outliers-lizia

Simple librery to remove outliers from data

Installation

npm install outliers-lizia

Usage

const res = outliers([1, 2, 1, 2, 3, 3, 2, 1, 2, 3, 100], 1, 1.6, 1)
/**
[1, 2, 1, 2, 3, 3, 2, 1, 2, 3]
*/
assert(res.length === 10);

API

outliers-lizia -> {outliersRemoving, getStats}

outliersRemoving(arrayOfData = [] [, dim = 1, numSigma = 1.645, dg = 0, timeSeries])

arrayOfData = [x_{1}, x_{2}, x_{3}, ...,x_{NxD}] - Data to be analysed and remove the outliers, where N is the number of observvations and D the dimension of every observation.

dim = Number - Default value is 1, and is the number of dimensions of observations.

numSigma = Number - Default value is 1.645 and is the number of sigma to be used in the filter of outliers removing.

dg = Number - Default value is zero and is the parameter used to calculate the SD. Example: SD^2= Sum((x_i- E{x})^2/(N-dg))

timeSeries = Number || Array || Function - this is the value what will be used like average of data, can be a number if dimensions is 1, a array constant if dim is greater than 1, can be a function if is a time serie.

*If is a function: timeSeries(datum, index, numberDatum) -> Number

datum = [x_1,...,x_D]

index = Number - is the index of datum, index is a number in range [0,D-1]. This function is evaluated D times.

numberDatum = Number - is the index of datum in data sets given, numberDatum is a number in range [0,N-1].

getStats(data, [dim = 1, dg = 0, timeSeries])

data = [x_{1}, x_{2}, x_{3}, ...,x_{NxD}] - Data to be analysed and remove the outliers, where N is the number of observvations and D the dimension of every observation.

dim = Number - Default value is 1, and is the number of dimensions of observations.

numSigma = Number - Default value is 1.645 and is the number of sigma to be used in the filter of outliers removing.

dg = Number - Default value is zero and is the parameter used to calculate the SD. Example: SD^2= Sum((x_i- E{x})^2/(N-dg))

timeSeries = Number || Array || Function - this is the value what will be used like average of data, can be a number if dimensions is 1, a array constant if dim is greater than 1, can be a function if is a time serie.

*If is a function: timeSeries(datum, index, numberDatum) -> Number

datum = [x_1,...,x_D]

index = Number - is the index of datum, index is a number in range [0,D-1]. This function is evaluated D times.

numberDatum = Number - is the index of datum in data sets given, numberDatum is a number in range [0,N-1].

How does it remove to higth dimension data (Elipse)

Example of two dimensions:

datum = [x_1, x_2]

is removed if:

(x_1- E_1)^2/sigma_1^2 + (x_2- E_2)^2/sigma_2^2 > numSigma 

This because independence of observations is considered:


P(A & B) = P(A) P(B) ≈ e^[-(x_1- E_1)^2/sigma_1^2]*e^[-(x_2- E_2)^2/sigma_2^2] 

= e^[-(x_1- E_1)^2/sigma_1^2-(x_1- E_1)^2/sigma_1^2)]

the value default is obvius bacause factor sqrt(2) in normal distrubution and generalization to higther dimension too.

** & = intersection
U = union