Demonstrating jenks natural breaks implemented in simple-statistics.
Rendered by d3js, based on an example by Mike Bostock.
Demonstrating jenks natural breaks implemented in simple-statistics.
Rendered by d3js, based on an example by Mike Bostock.
| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| body { | |
| font:normal 14px sans-serif; | |
| } | |
| #form { | |
| position: absolute; | |
| top: 10px; | |
| left: 10px; | |
| } | |
| input { | |
| margin-right: 10px; | |
| } | |
| .states { | |
| fill: none; | |
| stroke: #fff; | |
| stroke-linejoin: round; | |
| } | |
| path { | |
| -webkit-transition: fill 200ms linear; | |
| } | |
| .q0-9 { fill:rgb(247,251,255); } | |
| .q1-9 { fill:rgb(222,235,247); } | |
| .q2-9 { fill:rgb(198,219,239); } | |
| .q3-9 { fill:rgb(158,202,225); } | |
| .q4-9 { fill:rgb(107,174,214); } | |
| .q5-9 { fill:rgb(66,146,198); } | |
| .q6-9 { fill:rgb(33,113,181); } | |
| .q7-9 { fill:rgb(8,81,156); } | |
| .q8-9 { fill:rgb(8,48,107); } | |
| </style> | |
| <body> | |
| <div id='form'> | |
| <input checked='true' type='radio' name='scale' id='jenks9' /><label for='jenks9'>jenks 9</label> | |
| <input type='radio' name='scale' id='quantize' /><label for='quantize'>quantize</label> | |
| </div> | |
| <script src="http://d3js.org/d3.v3.min.js"></script> | |
| <script src="simple_statistics.js"></script> | |
| <script src="http://d3js.org/queue.v1.min.js"></script> | |
| <script src="http://d3js.org/topojson.v0.min.js"></script> | |
| <script> | |
| var width = 960, | |
| height = 500; | |
| var scales = {}; | |
| scales.quantize = d3.scale.quantize() | |
| .domain([0, .15]) | |
| .range(d3.range(9).map(function(i) { return "q" + i + "-9"; })); | |
| var path = d3.geo.path(); | |
| var svg = d3.select("body").append("svg") | |
| .attr("width", width) | |
| .attr("height", height); | |
| queue() | |
| .defer(d3.json, "/d/4090846/us.json") | |
| .defer(d3.tsv, "unemployment.tsv") | |
| .await(ready); | |
| function ready(error, us, unemployment) { | |
| var rateById = {}; | |
| unemployment.forEach(function(d) { rateById[d.id] = +d.rate; }); | |
| scales.jenks9 = d3.scale.threshold() | |
| .domain(ss.jenks(unemployment.map(function(d) { return +d.rate; }), 9)) | |
| .range(d3.range(9).map(function(i) { return "q" + i + "-9"; })); | |
| var counties = svg.append("g") | |
| .attr("class", "counties") | |
| .selectAll("path") | |
| .data(topojson.object(us, us.objects.counties).geometries) | |
| .enter().append("path") | |
| .attr("d", path); | |
| d3.selectAll('input').on('change', function() { | |
| setScale(this.id); | |
| }); | |
| function setScale(s) { | |
| counties.attr("class", function(d) { return scales[s](rateById[d.id]); }) | |
| } | |
| setScale('jenks9'); | |
| svg.append("path") | |
| .datum(topojson.mesh(us, us.objects.states, function(a, b) { return a.id !== b.id; })) | |
| .attr("class", "states") | |
| .attr("d", path); | |
| } | |
| </script> |
| // # simple-statistics | |
| // | |
| // A simple, literate statistics system. The code below uses the | |
| // [Javascript module pattern](http://www.adequatelygood.com/2010/3/JavaScript-Module-Pattern-In-Depth), | |
| // eventually assigning `simple-statistics` to `ss` in browsers or the | |
| // `exports object for node.js | |
| (function() { | |
| var ss = {}; | |
| if (typeof module !== 'undefined') { | |
| // Assign the `ss` object to exports, so that you can require | |
| // it in [node.js](http://nodejs.org/) | |
| exports = module.exports = ss; | |
| } else { | |
| // Otherwise, in a browser, we assign `ss` to the window object, | |
| // so you can simply refer to it as `ss`. | |
| this.ss = ss; | |
| } | |
| // # [Linear Regression](http://en.wikipedia.org/wiki/Linear_regression) | |
| // | |
| // [Simple linear regression](http://en.wikipedia.org/wiki/Simple_linear_regression) | |
| // is a simple way to find a fitted line | |
| // between a set of coordinates. | |
| ss.linear_regression = function() { | |
| var linreg = {}, | |
| data = []; | |
| // Assign data to the model. Data is assumed to be an array. | |
| linreg.data = function(x) { | |
| if (!arguments.length) return data; | |
| data = x.slice(); | |
| return linreg; | |
| }; | |
| // ## Fitting The Regression Line | |
| // | |
| // This is called after `.data()` and returns the | |
| // equation `y = f(x)` which gives the position | |
| // of the regression line at each point in `x`. | |
| linreg.line = function() { | |
| //if there's only one point, arbitrarily choose a slope of 0 | |
| //and a y-intercept of whatever the y of the initial point is | |
| if (data.length == 1) { | |
| m = 0; | |
| b = data[0][1]; | |
| } else { | |
| // Initialize our sums and scope the `m` and `b` | |
| // variables that define the line. | |
| var sum_x = 0, sum_y = 0, | |
| sum_xx = 0, sum_xy = 0, | |
| m, b; | |
| // Gather the sum of all x values, the sum of all | |
| // y values, and the sum of x^2 and (x*y) for each | |
| // value. | |
| // | |
| // In math notation, these would be SS_x, SS_y, SS_xx, and SS_xy | |
| for (var i = 0; i < data.length; i++) { | |
| sum_x += data[i][0]; | |
| sum_y += data[i][1]; | |
| sum_xx += data[i][0] * data[i][0]; | |
| sum_xy += data[i][0] * data[i][1]; | |
| } | |
| // `m` is the slope of the regression line | |
| m = ((data.length * sum_xy) - (sum_x * sum_y)) / | |
| ((data.length * sum_xx) - (sum_x * sum_x)); | |
| // `b` is the y-intercept of the line. | |
| b = (sum_y / data.length) - ((m * sum_x) / data.length); | |
| } | |
| // Return a function that computes a `y` value for each | |
| // x value it is given, based on the values of `b` and `a` | |
| // that we just computed. | |
| return function(x) { | |
| return b + (m * x); | |
| }; | |
| }; | |
| return linreg; | |
| }; | |
| // # [R Squared](http://en.wikipedia.org/wiki/Coefficient_of_determination) | |
| // | |
| // The r-squared value of data compared with a function `f` | |
| // is the sum of the squared differences between the prediction | |
| // and the actual value. | |
| ss.r_squared = function(data, f) { | |
| if (data.length < 2) return 1; | |
| // Compute the average y value for the actual | |
| // data set in order to compute the | |
| // _total sum of squares_ | |
| var sum = 0, average; | |
| for (var i = 0; i < data.length; i++) { | |
| sum += data[i][1]; | |
| } | |
| average = sum / data.length; | |
| // Compute the total sum of squares - the | |
| // squared difference between each point | |
| // and the average of all points. | |
| var sum_of_squares = 0; | |
| for (var j = 0; j < data.length; j++) { | |
| sum_of_squares += Math.pow(average - data[j][1], 2); | |
| } | |
| // Finally estimate the error: the squared | |
| // difference between the estimate and the actual data | |
| // value at each point. | |
| var err = 0; | |
| for (var k = 0; k < data.length; k++) { | |
| err += Math.pow(data[k][1] - f(data[k][0]), 2); | |
| } | |
| // As the error grows larger, it's ratio to the | |
| // sum of squares increases and the r squared | |
| // value grows lower. | |
| return 1 - (err / sum_of_squares); | |
| }; | |
| // # [Bayesian Classifier](http://en.wikipedia.org/wiki/Naive_Bayes_classifier) | |
| // | |
| // This is a naïve bayesian classifier that takes | |
| // singly-nested objects. | |
| ss.bayesian = function() { | |
| // The `bayes_model` object is what will be exposed | |
| // by this closure, with all of its extended methods, and will | |
| // have access to all scope variables, like `total_count`. | |
| var bayes_model = {}, | |
| // The number of items that are currently | |
| // classified in the model | |
| total_count = 0, | |
| // Every item classified in the model | |
| data = {}; | |
| // ## Train | |
| // Train the classifier with a new item, which has a single | |
| // dimension of Javascript literal keys and values. | |
| bayes_model.train = function(item, category) { | |
| // If the data object doesn't have any values | |
| // for this category, create a new object for it. | |
| if (!data[category]) data[category] = {}; | |
| // Iterate through each key in the item. | |
| for (var k in item) { | |
| var v = item[k]; | |
| // Initialize the nested object `data[category][k][item[k]]` | |
| // with an object of keys that equal 0. | |
| if (data[category][k] === undefined) data[category][k] = {}; | |
| if (data[category][k][v] === undefined) data[category][k][v] = 0; | |
| // And increment the key for this key/value combination. | |
| data[category][k][item[k]]++; | |
| } | |
| // Increment the number of items classified | |
| total_count++; | |
| }; | |
| // ## Score | |
| // Generate a score of how well this item matches all | |
| // possible categories based on its attributes | |
| bayes_model.score = function(item) { | |
| // Initialize an empty array of odds per category. | |
| var odds = {}, category; | |
| // Iterate through each key in the item, | |
| // then iterate through each category that has been used | |
| // in previous calls to `.train()` | |
| for (var k in item) { | |
| var v = item[k]; | |
| for (category in data) { | |
| // Create an empty object for storing key - value combinations | |
| // for this category. | |
| if (odds[category] === undefined) odds[category] = {}; | |
| // If this item doesn't even have a property, it counts for nothing, | |
| // but if it does have the property that we're looking for from | |
| // the item to categorize, it counts based on how popular it is | |
| // versus the whole population. | |
| if (data[category][k]) { | |
| odds[category][k + '_' + v] = (data[category][k][v] || 0) / total_count; | |
| } else { | |
| odds[category][k + '_' + v] = 0; | |
| } | |
| } | |
| } | |
| // Set up a new object that will contain sums of these odds by category | |
| var odds_sums = {}; | |
| for (category in odds) { | |
| // Tally all of the odds for each category-combination pair - | |
| // the non-existence of a category does not add anything to the | |
| // score. | |
| for (var combination in odds[category]) { | |
| if (odds_sums[category] === undefined) odds_sums[category] = 0; | |
| odds_sums[category] += odds[category][combination]; | |
| } | |
| } | |
| return odds_sums; | |
| }; | |
| // Return the completed model. | |
| return bayes_model; | |
| }; | |
| // # sum | |
| // | |
| // is simply the result of adding all numbers | |
| // together, starting from zero. | |
| // | |
| // This runs on `O(n)`, linear time in respect to the array | |
| ss.sum = function(x) { | |
| var sum = 0; | |
| for (var i = 0; i < x.length; i++) { | |
| sum += x[i]; | |
| } | |
| return sum; | |
| }; | |
| // # mean | |
| // | |
| // is the sum over the number of values | |
| // | |
| // This runs on `O(n)`, linear time in respect to the array | |
| ss.mean = function(x) { | |
| // The mean of no numbers is null | |
| if (x.length === 0) return null; | |
| return ss.sum(x) / x.length; | |
| }; | |
| // # geometric mean | |
| // | |
| // a mean function that is more useful for numbers in different | |
| // ranges. | |
| // | |
| // this is the nth root of the input numbers multipled by each other | |
| // | |
| // This runs on `O(n)`, linear time in respect to the array | |
| ss.geometric_mean = function(x) { | |
| // The mean of no numbers is null | |
| if (x.length === 0) return null; | |
| // the starting value. | |
| var value = 1; | |
| for (var i = 0; i < x.length; i++) { | |
| // the geometric mean is only valid for positive numbers | |
| if (x[i] <= 0) return null; | |
| // repeatedly multiply the value by each number | |
| value *= x[i]; | |
| } | |
| return Math.pow(value, 1 / x.length); | |
| }; | |
| // Alias this into its common name | |
| ss.average = ss.mean; | |
| // # min | |
| // | |
| // This is simply the minimum number in the set. | |
| // | |
| // This runs on `O(n)`, linear time in respect to the array | |
| ss.min = function(x) { | |
| var min; | |
| for (var i = 0; i < x.length; i++) { | |
| // On the first iteration of this loop, min is | |
| // undefined and is thus made the minimum element in the array | |
| if (x[i] < min || min === undefined) min = x[i]; | |
| } | |
| return min; | |
| }; | |
| // # max | |
| // | |
| // This is simply the maximum number in the set. | |
| // | |
| // This runs on `O(n)`, linear time in respect to the array | |
| ss.max = function(x) { | |
| var max; | |
| for (var i = 0; i < x.length; i++) { | |
| // On the first iteration of this loop, min is | |
| // undefined and is thus made the minimum element in the array | |
| if (x[i] > max || max === undefined) max = x[i]; | |
| } | |
| return max; | |
| }; | |
| // # [variance](http://en.wikipedia.org/wiki/Variance) | |
| // | |
| // is the sum of squared deviations from the mean | |
| ss.variance = function(x) { | |
| // The variance of no numbers is null | |
| if (x.length === 0) return null; | |
| var mean = ss.mean(x), | |
| deviations = []; | |
| // Make a list of squared deviations from the mean. | |
| for (var i = 0; i < x.length; i++) { | |
| deviations.push(Math.pow(x[i] - mean, 2)); | |
| } | |
| // Find the mean value of that list | |
| return ss.mean(deviations); | |
| }; | |
| // # [standard deviation](http://en.wikipedia.org/wiki/Standard_deviation) | |
| // | |
| // is just the square root of the variance. | |
| ss.standard_deviation = function(x) { | |
| // The standard deviation of no numbers is null | |
| if (x.length === 0) return null; | |
| return Math.sqrt(ss.variance(x)); | |
| }; | |
| ss.sum_squared_deviations = function(x) { | |
| // The variance of no numbers is null | |
| if (x.length <= 1) return null; | |
| var mean = ss.mean(x), | |
| sum = 0; | |
| // Make a list of squared deviations from the mean. | |
| for (var i = 0; i < x.length; i++) { | |
| sum += Math.pow(x[i] - mean, 2); | |
| } | |
| return sum; | |
| }; | |
| // # [variance](http://en.wikipedia.org/wiki/Variance) | |
| // | |
| // is the sum of squared deviations from the mean | |
| ss.sample_variance = function(x) { | |
| var sum_squared_deviations = ss.sum_squared_deviations(x); | |
| if (sum_squared_deviations === null) return null; | |
| // Find the mean value of that list | |
| return sum_squared_deviations / (x.length - 1); | |
| }; | |
| // # [standard deviation](http://en.wikipedia.org/wiki/Standard_deviation) | |
| // | |
| // is just the square root of the variance. | |
| ss.sample_standard_deviation = function(x) { | |
| // The standard deviation of no numbers is null | |
| if (x.length <= 1) return null; | |
| return Math.sqrt(ss.sample_variance(x)); | |
| }; | |
| // # [covariance](http://en.wikipedia.org/wiki/Covariance) | |
| // | |
| // sample covariance of two datasets: | |
| // how much do the two datasets move together? | |
| // x and y are two datasets, represented as arrays of numbers. | |
| ss.sample_covariance = function(x, y) { | |
| // The two datasets must have the same length which must be more than 1 | |
| if (x.length <= 1 || x.length != y.length){ | |
| return null; | |
| } | |
| // determine the mean of each dataset so that we can judge each | |
| // value of the dataset fairly as the difference from the mean. this | |
| // way, if one dataset is [1, 2, 3] and [2, 3, 4], their covariance | |
| // does not suffer because of the difference in absolute values | |
| var xmean = ss.mean(x), | |
| ymean = ss.mean(y), | |
| sum = 0; | |
| // for each pair of values, the covariance increases when their | |
| // difference from the mean is associated - if both are well above | |
| // or if both are well below | |
| // the mean, the covariance increases significantly. | |
| for (var i = 0; i < x.length; i++){ | |
| sum += (x[i] - xmean) * (y[i] - ymean); | |
| } | |
| // the covariance is weighted by the length of the datasets. | |
| return sum / (x.length - 1); | |
| }; | |
| // # [correlation](http://en.wikipedia.org/wiki/Correlation_and_dependence) | |
| // | |
| // Gets a measure of how correlated two datasets are, between -1 and 1 | |
| ss.sample_correlation = function(x, y) { | |
| var cov = ss.sample_covariance(x, y), | |
| xstd = ss.sample_standard_deviation(x), | |
| ystd = ss.sample_standard_deviation(y); | |
| if (cov === null || xstd === null || ystd === null) { | |
| return null; | |
| } | |
| return cov / xstd / ystd; | |
| }; | |
| // # [median](http://en.wikipedia.org/wiki/Median) | |
| ss.median = function(x) { | |
| // The median of an empty list is null | |
| if (x.length === 0) return null; | |
| // Sorting the array makes it easy to find the center, but | |
| // use `.slice()` to ensure the original array `x` is not modified | |
| var sorted = x.slice().sort(function (a, b) { return a - b; }); | |
| // If the length of the list is odd, it's the central number | |
| if (sorted.length % 2 === 1) { | |
| return sorted[(sorted.length - 1) / 2]; | |
| // Otherwise, the median is the average of the two numbers | |
| // at the center of the list | |
| } else { | |
| var a = sorted[(sorted.length / 2) - 1]; | |
| var b = sorted[(sorted.length / 2)]; | |
| return (a + b) / 2; | |
| } | |
| }; | |
| // # [mode](http://bit.ly/W5K4Yt) | |
| // This implementation is inspired by [science.js](https://github.com/jasondavies/science.js/blob/master/src/stats/mode.js) | |
| ss.mode = function(x) { | |
| // Handle edge cases: | |
| // The median of an empty list is null | |
| if (x.length === 0) return null; | |
| else if (x.length === 1) return x[0]; | |
| // Sorting the array lets us iterate through it below and be sure | |
| // that every time we see a new number it's new and we'll never | |
| // see the same number twice | |
| var sorted = x.slice().sort(function (a, b) { return a - b; }); | |
| // This assumes it is dealing with an array of size > 1, since size | |
| // 0 and 1 are handled immediately. Hence it starts at index 1 in the | |
| // array. | |
| var last = sorted[0], | |
| // store the mode as we find new modes | |
| mode, | |
| // store how many times we've seen the mode | |
| max_seen = 0, | |
| // how many times the current candidate for the mode | |
| // has been seen | |
| seen_this = 1; | |
| // end at sorted.length + 1 to fix the case in which the mode is | |
| // the highest number that occurs in the sequence. the last iteration | |
| // compares sorted[i], which is undefined, to the highest number | |
| // in the series | |
| for (var i = 1; i < sorted.length + 1; i++) { | |
| // we're seeing a new number pass by | |
| if (sorted[i] !== last) { | |
| // the last number is the new mode since we saw it more | |
| // often than the old one | |
| if (seen_this > max_seen) { | |
| max_seen = seen_this; | |
| seen_this = 1; | |
| mode = last; | |
| } | |
| last = sorted[i]; | |
| // if this isn't a new number, it's one more occurrence of | |
| // the potential mode | |
| } else { seen_this++; } | |
| } | |
| return mode; | |
| }; | |
| // # [t-test](http://en.wikipedia.org/wiki/Student's_t-test) | |
| // | |
| // This is to compute a one-sample t-test, comparing the mean | |
| // of a sample to a known value, x. | |
| // | |
| // in this case, we're trying to determine whether the | |
| // population mean is equal to the value that we know, which is `x` | |
| // here. usually the results here are used to look up a | |
| // [p-value](http://en.wikipedia.org/wiki/P-value), which, for | |
| // a certain level of significance, will let you determine that the | |
| // null hypothesis can or cannot be rejected. | |
| ss.t_test = function(sample, x) { | |
| // The mean of the sample | |
| var sample_mean = ss.mean(sample); | |
| // The standard deviation of the sample | |
| var sd = ss.standard_deviation(sample); | |
| // Square root the length of the sample | |
| var rootN = Math.sqrt(sample.length); | |
| // Compute the known value against the sample, | |
| // returning the t value | |
| return (sample_mean - x) / (sd / rootN); | |
| }; | |
| // # quantile | |
| // This is a population quantile, since we assume to know the entire | |
| // dataset in this library. Thus I'm trying to follow the | |
| // [Quantiles of a Population](http://en.wikipedia.org/wiki/Quantile#Quantiles_of_a_population) | |
| // algorithm from wikipedia. | |
| // | |
| // Sample is a one-dimensional array of numbers, | |
| // and p is a decimal number from 0 to 1. In terms of a k/q | |
| // quantile, p = k/q - it's just dealing with fractions or dealing | |
| // with decimal values. | |
| ss.quantile = function(sample, p) { | |
| // We can't derive quantiles from an empty list | |
| if (sample.length === 0) return null; | |
| // invalid bounds. Microsoft Excel accepts 0 and 1, but | |
| // we won't. | |
| if (p >= 1 || p <= 0) return null; | |
| // Sort a copy of the array. We'll need a sorted array to index | |
| // the values in sorted order. | |
| var sorted = sample.slice().sort(function (a, b) { return a - b; }); | |
| // Find a potential index in the list. In Wikipedia's terms, this | |
| // is I<sub>p</sub>. | |
| var idx = (sorted.length) * p; | |
| // If this isn't an integer, we'll round up to the next value in | |
| // the list. | |
| if (idx % 1 !== 0) { | |
| return sorted[Math.ceil(idx) - 1]; | |
| } else if (sample.length % 2 === 0) { | |
| // If the list has even-length and we had an integer in the | |
| // first place, we'll take the average of this number | |
| // and the next value, if there is one | |
| return (sorted[idx - 1] + sorted[idx]) / 2; | |
| } else { | |
| // Finally, in the simple case of an integer value | |
| // with an odd-length list, return the sample value at the index. | |
| return sorted[idx]; | |
| } | |
| }; | |
| // Compute the matrices required for Jenks breaks. These matrices | |
| // can be used for any classing of data with `classes <= n_classes` | |
| ss.jenksMatrices = function(data, n_classes) { | |
| // in the original implementation, these matrices are referred to | |
| // as `LC` and `OP` | |
| // | |
| // * lower_class_limits (LC): optimal lower class limits | |
| // * variance_combinations (OP): optimal variance combinations for all classes | |
| var lower_class_limits = [], | |
| variance_combinations = [], | |
| // loop counters | |
| i, j, | |
| // the variance, as computed at each step in the calculation | |
| variance = 0; | |
| // Initialize and fill each matrix with zeroes | |
| for (i = 0; i < data.length + 1; i++) { | |
| var tmp1 = [], tmp2 = []; | |
| for (j = 0; j < n_classes + 1; j++) { | |
| tmp1.push(0); | |
| tmp2.push(0); | |
| } | |
| lower_class_limits.push(tmp1); | |
| variance_combinations.push(tmp2); | |
| } | |
| for (i = 1; i < n_classes + 1; i++) { | |
| lower_class_limits[1][i] = 1; | |
| variance_combinations[1][i] = 0; | |
| // in the original implementation, 9999999 is used but | |
| // since Javascript has `Infinity`, we use that. | |
| for (j = 2; j < data.length + 1; j++) { | |
| variance_combinations[j][i] = Infinity; | |
| } | |
| } | |
| for (var l = 2; l < data.length + 1; l++) { | |
| // `SZ` originally. this is the sum of the values seen thus | |
| // far when calculating variance. | |
| var sum = 0, | |
| // `ZSQ` originally. the sum of squares of values seen | |
| // thus far | |
| sum_squares = 0, | |
| // `WT` originally. This is the number of | |
| w = 0, | |
| // `IV` originally | |
| i4 = 0; | |
| // in several instances, you could say `Math.pow(x, 2)` | |
| // instead of `x * x`, but this is slower in some browsers | |
| // introduces an unnecessary concept. | |
| for (var m = 1; m < l + 1; m++) { | |
| // `III` originally | |
| var lower_class_limit = l - m + 1, | |
| val = data[lower_class_limit - 1]; | |
| // here we're estimating variance for each potential classing | |
| // of the data, for each potential number of classes. `w` | |
| // is the number of data points considered so far. | |
| w++; | |
| // increase the current sum and sum-of-squares | |
| sum += val; | |
| sum_squares += val * val; | |
| // the variance at this point in the sequence is the difference | |
| // between the sum of squares and the total x 2, over the number | |
| // of samples. | |
| variance = sum_squares - (sum * sum) / w; | |
| i4 = lower_class_limit - 1; | |
| if (i4 !== 0) { | |
| for (j = 2; j < n_classes + 1; j++) { | |
| if (variance_combinations[l][j] >= | |
| (variance + variance_combinations[i4][j - 1])) { | |
| lower_class_limits[l][j] = lower_class_limit; | |
| variance_combinations[l][j] = variance + | |
| variance_combinations[i4][j - 1]; | |
| } | |
| } | |
| } | |
| } | |
| lower_class_limits[l][1] = 1; | |
| variance_combinations[l][1] = variance; | |
| } | |
| return { | |
| lower_class_limits: lower_class_limits, | |
| variance_combinations: variance_combinations | |
| }; | |
| }; | |
| // # [Jenks natural breaks optimization](http://en.wikipedia.org/wiki/Jenks_natural_breaks_optimization) | |
| // | |
| // Implementations: [1](http://danieljlewis.org/files/2010/06/Jenks.pdf) (python), | |
| // [2](https://github.com/vvoovv/djeo-jenks/blob/master/main.js) (buggy), | |
| // [3](https://github.com/simogeo/geostats/blob/master/lib/geostats.js#L407) (works) | |
| ss.jenks = function(data, n_classes) { | |
| // sort data in numerical order | |
| data = data.slice().sort(function (a, b) { return a - b; }); | |
| // get our basic matrices | |
| var matrices = ss.jenksMatrices(data, n_classes), | |
| // we only need lower class limits here | |
| lower_class_limits = matrices.lower_class_limits, | |
| k = data.length - 1, | |
| kclass = [], | |
| countNum = n_classes; | |
| // the calculation of classes will never include the upper and | |
| // lower bounds, so we need to explicitly set them | |
| kclass[n_classes] = data[data.length - 1]; | |
| kclass[0] = data[0]; | |
| // the lower_class_limits matrix is used as indexes into itself | |
| // here: the `k` variable is reused in each iteration. | |
| while (countNum > 1) { | |
| kclass[countNum - 1] = data[lower_class_limits[k][countNum] - 2]; | |
| k = lower_class_limits[k][countNum] - 1; | |
| countNum--; | |
| } | |
| return kclass; | |
| }; | |
| // # Mixin | |
| // | |
| // Mixin simple_statistics to the Array native object. This is an optional | |
| // feature that lets you treat simple_statistics as a native feature | |
| // of Javascript. | |
| ss.mixin = function() { | |
| var support = !!(Object.defineProperty && Object.defineProperties); | |
| if (!support) throw new Error('without defineProperty, simple-statistics cannot be mixed in'); | |
| // only methods which work on basic arrays in a single step | |
| // are supported | |
| var arrayMethods = ['median', 'standard_deviation', 'sum', | |
| 'mean', 'min', 'max', 'quantile', 'geometric_mean']; | |
| // create a closure with a method name so that a reference | |
| // like `arrayMethods[i]` doesn't follow the loop increment | |
| function wrap(method) { | |
| return function() { | |
| // cast any arguments into an array, since they're | |
| // natively objects | |
| var args = Array.prototype.slice.apply(arguments); | |
| // make the first argument the array itself | |
| args.unshift(this); | |
| // return the result of the ss method | |
| return ss[method].apply(ss, args); | |
| }; | |
| } | |
| // for each array function, define a function off of the Array | |
| // prototype which automatically gets the array as the first | |
| // argument. We use [defineProperty](https://developer.mozilla.org/en-US/docs/JavaScript/Reference/Global_Objects/Object/defineProperty) | |
| // because it allows these properties to be non-enumerable: | |
| // `for (var in x)` loops will not run into problems with this | |
| // implementation. | |
| for (var i = 0; i < arrayMethods.length; i++) { | |
| Object.defineProperty(Array.prototype, arrayMethods[i], { | |
| value: wrap(arrayMethods[i]), | |
| configurable: true, | |
| enumerable: false, | |
| writable: true | |
| }); | |
| } | |
| }; | |
| })(this); |
| id | rate | |
|---|---|---|
| 1001 | .097 | |
| 1003 | .091 | |
| 1005 | .134 | |
| 1007 | .121 | |
| 1009 | .099 | |
| 1011 | .164 | |
| 1013 | .167 | |
| 1015 | .108 | |
| 1017 | .186 | |
| 1019 | .118 | |
| 1021 | .099 | |
| 1023 | .127 | |
| 1025 | .17 | |
| 1027 | .159 | |
| 1029 | .104 | |
| 1031 | .085 | |
| 1033 | .114 | |
| 1035 | .195 | |
| 1037 | .14 | |
| 1039 | .101 | |
| 1041 | .097 | |
| 1043 | .096 | |
| 1045 | .093 | |
| 1047 | .211 | |
| 1049 | .143 | |
| 1051 | .09 | |
| 1053 | .129 | |
| 1055 | .107 | |
| 1057 | .128 | |
| 1059 | .123 | |
| 1061 | .1 | |
| 1063 | .147 | |
| 1065 | .127 | |
| 1067 | .099 | |
| 1069 | .089 | |
| 1071 | .118 | |
| 1073 | .107 | |
| 1075 | .148 | |
| 1077 | .105 | |
| 1079 | .136 | |
| 1081 | .086 | |
| 1083 | .093 | |
| 1085 | .185 | |
| 1087 | .114 | |
| 1089 | .075 | |
| 1091 | .148 | |
| 1093 | .152 | |
| 1095 | .092 | |
| 1097 | .111 | |
| 1099 | .187 | |
| 1101 | .102 | |
| 1103 | .104 | |
| 1105 | .198 | |
| 1107 | .13 | |
| 1109 | .087 | |
| 1111 | .151 | |
| 1113 | .126 | |
| 1115 | .107 | |
| 1117 | .076 | |
| 1119 | .139 | |
| 1121 | .136 | |
| 1123 | .137 | |
| 1125 | .09 | |
| 1127 | .119 | |
| 1129 | .151 | |
| 1131 | .256 | |
| 1133 | .175 | |
| 2013 | .101 | |
| 2016 | .084 | |
| 2020 | .07 | |
| 2050 | .148 | |
| 2060 | .036 | |
| 2068 | .034 | |
| 2070 | .084 | |
| 2090 | .069 | |
| 2100 | .062 | |
| 2110 | .057 | |
| 2122 | .097 | |
| 2130 | .061 | |
| 2150 | .066 | |
| 2164 | .059 | |
| 2170 | .088 | |
| 2180 | .121 | |
| 2185 | .057 | |
| 2188 | .132 | |
| 2201 | .136 | |
| 2220 | .059 | |
| 2232 | .073 | |
| 2240 | .081 | |
| 2261 | .064 | |
| 2270 | .204 | |
| 2280 | .098 | |
| 2282 | .063 | |
| 2290 | .136 | |
| 4001 | .148 | |
| 4003 | .074 | |
| 4005 | .077 | |
| 4007 | .109 | |
| 4009 | .144 | |
| 4011 | .215 | |
| 4012 | .089 | |
| 4013 | .085 | |
| 4015 | .102 | |
| 4017 | .142 | |
| 4019 | .084 | |
| 4021 | .118 | |
| 4023 | .172 | |
| 4025 | .095 | |
| 4027 | .242 | |
| 5001 | .143 | |
| 5003 | .091 | |
| 5005 | .082 | |
| 5007 | .053 | |
| 5009 | .064 | |
| 5011 | .078 | |
| 5013 | .062 | |
| 5015 | .043 | |
| 5017 | .096 | |
| 5019 | .063 | |
| 5021 | .104 | |
| 5023 | .059 | |
| 5025 | .06 | |
| 5027 | .081 | |
| 5029 | .065 | |
| 5031 | .059 | |
| 5033 | .066 | |
| 5035 | .099 | |
| 5037 | .071 | |
| 5039 | .076 | |
| 5041 | .099 | |
| 5043 | .091 | |
| 5045 | .06 | |
| 5047 | .059 | |
| 5049 | .061 | |
| 5051 | .066 | |
| 5053 | .057 | |
| 5055 | .082 | |
| 5057 | .086 | |
| 5059 | .073 | |
| 5061 | .072 | |
| 5063 | .078 | |
| 5065 | .077 | |
| 5067 | .092 | |
| 5069 | .092 | |
| 5071 | .061 | |
| 5073 | .086 | |
| 5075 | .079 | |
| 5077 | .082 | |
| 5079 | .082 | |
| 5081 | .056 | |
| 5083 | .077 | |
| 5085 | .052 | |
| 5087 | .053 | |
| 5089 | .112 | |
| 5091 | .045 | |
| 5093 | .113 | |
| 5095 | .074 | |
| 5097 | .058 | |
| 5099 | .087 | |
| 5101 | .062 | |
| 5103 | .071 | |
| 5105 | .056 | |
| 5107 | .088 | |
| 5109 | .063 | |
| 5111 | .075 | |
| 5113 | .064 | |
| 5115 | .062 | |
| 5117 | .067 | |
| 5119 | .06 | |
| 5121 | .073 | |
| 5123 | .094 | |
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| 5131 | .062 | |
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| 5137 | .066 | |
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| 5141 | .091 | |
| 5143 | .05 | |
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| 5149 | .064 | |
| 6001 | .113 | |
| 6003 | .152 | |
| 6005 | .121 | |
| 6007 | .122 | |
| 6009 | .143 | |
| 6011 | .145 | |
| 6013 | .112 | |
| 6015 | .119 | |
| 6017 | .112 | |
| 6019 | .141 | |
| 6021 | .138 | |
| 6023 | .103 | |
| 6025 | .301 | |
| 6027 | .095 | |
| 6029 | .139 | |
| 6031 | .139 | |
| 6033 | .147 | |
| 6035 | .118 | |
| 6037 | .127 | |
| 6039 | .123 | |
| 6041 | .08 | |
| 6043 | .088 | |
| 6045 | .101 | |
| 6047 | .157 | |
| 6049 | .111 | |
| 6051 | .103 | |
| 6053 | .1 | |
| 6055 | .087 | |
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| 6073 | .102 | |
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| 6099 | .153 | |
| 6101 | .151 | |
| 6103 | .137 | |
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| 6109 | .127 | |
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| 6115 | .178 | |
| 8001 | .081 | |
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| 8007 | .062 | |
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| 8011 | .05 | |
| 8013 | .055 | |
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| 8015 | .051 | |
| 8017 | .02 | |
| 8019 | .07 | |
| 8021 | .051 | |
| 8023 | .084 | |
| 8025 | .076 | |
| 8027 | .052 | |
| 8029 | .066 | |
| 8031 | .077 | |
| 8033 | .132 | |
| 8035 | .059 | |
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| 8039 | .06 | |
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| 8045 | .058 | |
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| 8053 | .022 | |
| 8055 | .072 | |
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| 8065 | .071 | |
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| 8069 | .056 | |
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| 8077 | .082 | |
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| 8089 | .058 | |
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| 8099 | .05 | |
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| 8107 | .06 | |
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| 8119 | .067 | |
| 8121 | .032 | |
| 8123 | .075 | |
| 8125 | .026 | |
| 9001 | .078 | |
| 9003 | .088 | |
| 9005 | .079 | |
| 9007 | .067 | |
| 9009 | .089 | |
| 9011 | .076 | |
| 9013 | .067 | |
| 9015 | .09 | |
| 10001 | .079 | |
| 10003 | .086 | |
| 10005 | .073 | |
| 11001 | .117 | |
| 12001 | .071 | |
| 12003 | .114 | |
| 12005 | .089 | |
| 12007 | .083 | |
| 12009 | .111 | |
| 12011 | .098 | |
| 12013 | .082 | |
| 12015 | .127 | |
| 12017 | .121 | |
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| 12027 | .117 | |
| 12029 | .123 | |
| 12031 | .112 | |
| 12033 | .098 | |
| 12035 | .162 | |
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| 12041 | .1 | |
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| 13021 | .1 | |
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| 13051 | .085 | |
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| 13065 | .11 | |
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| 13111 | .1 | |
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| 13303 | .14 | |
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| 16075 | .077 | |
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| 54095 | .108 | |
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| 54101 | .104 | |
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| 55009 | .071 | |
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| 55035 | .06 | |
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| 72003 | .179 | |
| 72005 | .178 | |
| 72007 | .182 | |
| 72009 | .192 | |
| 72011 | .183 | |
| 72013 | .167 | |
| 72015 | .227 | |
| 72017 | .201 | |
| 72019 | .196 | |
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| 72023 | .135 | |
| 72025 | .158 | |
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| 72045 | .234 | |
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| 72054 | .215 | |
| 72055 | .199 | |
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| 72059 | .226 | |
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| 72065 | .165 | |
| 72067 | .164 | |
| 72069 | .208 | |
| 72071 | .191 | |
| 72073 | .219 | |
| 72075 | .186 | |
| 72077 | .191 | |
| 72079 | .186 | |
| 72081 | .175 | |
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| 72089 | .202 | |
| 72091 | .192 | |
| 72093 | .199 | |
| 72095 | .259 | |
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| 72099 | .18 | |
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| 72125 | .178 | |
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| 72141 | .258 | |
| 72143 | .163 | |
| 72145 | .176 | |
| 72147 | .277 | |
| 72149 | .198 | |
| 72151 | .241 | |
| 72153 | .16 |