest of observations.

PCA(Principal Component Analysis) is an example of linear models for anomaly detection. Then the distance of each data point to plane that fits the sub-space is being calculated.

Linear Models: These methods model the data into a lower dimensional sub-spaces with the use of linear correlations.

The points with low probability of membership are marked as outliers. Finally, they calculate probability of membership of each data point to calculated distribution.

Then using the expectation-maximization(EM) methods they estimate the parameters of the model.

Probabilistic and Statistical Models: These models assume specific distributions for data.

They can be used as final steps for interpreting outputs of other outlier detection methods. These are good heuristics for initial analysis of data but they don’t have much value in multivariate settings.

Z-test and Student’s t-test are examples of these statistical methods. In these types of analysis, it is assumed that values which are too large or too small are outliers.

Extreme Value Analysis: This is the most basic form of outlier detection and only good for 1-dimension data.

Charu Aggarwal in his book Outlier Analysis classifies Outlier detection models in following groups: There are several approaches for detecting Outliers. There are many modeling techniques which are resistant to outliers or reduce the impact of them, but still detecting outliers and understanding them can lead to interesting findings. We generally define outliers as samples that are exceptionally far from the mainstream of data.There is no rigid mathematical definition of what constitutes an outlier determining whether or not an observation is an outlier is ultimately a subjective exercise. One of the challenges in data analysis in general and predictive modeling in particular is dealing with outliers. This post is a summary of 3 different posts about outlier detection methods.