梯度下降 test | JShare

var data = [[161.2, 51.6], [167.5, 59.0], [159.5, 49.2], [157.0, 63.0], [155.8, 53.6],
			[170.0, 59.0], [159.1, 47.6], [166.0, 69.8], [176.2, 66.8], [160.2, 75.2],
			[172.5, 55.2], [170.9, 54.2], [172.9, 62.5], [153.4, 42.0], [160.0, 50.0],
			[147.2, 49.8], [168.2, 49.2], [175.0, 73.2], [157.0, 47.8], [167.6, 68.8],
			[159.5, 50.6], [175.0, 82.5], [166.8, 57.2], [176.5, 87.8], [170.2, 72.8],
			[174.0, 54.5], [173.0, 59.8], [179.9, 67.3], [170.5, 67.8], [160.0, 47.0],
			[154.4, 46.2], [162.0, 55.0], [176.5, 83.0], [160.0, 54.4], [152.0, 45.8],
			[162.1, 53.6], [170.0, 73.2], [160.2, 52.1], [161.3, 67.9], [166.4, 56.6],
			[168.9, 62.3], [163.8, 58.5], [167.6, 54.5], [160.0, 50.2], [161.3, 60.3],
			[167.6, 58.3], [165.1, 56.2], [160.0, 50.2], [170.0, 72.9], [157.5, 59.8],
			[167.6, 61.0], [160.7, 69.1], [163.2, 55.9], [152.4, 46.5], [157.5, 54.3],
			[168.3, 54.8], [180.3, 60.7], [165.5, 60.0], [165.0, 62.0], [164.5, 60.3],
			[156.0, 52.7], [160.0, 74.3], [163.0, 62.0], [165.7, 73.1], [161.0, 80.0],
			[162.0, 54.7], [166.0, 53.2], [174.0, 75.7], [172.7, 61.1], [167.6, 55.7],
			[151.1, 48.7], [164.5, 52.3], [163.5, 50.0], [152.0, 59.3], [169.0, 62.5],
			[164.0, 55.7], [161.2, 54.8], [155.0, 45.9], [170.0, 70.6], [176.2, 67.2],
			[170.0, 69.4], [162.5, 58.2], [170.3, 64.8], [164.1, 71.6], [169.5, 52.8],
			[163.2, 59.8], [154.5, 49.0], [159.8, 50.0], [173.2, 69.2], [170.0, 55.9],
			[161.4, 63.4], [169.0, 58.2], [166.2, 58.6], [159.4, 45.7], [162.5, 52.2],
			[159.0, 48.6], [162.8, 57.8], [159.0, 55.6], [179.8, 66.8], [162.9, 59.4],
			[161.0, 53.6], [151.1, 73.2], [168.2, 53.4], [168.9, 69.0], [173.2, 58.4],
			[171.8, 56.2], [178.0, 70.6], [164.3, 59.8], [163.0, 72.0], [168.5, 65.2],
			[166.8, 56.6], [172.7, 105.2], [163.5, 51.8], [169.4, 63.4], [167.8, 59.0],
			[159.5, 47.6], [167.6, 63.0], [161.2, 55.2], [160.0, 45.0], [163.2, 54.0],
			[162.2, 50.2], [161.3, 60.2], [149.5, 44.8], [157.5, 58.8], [163.2, 56.4],
			[172.7, 62.0], [155.0, 49.2], [156.5, 67.2], [164.0, 53.8], [160.9, 54.4],
			[162.8, 58.0], [167.0, 59.8], [160.0, 54.8], [160.0, 43.2], [168.9, 60.5],
			[158.2, 46.4], [156.0, 64.4], [160.0, 48.8], [167.1, 62.2], [158.0, 55.5],
			[167.6, 57.8], [156.0, 54.6], [162.1, 59.2], [173.4, 52.7], [159.8, 53.2],
			[170.5, 64.5], [159.2, 51.8], [157.5, 56.0], [161.3, 63.6], [162.6, 63.2],
			[160.0, 59.5], [168.9, 56.8], [165.1, 64.1], [162.6, 50.0], [165.1, 72.3],
			[166.4, 55.0], [160.0, 55.9], [152.4, 60.4], [170.2, 69.1], [162.6, 84.5],
			[170.2, 55.9], [158.8, 55.5], [172.7, 69.5], [167.6, 76.4], [162.6, 61.4],
			[167.6, 65.9], [156.2, 58.6], [175.2, 66.8], [172.1, 56.6], [162.6, 58.6],
			[160.0, 55.9], [165.1, 59.1], [182.9, 81.8], [166.4, 70.7], [165.1, 56.8],
			[177.8, 60.0], [165.1, 58.2], [175.3, 72.7], [154.9, 54.1], [158.8, 49.1],
			[172.7, 75.9], [168.9, 55.0], [161.3, 57.3], [167.6, 55.0], [165.1, 65.5],
			[175.3, 65.5], [157.5, 48.6], [163.8, 58.6], [167.6, 63.6], [165.1, 55.2],
			[165.1, 62.7], [168.9, 56.6], [162.6, 53.9], [164.5, 63.2], [176.5, 73.6],
			[168.9, 62.0], [175.3, 63.6], [159.4, 53.2], [160.0, 53.4], [170.2, 55.0],
			[162.6, 70.5], [167.6, 54.5], [162.6, 54.5], [160.7, 55.9], [160.0, 59.0],
			[157.5, 63.6], [162.6, 54.5], [152.4, 47.3], [170.2, 67.7], [165.1, 80.9],
			[172.7, 70.5], [165.1, 60.9], [170.2, 63.6], [170.2, 54.5], [170.2, 59.1],
			[161.3, 70.5], [167.6, 52.7], [167.6, 62.7], [165.1, 86.3], [162.6, 66.4],
			[152.4, 67.3], [168.9, 63.0], [170.2, 73.6], [175.2, 62.3], [175.2, 57.7],
			[160.0, 55.4], [165.1, 104.1], [174.0, 55.5], [170.2, 77.3], [160.0, 80.5],
			[167.6, 64.5], [167.6, 72.3], [167.6, 61.4], [154.9, 58.2], [162.6, 81.8],
			[175.3, 63.6], [171.4, 53.4], [157.5, 54.5], [165.1, 53.6], [160.0, 60.0],
			[174.0, 73.6], [162.6, 61.4], [174.0, 55.5], [162.6, 63.6], [161.3, 60.9],
			[156.2, 60.0], [149.9, 46.8], [169.5, 57.3], [160.0, 64.1], [175.3, 63.6],
			[169.5, 67.3], [160.0, 75.5], [172.7, 68.2], [162.6, 61.4], [157.5, 76.8],
			[176.5, 71.8], [164.4, 55.5], [160.7, 48.6], [174.0, 66.4], [163.8, 67.3]];
let chart = Highcharts.chart('container', {
	chart: {
		type: 'scatter',
		zoomType: 'xy'
	},
	title: {
		text: '507 人按性别划分的身高和体重分布图'
	},
	subtitle: {
		text: '数据来源: Heinz  2003'
	},
	xAxis: {
		title: {
			enabled: true,
			text: '身高 (cm)'
		},
		startOnTick: true,
		endOnTick: true,
		showLastLabel: true
	},
	yAxis: {
		title: {
			text: '体重 (kg)'
		}
	},
	legend: {
		layout: 'vertical',
		align: 'left',
		verticalAlign: 'top',
		x: 100,
		y: 70,
		floating: true,
		backgroundColor: (Highcharts.theme && Highcharts.theme.legendBackgroundColor) || '#FFFFFF',
		borderWidth: 1
	},
	plotOptions: {
		scatter: {
			marker: {
				radius: 5,
				states: {
					hover: {
						enabled: true,
						lineColor: 'rgb(100,100,100)'
					}
				}
			},
			states: {
				hover: {
					marker: {
						enabled: false
					}
				}
			},
			tooltip: {
				headerFormat: '<b>{series.name}</b><br>',
				pointFormat: '{point.x} cm, {point.y} kg'
			}
		}
	},
	series: [{
		name: '女',
		color: 'rgba(223, 83, 83, .5)',
		data: data,
	}, {
		name: '预测',
		type: 'line',
		color: 'rgba(119, 152, 191, .5)',
		data: []
	}]
});
let chartLoss = Highcharts.chart('container_loss', {
	title: {
		text: '损失率'
	},
	yAxis: {
		title: {
			text: '损失率'
		}
	},
	legend: {
		layout: 'vertical',
		align: 'right',
		verticalAlign: 'middle'
	},
	series: [{
		name: '损失率',
		data: []
	}],
	responsive: {
		rules: [{
			condition: {
				maxWidth: 500
			},
			chartOptions: {
				legend: {
					layout: 'horizontal',
					align: 'center',
					verticalAlign: 'bottom'
				}
			}
		}]
	}
});
/**
   * 模型
   * y = a + bx;
   */
function drawLine(a, b) {
	chart.series[1].addPoint([146, a + (146 * b)], true);
	chart.series[1].addPoint([185, a + (185 * b)], true);
}
/**
   * 代价函数 均方差计算
   */
function cost(a, b){
	let sum = data.reduce((pre, current)=>{
		return pre + ((a + current[0] * b) - current[1])*((a + current[0] * b) - current[1]);
	}, 0);
	return sum / 2 / data.length;
}
/**
   * 计算梯度
   * @param a
   * @param b
   */
function gradientA(a, b){
	let sum = data.reduce((pre, current)=>{
		return pre + ((a + current[0] * b) - current[1]) * (a + current[0] * b);
	}, 0);
	return sum / data.length;
}
function gradientB(a, b){
	let sum = data.reduce((pre, current)=>{
		return pre + ((a + current[0] * b) - current[1]);
	}, 0);
	return sum / data.length;
}
let batch = 200;
let alpha = 0.001;
let args = [0, 0]; // 初始化 a b 值
function step() {
	let costNumber = (cost(args[0], args[1]));
	console.log('cost', costNumber);
	chartLoss.series[0].addPoint(costNumber, true, false, false);
	args[0] -= alpha * gradientA(args[0], args[1]);
	args[1] -= alpha * gradientB(args[0], args[1]);
	if((--batch > 0)) {
		window.requestAnimationFrame(()=>{step()});
	} else {
		drawLine(args[0], args[1]);
	}
}
step();

<div id="container" style="min-width:400px;height:400px"></div>
<div id="container_loss" style="min-width:400px;height:400px"></div>

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梯度下降 test | JShare

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