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Last active February 19, 2017 15:02
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Convolution: smoothing noisy data
Raw
readme.md

1d convolution

Raw
global.csv
year annual_mean
1880 -0.31
1881 -0.22
1882 -0.28
1883 -0.3
1884 -0.33
1885 -0.32
1886 -0.29
1887 -0.35
1888 -0.28
1889 -0.18
1890 -0.4
1891 -0.29
1892 -0.33
1893 -0.34
1894 -0.35
1895 -0.27
1896 -0.19
1897 -0.16
1898 -0.3
1899 -0.19
1900 -0.11
1901 -0.18
1902 -0.28
1903 -0.32
1904 -0.36
1905 -0.27
1906 -0.22
1907 -0.42
1908 -0.36
1909 -0.37
1910 -0.36
1911 -0.37
1912 -0.34
1913 -0.34
1914 -0.17
1915 -0.11
1916 -0.31
1917 -0.39
1918 -0.35
1919 -0.22
1920 -0.22
1921 -0.16
1922 -0.27
1923 -0.23
1924 -0.24
1925 -0.19
1926 -0.04
1927 -0.17
1928 -0.15
1929 -0.29
1930 -0.11
1931 -0.04
1932 -0.1
1933 -0.22
1934 -0.1
1935 -0.15
1936 -0.07
1937 0.04
1938 0.08
1939 -0.01
1940 0.02
1941 0.08
1942 0.01
1943 0.08
1944 0.18
1945 0.05
1946 -0.07
1947 -0.01
1948 -0.05
1949 -0.07
1950 -0.17
1951 -0.05
1952 0.01
1953 0.09
1954 -0.11
1955 -0.12
1956 -0.19
1957 0.08
1958 0.08
1959 0.05
1960 -0.01
1961 0.07
1962 0.03
1963 0.07
1964 -0.21
1965 -0.12
1966 -0.03
1967 0
1968 -0.04
1969 0.08
1970 0.03
1971 -0.1
1972 0
1973 0.15
1974 -0.07
1975 -0.03
1976 -0.15
1977 0.14
1978 0.03
1979 0.1
1980 0.2
1981 0.27
1982 0.06
1983 0.27
1984 0.1
1985 0.06
1986 0.13
1987 0.28
1988 0.33
1989 0.21
1990 0.37
1991 0.36
1992 0.13
1993 0.14
1994 0.24
1995 0.4
1996 0.31
1997 0.42
1998 0.59
1999 0.34
2000 0.36
2001 0.5
2002 0.58
2003 0.57
2004 0.49
2005 0.63
2006 0.56
2007 0.59
2008 0.44
2009 0.57
2010 0.64
2011 0.52
2012 0.52
Raw
index.html
<html>
<head>
<title>1D convolution filter</title>
<style type="text/css">
body{
font-family: sans-serif;
}
svg{
//border: 1px solid #eee;
}
.chart-line{
fill:none;
stroke-width:1px;
}
.raw{
stroke:#aaa;
}
.smoothed{
stroke:#93f;
}
.axis path {
display: none;
}
.axis line {
shape-rendering: crispEdges;
stroke: #777;
stroke-dasharray: 1,5;
}
.axis .minor line {
stroke: #eee;
stroke-dasharray: 2,2;
}
</style>
</head>
<body>
<h1>global temperature anomaly data annual</h1>
<div id='chart'></div>
<div class='key'>
</div>
</body>
<script src="http://d3js.org/d3.v3.min.js"></script>
<script type="text/javascript">
var margin = {
left:30,
right:30,
top:30,
bottom:30
}
d3.csv('global.csv',function(temperatureData){
var width = 700;
var height = 500;
var kernel = normaliseKernel( [0.1, 0.2, 0.3, 0.2, 0.1] );// gaussian smoothing
var raw = temperatureData.map(function(d){
return parseFloat(d.annual_mean);
});
var smoothed = convolute(temperatureData, kernel, function(datum){
return parseFloat(datum.annual_mean);
});
var y = d3.scale.linear()
.domain( d3.extent( raw ) )
.range( [height-margin.top, margin.bottom] );
var x = d3.scale.linear()
.domain( [0, raw.length] )
.range( [margin.left, width-margin.right] );
var line = d3.svg.line()
.x(function(d,i) { return x(i); })
.y(function(d,i) { return y(d); });
var svg = d3.select('#chart').append('svg').attr('height', height).attr('width', width).append('g')
svg.append('path')
.datum(raw)
.attr("class", "chart-line raw")
.attr("d", line);
svg.append('path')
.datum(smoothed)
.attr("class", "chart-line smoothed")
.attr("d", line);
var ticks = d3.extent( raw );
ticks.push(0)
ticks = ticks.sort();
var yAxis = d3.svg.axis()
.scale(y)
.tickSize(width - (margin.left+margin.right))
.tickValues( ticks )
.orient("right");
svg.append("g")
.attr("class", "x axis")
.attr("transform", "translate("+margin.left+",0)")
.call(yAxis);
})
function convolute(data, kernel, accessor){
var kernel_center = Math.floor(kernel.length/2);
var left_size = kernel_center;
var right_size = kernel.length - (kernel_center-1);
if(accessor == undefined){
accessor = function(datum){
return datum;
}
}
function constrain(i,range){
if(i<range[0]){
i=0;
}
if(i>range[1]){
i=range[1];
}
return i;
}
var convoluted_data = data.map(function(d,i){
var s = 0;
for(var k=0; k < kernel.length; k++){
var index = constrain( ( i + (k-kernel_center) ), [0, data.length-1] );
s += kernel[k] * accessor(data[index]);
}
return s;
});
return convoluted_data;
}
function normaliseKernel(a){
function arraySum(a){
var s = 0;
for (var i =0;i<a.length;i++){
s += a[i];
}
return s;
}
var sum_a = arraySum(a);
var scale_factor = sum_a / 1;
a = a.map(function(d){
return d / scale_factor;
})
return a;
}
</script>
</html>
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