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Median diff improved #6

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105dd03
Consecutive Outliers and post outlier Data retention resolved
0xparashar Feb 20, 2017
1d6bfdf
Lint Changes
0xparashar Feb 20, 2017
fc38866
medianDiff improved
0xparashar Feb 20, 2017
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315 changes: 173 additions & 142 deletions stats.js
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Original file line number Diff line number Diff line change
Expand Up @@ -7,145 +7,176 @@
* - Remove outliers from an array of numbers
*/

var outlierMethod = {
MAD: 'MAD',
medianDiff: 'medianDiff'
}

function mean (arr) {
return (arr.reduce(function (prev, curr) {
return prev + curr
}) / arr.length)
}

function variance (arr) {
var dataMean = mean(arr)

return mean(arr.map(function (val) {
return Math.pow(val - dataMean, 2)
}))
}

function stdev (arr) {
return Math.sqrt(variance(arr))
}

function median (arr) {
var half = Math.floor(arr.length / 2)
arr = arr.slice(0).sort(numSorter)

if (arr.length % 2) { // Odd length, true middle element
return arr[half]
} else { // Even length, average middle two elements
return (arr[half - 1] + arr[half]) / 2.0
}
}

function medianAbsoluteDeviation (arr, dataMedian) {
dataMedian = dataMedian || median(arr)
var absoluteDeviation = arr.map(function (val) {
return Math.abs(val - dataMedian)
})

return median(absoluteDeviation)
}

function numSorter (a, b) {
return a - b
}

// Iglewicz and Hoaglin method
// values with a Z-score > 3.5 are considered potential outliers
function isMADoutlier (val, threshold, dataMedian, dataMAD) {
return Math.abs((0.6745 * (val - dataMedian)) / dataMAD) > threshold
}

function indexOfMADoutliers (arr, threshold) {
threshold = threshold || 3.5 // Default recommended threshold
var dataMedian = median(arr)
var dataMAD = medianAbsoluteDeviation(arr, dataMedian)

return arr.reduce(function (res, val, i) {
if (isMADoutlier(val, threshold, dataMedian, dataMAD)) {
res.push(i)
}
return res
}, [])
}

function filterMADoutliers (arr, threshold) {
threshold = threshold || 3.5 // Default recommended threshold
var dataMedian = median(arr)
var dataMAD = medianAbsoluteDeviation(arr, dataMedian)

return arr.filter(function (val) {
return !isMADoutlier(val, threshold, dataMedian, dataMAD)
})
}

// Median filtering from difference between values
function differences (arr) {
return arr.map(function (d, i) {
return Math.round(Math.abs(d - (arr[i - 1] || d[0]))) + 1
})
}

function isMedianDiffOutlier (threshold, difference, medianDiff) {
return difference / medianDiff > threshold
}

function indexOfMedianDiffOutliers (arr, threshold) {
threshold = threshold || 3 // Default threshold of 3 std
var differencesArr = differences(arr)
var medianDiff = median(differencesArr)

return arr.reduce(function (res, val, i) {
if (isMedianDiffOutlier(threshold, differencesArr[i], medianDiff)) {
res.push(i)
}
return res
}, [])
}

function filterMedianDiffOutliers (arr, threshold) {
threshold = threshold || 3 // Default threshold of 3 std
var differencesArr = differences(arr)
var medianDiff = median(differencesArr)

return arr.filter(function (_, i) {
return !isMedianDiffOutlier(threshold, differencesArr[i], medianDiff)
})
}

function filterOutliers (arr, method, threshold) {
switch (method) {
case outlierMethod.MAD:
return filterMADoutliers(arr, threshold)
default:
return filterMedianDiffOutliers(arr, threshold)
}
}

function indexOfOutliers (arr, method, threshold) {
switch (method) {
case outlierMethod.MAD:
return indexOfMADoutliers(arr, threshold)
default:
return indexOfMedianDiffOutliers(arr, threshold)
}
}

module.exports = {
stdev: stdev,
mean: mean,
median: median,
MAD: medianAbsoluteDeviation,
numSorter: numSorter,
outlierMethod: outlierMethod,
filterOutliers: filterOutliers,
indexOfOutliers: indexOfOutliers,
filterMADoutliers: filterMADoutliers,
indexOfMADoutliers: indexOfMADoutliers,
filterMedianDiffOutliers: filterMedianDiffOutliers,
indexOfMedianDiffOutliers: indexOfMedianDiffOutliers
}
var outlierMethod = {
MAD: 'MAD',
medianDiff: 'medianDiff'
}

function mean (arr) {
return (arr.reduce(function (prev, curr) {
return prev + curr
}) / arr.length)
}

function variance (arr) {
var dataMean = mean(arr)

return mean(arr.map(function (val) {
return Math.pow(val - dataMean, 2)
}))
}

function stdev (arr) {
return Math.sqrt(variance(arr))
}

function median (arr) {
var half = Math.floor(arr.length / 2)
arr = arr.slice(0).sort(numSorter)

if (arr.length % 2) { // Odd length, true middle element
return arr[half]
} else { // Even length, average middle two elements
return (arr[half - 1] + arr[half]) / 2.0
}
}

function medianAbsoluteDeviation (arr, dataMedian) {
dataMedian = dataMedian || median(arr)
var absoluteDeviation = arr.map(function (val) {
return Math.abs(val - dataMedian)
})

return median(absoluteDeviation)
}

function numSorter (a, b) {
return a - b
}

// Iglewicz and Hoaglin method
// values with a Z-score > 3.5 are considered potential outliers
function isMADoutlier (val, threshold, dataMedian, dataMAD) {
return Math.abs((0.6745 * (val - dataMedian)) / dataMAD) > threshold
}

function indexOfMADoutliers (arr, threshold) {
threshold = threshold || 3.5 // Default recommended threshold
var dataMedian = median(arr)
var dataMAD = medianAbsoluteDeviation(arr, dataMedian)

return arr.reduce(function (res, val, i) {
if (isMADoutlier(val, threshold, dataMedian, dataMAD)) {
res.push(i)
}
return res
}, [])
}

function filterMADoutliers (arr, threshold) {
threshold = threshold || 3.5 // Default recommended threshold
var dataMedian = median(arr)
var dataMAD = medianAbsoluteDeviation(arr, dataMedian)

return arr.filter(function (val) {
return !isMADoutlier(val, threshold, dataMedian, dataMAD)
})
}

// Median filtering from difference between values
function differences (arr) {
return arr.map(function (d, i) {
return Math.round(Math.abs(d - (arr[i - 1] || d[0]))) + 1
})
}

function isMedianDiffOutlier (threshold, difference, medianDiff) {
return difference / medianDiff > threshold
}

function indexOfMedianDiffOutliers (arr, threshold) {
threshold = threshold || 3 // Default threshold of 3 std
var differencesArr = differences(arr)
var medianArr = median(arr)
var medianDiff = median(differencesArr)
var flag = true
var index = 0

return arr.reduce(function (res, val, i) {
if (i > 0 && flag) {
flag = !isMedianDiffOutlier(threshold, differencesArr[i], medianDiff)
index = i
if (isMedianDiffOutlier(threshold, differencesArr[i], medianDiff)) {
res.push(i)
}
} else {
if (i !== 0) {
flag = !(Math.round(Math.abs(arr[index - 1] - arr[i] + 1) / medianDiff) > threshold)
if ((Math.round(Math.abs(arr[index - 1] - arr[i])) + 1) / medianDiff > threshold) {
res.push(i)
}
} else {
if (!(arr[i] < medianArr + threshold * medianDiff)) {
res.push(i)
}
}
}
return res
}, [])
}

function filterMedianDiffOutliers (arr, threshold) {
threshold = threshold || 3 // Default threshold of 3 std
var differencesArr = differences(arr)
var medianArr = median(arr)
var medianDiff = median(differencesArr)
var flag = true
var index = 0
return arr.filter(function (_, i) {
if (i > 0 && flag) {
flag = !isMedianDiffOutlier(threshold, differencesArr[i], medianDiff)
index = i
return !isMedianDiffOutlier(threshold, differencesArr[i], medianDiff)
} else {
if (i !== 0) {
flag = !(Math.round(Math.abs(arr[index - 1] - arr[i] + 1) / medianDiff) > threshold)
return !((Math.round(Math.abs(arr[index - 1] - arr[i])) + 1) / medianDiff > threshold)
} else {
return arr[i] < medianArr + threshold * medianDiff
}
}
})
}

function filterOutliers (arr, method, threshold) {
switch (method) {
case outlierMethod.MAD:
return filterMADoutliers(arr, threshold)
default:
return filterMedianDiffOutliers(arr, threshold)
}
}

function indexOfOutliers (arr, method, threshold) {
switch (method) {
case outlierMethod.MAD:
return indexOfMADoutliers(arr, threshold)
default:
return indexOfMedianDiffOutliers(arr, threshold)
}
}

module.exports = {
stdev: stdev,
mean: mean,
median: median,
MAD: medianAbsoluteDeviation,
numSorter: numSorter,
outlierMethod: outlierMethod,
filterOutliers: filterOutliers,
indexOfOutliers: indexOfOutliers,
filterMADoutliers: filterMADoutliers,
indexOfMADoutliers: indexOfMADoutliers,
filterMedianDiffOutliers: filterMedianDiffOutliers,
indexOfMedianDiffOutliers: indexOfMedianDiffOutliers
}
6 changes: 3 additions & 3 deletions test.js
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ var stats = require('./stats')

var arrOddLen = [-2, 1, 2, 2, 3, 4, 15]
var arrEvenLen = [1, 2, 2, 3.4, 2.2, 19, 5.2, 1.3, 3.3, 4.1]
var randomData = [0.9, 0.74, 0.41, 2518, 0.64, 1.7, 0.63, 0.39,
var randomData = [0.9, 0.74, 0.41, 2518, 64, 1.7, 0.63, 0.39,
1.54, 0.277, 2.27, 0.37, 0.56, 0.2005, 3, 2.15, 0.78, 3.15, 2,
0.29, 0.76, 1.38, 1.09, 2.6, 1.26, 0.83, 0.63, 2.98, 1.4, 0.36,
0.59, 2.1, 1.58, 0.211, 0.65, 1.18, 2.95, 0.7, 0.22, 0.55, 0.37,
Expand Down Expand Up @@ -131,9 +131,9 @@ describe('Filter Outliers', function () {

describe('Index of Outliers', function () {
assert.equal(stats.indexOfOutliers(randomData).length, 2)
assert.equal(stats.indexOfOutliers(randomData, stats.outlierMethod.MAD).length, 10)
assert.equal(stats.indexOfOutliers(randomData, stats.outlierMethod.MAD).length, 11)

var arr = [5000, 4900, 1000, 3000, 4400, 1200300, 5000, 5500, 126500]
assert.equal(stats.indexOfOutliers(arr, stats.outlierMethod.MAD).join(','), '2,5,8')
assert.equal(stats.indexOfOutliers(arr, stats.outlierMethod.MedianDiff).join(','), '5,6,8')
assert.equal(stats.indexOfOutliers(arr, stats.outlierMethod.MedianDiff).join(','), '5,8')
})