简单理解
就是用一条直线较为精确地描述数据之间的关系, 这样当出现新的数据的时候, 就能够预测出一个简单的值。
一些概念:
回归平均值(regression to the mean)
因变量(dependent variable): y=a1x1+a2x2+a3x3......+anxn 中的y, 即需要预测的值
自变量(independent variables): y=a1x1+a2x2+a3x3......+anxn 中的x1, x2 ... xn, 即预测变量
广义线性回归(GLM, Generalized Linear Model), 如逻辑回归, 泊松分布等......
最小二乘法
法国数学家，阿德里安-馬里·勒讓德（1752－1833）提出让总的误差的平方最小的
就是真值，这是基于，如果误差是随机的，应该围绕真值上下波动。
就是真值，这是基于，如果误差是随机的，应该围绕真值上下波动。
梯度下降算法
先确定向下一步的步伐大小, 即Learning Rate
任意给定一个初始值
确定一个向下的方向, 并向下走预先规定的步伐, 并更新当下降的高度小于某个定义的值, 则停止下降。
需要注意的是导数=0取得的解不一定是最优解, 很可能是某个局部最优解。
损失函数 (Cost Function)
损失函数分为经验风险损失函数和结构风险损失函数，经验风险损失函数反映的是预测结果和实际结果之间的差别
结构风险损失函数则是经验风险损失函数加上正则项(L0、L1（Lasso）、L2（Ridge）)
常用损失函数
0-1损失函数 (gold standard 标准式)
预测值和目标值不相等为1，否则为0
该损失函数不考虑预测值和真实值的误差程度，也就是说只要预测错误，预测错误差一点和差很多是一样的。
感知机就是用的这种损失函数，但是由于相等这个条件太过严格，我们可以放宽条件，即满足 |Y−f(X)|<T时认为相等
这种损失函数用在实际场景中比较少，更多的是用俩衡量其他损失函数的效果。
绝对值损失函数
平方损失函数(squared loss)
- 实际结果和观测结果之间差距的平方和，一般用在线性回归中，可以理解为最小二乘法
对数损失函数(Logarithmic loss)
主要在逻辑回归中使用，样本预测值和实际值的误差符合高斯分布，使用极大似然估计的方法，取对数得到损失函数
损失函数L(Y,P(Y|X))L(Y,P(Y|X))是指样本X在分类Y的情况下，使概率P(Y|X)达到最大值。
经典的对数损失函数包括entropy(信息熵)和softmax，一般在做分类问题的时候使用
- 回归时多用绝对值损失
- 拉普拉斯分布时，μ值为中位数）和平方损失（高斯分布时，μ值为均值）
指数损失函数(Exp-Loss)
在boosting算法中比较常见，比如Adaboosting中，标准形式是：
铰链损失函数(Hinge Loss)
- 铰链损失函数主要用在SVM中，Hinge Loss的标准形式为：
y为预测值, 在-1到+1之间，t为目标值（-1或+1）
其含义为，y的值在-1和+1之间就可以了，并不鼓励|y|>1, 即并不鼓励分类器过度自信，让某个正确分类的样本的距离分割线超过1并不会有任何奖励，从而使分类器可以更专注于整体的分类误差。
多元线性回归
大多数现实世界的分析不止一个自变量，大多数情况下，很有可能使用多元线性回归。
相关系数
- 两个变量之间的相关系数是一个数，它表示两个变量服从一条直线的关系有多麽紧密
- 相关系数就是指Pearson相关系数，它是数学家Pearson提出来的，相关系数的范围是-1~+1之间，两端的值表示一个完美的线性关系
Keras实现Demo
import numpy as np
np.random.seed(1337)
from keras.models import Sequential
from keras.layers import Dense
import matplotlib.pyplot as plt
# 生成数据
X = np.linspace(-1, 1, 200) #在返回（-1, 1）范围内的等差序列
np.random.shuffle(X) # 打乱顺序
Y = 0.5 * X + 2 + np.random.normal(0, 0.05, (200, )) #生成Y并添加噪声
# plot
plt.scatter(X, Y)
plt.show()
X_train, Y_train = X[:160], Y[:160] # 前160组数据为训练数据集
X_test, Y_test = X[160:], Y[160:] #后40组数据为测试数据集
# 构建神经网络模型
model = Sequential()
model.add(Dense(input_dim=1, units=1))
# 选定loss函数和优化器
model.compile(loss='mse', optimizer='sgd')
# 训练过程
print('Training -----------')
for step in range(501):
cost = model.train_on_batch(X_train, Y_train)
if step % 50 == 0:
print("After %d trainings, the cost: %f" % (step, cost))
# 测试过程
print('\nTesting ------------')
cost = model.evaluate(X_test, Y_test, batch_size=40)
print('test cost:', cost)
W, b = model.layers[0].get_weights()
print('Weights=', W, '\nbiases=', b)
# 将训练结果绘出
Y_pred = model.predict(X_test)
plt.scatter(X_test, Y_test)
plt.plot(X_test, Y_pred)
plt.show()
SparkMrLib实现Demo
lpsa.data
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代码:
import org.apache.spark.ml.feature.LabeledPoint import org.apache.spark.ml.linalg.Vectors import org.apache.spark.ml.regression.{LinearRegression, LinearRegressionModel, LinearRegressionSummary} import org.apache.spark.sql.{Dataset, Encoders, SparkSession} object LinearRegression1 { def main(args: Array[String]) { val spark = SparkSession .builder .master("local") .appName("LinearRegression") .getOrCreate() //scala. 隐式转换 import spark.implicits._ //读取样本数据 val data_path1 = "lpsa.data" val data1: Dataset[String] = spark.read.textFile(data_path1) val data2: Dataset[LabeledPoint] = data1.map { line => val parts = line.split(',') val features: Array[Double] = parts(1).split(' ').map(_.toDouble) LabeledPoint(parts(0).toDouble, Vectors.dense(features)); } // //1 为随机种子 val train2TestData: Array[Dataset[LabeledPoint]] = data2.randomSplit(Array(0.8, 0.2), 1) // 迭代次数 val numIterations = 100 val lir: LinearRegression = new LinearRegression() .setFeaturesCol("features") .setLabelCol("label") //收敛的值，越小结果越精确，但迭代次数也越大，花费更多时间 .setTol(1E-6) //迭代次数 .setMaxIter(numIterations) //是否需要截距，默认true // .setFitIntercept(false) val startTime = System.nanoTime() val model: LinearRegressionModel = lir.fit(train2TestData(0)) //训练模型所消耗的时间 val elapsedTime = (System.nanoTime() - startTime) / 1e9 println("Training time: " + elapsedTime +" seconds") //权重. println("Weights: " + model.coefficients) //截距. println("Intercept:" + model.intercept) //用测试集数据去评估模型，得到一个评估结果。 val summary: LinearRegressionSummary = model.evaluate(train2TestData(1)) //// //// //打印测试结果 summary.predictions.show() // // // //平均绝对误差，预测数据和原始数据对应点误差绝对值和的均值 println("平均绝对值误差: " + summary.meanAbsoluteError) //// //均方差，预测数据和原始数据对应点误差的平方和的均值 println("均方差: " + summary.meanSquaredError) //// //测试集的数据条目 println(summary.numInstances) /** * 训练完之后，可以将模型进行保存.. * model.save("model/lir.model") * 模型训练完毕后，以后用的时候可以直接加载模型，无需再训练 * val model = LinearRegressionModel.load("model/lir.model") */ spark.stop() } }执行结果
+---------+--------------------+------------------+ | label| features| prediction| +---------+--------------------+------------------+ |0.3715636|[-0.5078744753006...|1.6421433505218315| |1.3480731|[0.10778590023681...|1.8821794069229758| |1.7137979|[0.36627391851114...|2.7289870384929062| |1.8484548|[-0.2627917281138...| 2.539418711837841| |2.0476928|[-1.1539378999075...|0.8615391122353211| |2.5533438|[0.26634132994993...| 2.788666352465077| |2.7180005|[-0.0704736333296...|2.9210948847330584| |2.8063861|[-0.6852776524309...| 2.02853043658855| |2.8419982|[-0.7573102775567...|2.1731148778913285| |2.9626924|[-1.5240614015806...|0.8988821228525923| |3.2752562|[1.39927182372944...|3.1449164943520214| |3.5876769|[0.18015632325519...| 2.65539506621454| +---------+--------------------+------------------+ 平均绝对值误差: 0.8090483779032781 均方差: 0.9257651846620174 12
house_data.csv
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0.12329,0,10.01,0,0.547,5.913,92.9,2.3534,6,432,17.8,394.95,16.21,18.8 0.22212,0,10.01,0,0.547,6.092,95.4,2.548,6,432,17.8,396.9,17.09,18.7 0.14231,0,10.01,0,0.547,6.254,84.2,2.2565,6,432,17.8,388.74,10.45,18.5 0.17134,0,10.01,0,0.547,5.928,88.2,2.4631,6,432,17.8,344.91,15.76,18.3 0.13158,0,10.01,0,0.547,6.176,72.5,2.7301,6,432,17.8,393.3,12.04,21.2 0.15098,0,10.01,0,0.547,6.021,82.6,2.7474,6,432,17.8,394.51,10.3,19.2 0.13058,0,10.01,0,0.547,5.872,73.1,2.4775,6,432,17.8,338.63,15.37,20.4 0.14476,0,10.01,0,0.547,5.731,65.2,2.7592,6,432,17.8,391.5,13.61,19.3 0.06899,0,25.65,0,0.581,5.87,69.7,2.2577,2,188,19.1,389.15,14.37,22 0.07165,0,25.65,0,0.581,6.004,84.1,2.1974,2,188,19.1,377.67,14.27,20.3 0.09299,0,25.65,0,0.581,5.961,92.9,2.0869,2,188,19.1,378.09,17.93,20.5 0.15038,0,25.65,0,0.581,5.856,97,1.9444,2,188,19.1,370.31,25.41,17.3 0.09849,0,25.65,0,0.581,5.879,95.8,2.0063,2,188,19.1,379.38,17.58,18.8 0.16902,0,25.65,0,0.581,5.986,88.4,1.9929,2,188,19.1,385.02,14.81,21.4 0.38735,0,25.65,0,0.581,5.613,95.6,1.7572,2,188,19.1,359.29,27.26,15.7 0.25915,0,21.89,0,0.624,5.693,96,1.7883,4,437,21.2,392.11,17.19,16.2 0.32543,0,21.89,0,0.624,6.431,98.8,1.8125,4,437,21.2,396.9,15.39,18 0.88125,0,21.89,0,0.624,5.637,94.7,1.9799,4,437,21.2,396.9,18.34,14.3 0.34006,0,21.89,0,0.624,6.458,98.9,2.1185,4,437,21.2,395.04,12.6,19.2 1.19294,0,21.89,0,0.624,6.326,97.7,2.271,4,437,21.2,396.9,12.26,19.6 0.59005,0,21.89,0,0.624,6.372,97.9,2.3274,4,437,21.2,385.76,11.12,23 0.32982,0,21.89,0,0.624,5.822,95.4,2.4699,4,437,21.2,388.69,15.03,18.4 0.97617,0,21.89,0,0.624,5.757,98.4,2.346,4,437,21.2,262.76,17.31,15.6 0.55778,0,21.89,0,0.624,6.335,98.2,2.1107,4,437,21.2,394.67,16.96,18.1 0.32264,0,21.89,0,0.624,5.942,93.5,1.9669,4,437,21.2,378.25,16.9,17.4 0.35233,0,21.89,0,0.624,6.454,98.4,1.8498,4,437,21.2,394.08,14.59,17.1 0.2498,0,21.89,0,0.624,5.857,98.2,1.6686,4,437,21.2,392.04,21.32,13.3 0.54452,0,21.89,0,0.624,6.151,97.9,1.6687,4,437,21.2,396.9,18.46,17.8 0.2909,0,21.89,0,0.624,6.174,93.6,1.6119,4,437,21.2,388.08,24.16,14 1.62864,0,21.89,0,0.624,5.019,100,1.4394,4,437,21.2,396.9,34.41,14.4 3.32105,0,19.58,1,0.871,5.403,100,1.3216,5,403,14.7,396.9,26.82,13.4 4.0974,0,19.58,0,0.871,5.468,100,1.4118,5,403,14.7,396.9,26.42,15.6 2.77974,0,19.58,0,0.871,4.903,97.8,1.3459,5,403,14.7,396.9,29.29,11.8 2.37934,0,19.58,0,0.871,6.13,100,1.4191,5,403,14.7,172.91,27.8,13.8 2.15505,0,19.58,0,0.871,5.628,100,1.5166,5,403,14.7,169.27,16.65,15.6 2.36862,0,19.58,0,0.871,4.926,95.7,1.4608,5,403,14.7,391.71,29.53,14.6 2.33099,0,19.58,0,0.871,5.186,93.8,1.5296,5,403,14.7,356.99,28.32,17.8 2.73397,0,19.58,0,0.871,5.597,94.9,1.5257,5,403,14.7,351.85,21.45,15.4 1.6566,0,19.58,0,0.871,6.122,97.3,1.618,5,403,14.7,372.8,14.1,21.5 1.49632,0,19.58,0,0.871,5.404,100,1.5916,5,403,14.7,341.6,13.28,19.6 1.12658,0,19.58,1,0.871,5.012,88,1.6102,5,403,14.7,343.28,12.12,15.3 2.14918,0,19.58,0,0.871,5.709,98.5,1.6232,5,403,14.7,261.95,15.79,19.4 1.41385,0,19.58,1,0.871,6.129,96,1.7494,5,403,14.7,321.02,15.12,17 3.53501,0,19.58,1,0.871,6.152,82.6,1.7455,5,403,14.7,88.01,15.02,15.6 2.44668,0,19.58,0,0.871,5.272,94,1.7364,5,403,14.7,88.63,16.14,13.1 1.22358,0,19.58,0,0.605,6.943,97.4,1.8773,5,403,14.7,363.43,4.59,41.3 1.34284,0,19.58,0,0.605,6.066,100,1.7573,5,403,14.7,353.89,6.43,24.3 1.42502,0,19.58,0,0.871,6.51,100,1.7659,5,403,14.7,364.31,7.39,23.3 1.27346,0,19.58,1,0.605,6.25,92.6,1.7984,5,403,14.7,338.92,5.5,27 1.46336,0,19.58,0,0.605,7.489,90.8,1.9709,5,403,14.7,374.43,1.73,50 1.83377,0,19.58,1,0.605,7.802,98.2,2.0407,5,403,14.7,389.61,1.92,50 1.51902,0,19.58,1,0.605,8.375,93.9,2.162,5,403,14.7,388.45,3.32,50 2.24236,0,19.58,0,0.605,5.854,91.8,2.422,5,403,14.7,395.11,11.64,22.7 2.924,0,19.58,0,0.605,6.101,93,2.2834,5,403,14.7,240.16,9.81,25 2.01019,0,19.58,0,0.605,7.929,96.2,2.0459,5,403,14.7,369.3,3.7,50 1.80028,0,19.58,0,0.605,5.877,79.2,2.4259,5,403,14.7,227.61,12.14,23.8 2.3004,0,19.58,0,0.605,6.319,96.1,2.1,5,403,14.7,297.09,11.1,23.8 2.44953,0,19.58,0,0.605,6.402,95.2,2.2625,5,403,14.7,330.04,11.32,22.3 1.20742,0,19.58,0,0.605,5.875,94.6,2.4259,5,403,14.7,292.29,14.43,17.4 2.3139,0,19.58,0,0.605,5.88,97.3,2.3887,5,403,14.7,348.13,12.03,19.1 0.13914,0,4.05,0,0.51,5.572,88.5,2.5961,5,296,16.6,396.9,14.69,23.1 0.09178,0,4.05,0,0.51,6.416,84.1,2.6463,5,296,16.6,395.5,9.04,23.6 0.08447,0,4.05,0,0.51,5.859,68.7,2.7019,5,296,16.6,393.23,9.64,22.6 0.06664,0,4.05,0,0.51,6.546,33.1,3.1323,5,296,16.6,390.96,5.33,29.4 0.07022,0,4.05,0,0.51,6.02,47.2,3.5549,5,296,16.6,393.23,10.11,23.2 0.05425,0,4.05,0,0.51,6.315,73.4,3.3175,5,296,16.6,395.6,6.29,24.6 0.06642,0,4.05,0,0.51,6.86,74.4,2.9153,5,296,16.6,391.27,6.92,29.9 0.0578,0,2.46,0,0.488,6.98,58.4,2.829,3,193,17.8,396.9,5.04,37.2 0.06588,0,2.46,0,0.488,7.765,83.3,2.741,3,193,17.8,395.56,7.56,39.8 0.06888,0,2.46,0,0.488,6.144,62.2,2.5979,3,193,17.8,396.9,9.45,36.2 0.09103,0,2.46,0,0.488,7.155,92.2,2.7006,3,193,17.8,394.12,4.82,37.9 0.10008,0,2.46,0,0.488,6.563,95.6,2.847,3,193,17.8,396.9,5.68,32.5 0.08308,0,2.46,0,0.488,5.604,89.8,2.9879,3,193,17.8,391,13.98,26.4 0.06047,0,2.46,0,0.488,6.153,68.8,3.2797,3,193,17.8,387.11,13.15,29.6 0.05602,0,2.46,0,0.488,7.831,53.6,3.1992,3,193,17.8,392.63,4.45,50 0.07875,45,3.44,0,0.437,6.782,41.1,3.7886,5,398,15.2,393.87,6.68,32 0.12579,45,3.44,0,0.437,6.556,29.1,4.5667,5,398,15.2,382.84,4.56,29.8 0.0837,45,3.44,0,0.437,7.185,38.9,4.5667,5,398,15.2,396.9,5.39,34.9 0.09068,45,3.44,0,0.437,6.951,21.5,6.4798,5,398,15.2,377.68,5.1,37 0.06911,45,3.44,0,0.437,6.739,30.8,6.4798,5,398,15.2,389.71,4.69,30.5 0.08664,45,3.44,0,0.437,7.178,26.3,6.4798,5,398,15.2,390.49,2.87,36.4 0.02187,60,2.93,0,0.401,6.8,9.9,6.2196,1,265,15.6,393.37,5.03,31.1 0.01439,60,2.93,0,0.401,6.604,18.8,6.2196,1,265,15.6,376.7,4.38,29.1 0.01381,80,0.46,0,0.422,7.875,32,5.6484,4,255,14.4,394.23,2.97,50 0.04011,80,1.52,0,0.404,7.287,34.1,7.309,2,329,12.6,396.9,4.08,33.3 0.04666,80,1.52,0,0.404,7.107,36.6,7.309,2,329,12.6,354.31,8.61,30.3 0.03768,80,1.52,0,0.404,7.274,38.3,7.309,2,329,12.6,392.2,6.62,34.6 0.0315,95,1.47,0,0.403,6.975,15.3,7.6534,3,402,17,396.9,4.56,34.9 0.01778,95,1.47,0,0.403,7.135,13.9,7.6534,3,402,17,384.3,4.45,32.9 0.03445,82.5,2.03,0,0.415,6.162,38.4,6.27,2,348,14.7,393.77,7.43,24.1 0.02177,82.5,2.03,0,0.415,7.61,15.7,6.27,2,348,14.7,395.38,3.11,42.3 0.0351,95,2.68,0,0.4161,7.853,33.2,5.118,4,224,14.7,392.78,3.81,48.5 0.02009,95,2.68,0,0.4161,8.034,31.9,5.118,4,224,14.7,390.55,2.88,50 0.13642,0,10.59,0,0.489,5.891,22.3,3.9454,4,277,18.6,396.9,10.87,22.6 0.22969,0,10.59,0,0.489,6.326,52.5,4.3549,4,277,18.6,394.87,10.97,24.4 0.25199,0,10.59,0,0.489,5.783,72.7,4.3549,4,277,18.6,389.43,18.06,22.5 0.13587,0,10.59,1,0.489,6.064,59.1,4.2392,4,277,18.6,381.32,14.66,24.4 0.43571,0,10.59,1,0.489,5.344,100,3.875,4,277,18.6,396.9,23.09,20 0.17446,0,10.59,1,0.489,5.96,92.1,3.8771,4,277,18.6,393.25,17.27,21.7 0.37578,0,10.59,1,0.489,5.404,88.6,3.665,4,277,18.6,395.24,23.98,19.3 0.21719,0,10.59,1,0.489,5.807,53.8,3.6526,4,277,18.6,390.94,16.03,22.4 0.14052,0,10.59,0,0.489,6.375,32.3,3.9454,4,277,18.6,385.81,9.38,28.1 0.28955,0,10.59,0,0.489,5.412,9.8,3.5875,4,277,18.6,348.93,29.55,23.7 0.19802,0,10.59,0,0.489,6.182,42.4,3.9454,4,277,18.6,393.63,9.47,25 0.0456,0,13.89,1,0.55,5.888,56,3.1121,5,276,16.4,392.8,13.51,23.3 0.07013,0,13.89,0,0.55,6.642,85.1,3.4211,5,276,16.4,392.78,9.69,28.7 0.11069,0,13.89,1,0.55,5.951,93.8,2.8893,5,276,16.4,396.9,17.92,21.5 0.11425,0,13.89,1,0.55,6.373,92.4,3.3633,5,276,16.4,393.74,10.5,23 0.35809,0,6.2,1,0.507,6.951,88.5,2.8617,8,307,17.4,391.7,9.71,26.7 0.40771,0,6.2,1,0.507,6.164,91.3,3.048,8,307,17.4,395.24,21.46,21.7 0.62356,0,6.2,1,0.507,6.879,77.7,3.2721,8,307,17.4,390.39,9.93,27.5 0.6147,0,6.2,0,0.507,6.618,80.8,3.2721,8,307,17.4,396.9,7.6,30.1 0.31533,0,6.2,0,0.504,8.266,78.3,2.8944,8,307,17.4,385.05,4.14,44.8 0.52693,0,6.2,0,0.504,8.725,83,2.8944,8,307,17.4,382,4.63,50 0.38214,0,6.2,0,0.504,8.04,86.5,3.2157,8,307,17.4,387.38,3.13,37.6 0.41238,0,6.2,0,0.504,7.163,79.9,3.2157,8,307,17.4,372.08,6.36,31.6 0.29819,0,6.2,0,0.504,7.686,17,3.3751,8,307,17.4,377.51,3.92,46.7 0.44178,0,6.2,0,0.504,6.552,21.4,3.3751,8,307,17.4,380.34,3.76,31.5 0.537,0,6.2,0,0.504,5.981,68.1,3.6715,8,307,17.4,378.35,11.65,24.3 0.46296,0,6.2,0,0.504,7.412,76.9,3.6715,8,307,17.4,376.14,5.25,31.7 0.57529,0,6.2,0,0.507,8.337,73.3,3.8384,8,307,17.4,385.91,2.47,41.7 0.33147,0,6.2,0,0.507,8.247,70.4,3.6519,8,307,17.4,378.95,3.95,48.3 0.44791,0,6.2,1,0.507,6.726,66.5,3.6519,8,307,17.4,360.2,8.05,29 0.33045,0,6.2,0,0.507,6.086,61.5,3.6519,8,307,17.4,376.75,10.88,24 0.52058,0,6.2,1,0.507,6.631,76.5,4.148,8,307,17.4,388.45,9.54,25.1 0.51183,0,6.2,0,0.507,7.358,71.6,4.148,8,307,17.4,390.07,4.73,31.5 0.08244,30,4.93,0,0.428,6.481,18.5,6.1899,6,300,16.6,379.41,6.36,23.7 0.09252,30,4.93,0,0.428,6.606,42.2,6.1899,6,300,16.6,383.78,7.37,23.3 0.11329,30,4.93,0,0.428,6.897,54.3,6.3361,6,300,16.6,391.25,11.38,22 0.10612,30,4.93,0,0.428,6.095,65.1,6.3361,6,300,16.6,394.62,12.4,20.1 0.1029,30,4.93,0,0.428,6.358,52.9,7.0355,6,300,16.6,372.75,11.22,22.2 0.12757,30,4.93,0,0.428,6.393,7.8,7.0355,6,300,16.6,374.71,5.19,23.7 0.20608,22,5.86,0,0.431,5.593,76.5,7.9549,7,330,19.1,372.49,12.5,17.6 0.19133,22,5.86,0,0.431,5.605,70.2,7.9549,7,330,19.1,389.13,18.46,18.5 0.33983,22,5.86,0,0.431,6.108,34.9,8.0555,7,330,19.1,390.18,9.16,24.3 0.19657,22,5.86,0,0.431,6.226,79.2,8.0555,7,330,19.1,376.14,10.15,20.5 0.16439,22,5.86,0,0.431,6.433,49.1,7.8265,7,330,19.1,374.71,9.52,24.5 0.19073,22,5.86,0,0.431,6.718,17.5,7.8265,7,330,19.1,393.74,6.56,26.2 0.1403,22,5.86,0,0.431,6.487,13,7.3967,7,330,19.1,396.28,5.9,24.4 0.21409,22,5.86,0,0.431,6.438,8.9,7.3967,7,330,19.1,377.07,3.59,24.8 0.08221,22,5.86,0,0.431,6.957,6.8,8.9067,7,330,19.1,386.09,3.53,29.6 0.36894,22,5.86,0,0.431,8.259,8.4,8.9067,7,330,19.1,396.9,3.54,42.8 0.04819,80,3.64,0,0.392,6.108,32,9.2203,1,315,16.4,392.89,6.57,21.9 0.03548,80,3.64,0,0.392,5.876,19.1,9.2203,1,315,16.4,395.18,9.25,20.9 0.01538,90,3.75,0,0.394,7.454,34.2,6.3361,3,244,15.9,386.34,3.11,44 0.61154,20,3.97,0,0.647,8.704,86.9,1.801,5,264,13,389.7,5.12,50 0.66351,20,3.97,0,0.647,7.333,100,1.8946,5,264,13,383.29,7.79,36 0.65665,20,3.97,0,0.647,6.842,100,2.0107,5,264,13,391.93,6.9,30.1 0.54011,20,3.97,0,0.647,7.203,81.8,2.1121,5,264,13,392.8,9.59,33.8 0.53412,20,3.97,0,0.647,7.52,89.4,2.1398,5,264,13,388.37,7.26,43.1 0.52014,20,3.97,0,0.647,8.398,91.5,2.2885,5,264,13,386.86,5.91,48.8 0.82526,20,3.97,0,0.647,7.327,94.5,2.0788,5,264,13,393.42,11.25,31 0.55007,20,3.97,0,0.647,7.206,91.6,1.9301,5,264,13,387.89,8.1,36.5 0.76162,20,3.97,0,0.647,5.56,62.8,1.9865,5,264,13,392.4,10.45,22.8 0.7857,20,3.97,0,0.647,7.014,84.6,2.1329,5,264,13,384.07,14.79,30.7 0.57834,20,3.97,0,0.575,8.297,67,2.4216,5,264,13,384.54,7.44,50 0.5405,20,3.97,0,0.575,7.47,52.6,2.872,5,264,13,390.3,3.16,43.5 0.09065,20,6.96,1,0.464,5.92,61.5,3.9175,3,223,18.6,391.34,13.65,20.7 0.29916,20,6.96,0,0.464,5.856,42.1,4.429,3,223,18.6,388.65,13,21.1 0.16211,20,6.96,0,0.464,6.24,16.3,4.429,3,223,18.6,396.9,6.59,25.2 0.1146,20,6.96,0,0.464,6.538,58.7,3.9175,3,223,18.6,394.96,7.73,24.4 0.22188,20,6.96,1,0.464,7.691,51.8,4.3665,3,223,18.6,390.77,6.58,35.2 0.05644,40,6.41,1,0.447,6.758,32.9,4.0776,4,254,17.6,396.9,3.53,32.4 0.09604,40,6.41,0,0.447,6.854,42.8,4.2673,4,254,17.6,396.9,2.98,32 0.10469,40,6.41,1,0.447,7.267,49,4.7872,4,254,17.6,389.25,6.05,33.2 0.06127,40,6.41,1,0.447,6.826,27.6,4.8628,4,254,17.6,393.45,4.16,33.1 0.07978,40,6.41,0,0.447,6.482,32.1,4.1403,4,254,17.6,396.9,7.19,29.1 0.21038,20,3.33,0,0.4429,6.812,32.2,4.1007,5,216,14.9,396.9,4.85,35.1 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11.5779,0,18.1,0,0.7,5.036,97,1.77,24,666,20.2,396.9,25.68,9.7 8.64476,0,18.1,0,0.693,6.193,92.6,1.7912,24,666,20.2,396.9,15.17,13.8 13.3598,0,18.1,0,0.693,5.887,94.7,1.7821,24,666,20.2,396.9,16.35,12.7 8.71675,0,18.1,0,0.693,6.471,98.8,1.7257,24,666,20.2,391.98,17.12,13.1 5.87205,0,18.1,0,0.693,6.405,96,1.6768,24,666,20.2,396.9,19.37,12.5 7.67202,0,18.1,0,0.693,5.747,98.9,1.6334,24,666,20.2,393.1,19.92,8.5 38.3518,0,18.1,0,0.693,5.453,100,1.4896,24,666,20.2,396.9,30.59,5 9.91655,0,18.1,0,0.693,5.852,77.8,1.5004,24,666,20.2,338.16,29.97,6.3 25.0461,0,18.1,0,0.693,5.987,100,1.5888,24,666,20.2,396.9,26.77,5.6 14.2362,0,18.1,0,0.693,6.343,100,1.5741,24,666,20.2,396.9,20.32,7.2 9.59571,0,18.1,0,0.693,6.404,100,1.639,24,666,20.2,376.11,20.31,12.1 24.8017,0,18.1,0,0.693,5.349,96,1.7028,24,666,20.2,396.9,19.77,8.3 41.5292,0,18.1,0,0.693,5.531,85.4,1.6074,24,666,20.2,329.46,27.38,8.5 67.9208,0,18.1,0,0.693,5.683,100,1.4254,24,666,20.2,384.97,22.98,5 20.7162,0,18.1,0,0.659,4.138,100,1.1781,24,666,20.2,370.22,23.34,11.9 11.9511,0,18.1,0,0.659,5.608,100,1.2852,24,666,20.2,332.09,12.13,27.9 7.40389,0,18.1,0,0.597,5.617,97.9,1.4547,24,666,20.2,314.64,26.4,17.2 14.4383,0,18.1,0,0.597,6.852,100,1.4655,24,666,20.2,179.36,19.78,27.5 51.1358,0,18.1,0,0.597,5.757,100,1.413,24,666,20.2,2.6,10.11,15 14.0507,0,18.1,0,0.597,6.657,100,1.5275,24,666,20.2,35.05,21.22,17.2 18.811,0,18.1,0,0.597,4.628,100,1.5539,24,666,20.2,28.79,34.37,17.9 28.6558,0,18.1,0,0.597,5.155,100,1.5894,24,666,20.2,210.97,20.08,16.3 45.7461,0,18.1,0,0.693,4.519,100,1.6582,24,666,20.2,88.27,36.98,7 18.0846,0,18.1,0,0.679,6.434,100,1.8347,24,666,20.2,27.25,29.05,7.2 10.8342,0,18.1,0,0.679,6.782,90.8,1.8195,24,666,20.2,21.57,25.79,7.5 25.9406,0,18.1,0,0.679,5.304,89.1,1.6475,24,666,20.2,127.36,26.64,10.4 73.5341,0,18.1,0,0.679,5.957,100,1.8026,24,666,20.2,16.45,20.62,8.8 11.8123,0,18.1,0,0.718,6.824,76.5,1.794,24,666,20.2,48.45,22.74,8.4 11.0874,0,18.1,0,0.718,6.411,100,1.8589,24,666,20.2,318.75,15.02,16.7 7.02259,0,18.1,0,0.718,6.006,95.3,1.8746,24,666,20.2,319.98,15.7,14.2 12.0482,0,18.1,0,0.614,5.648,87.6,1.9512,24,666,20.2,291.55,14.1,20.8 7.05042,0,18.1,0,0.614,6.103,85.1,2.0218,24,666,20.2,2.52,23.29,13.4 8.79212,0,18.1,0,0.584,5.565,70.6,2.0635,24,666,20.2,3.65,17.16,11.7 15.8603,0,18.1,0,0.679,5.896,95.4,1.9096,24,666,20.2,7.68,24.39,8.3 12.2472,0,18.1,0,0.584,5.837,59.7,1.9976,24,666,20.2,24.65,15.69,10.2 37.6619,0,18.1,0,0.679,6.202,78.7,1.8629,24,666,20.2,18.82,14.52,10.9 7.36711,0,18.1,0,0.679,6.193,78.1,1.9356,24,666,20.2,96.73,21.52,11 9.33889,0,18.1,0,0.679,6.38,95.6,1.9682,24,666,20.2,60.72,24.08,9.5 8.49213,0,18.1,0,0.584,6.348,86.1,2.0527,24,666,20.2,83.45,17.64,14.5 10.0623,0,18.1,0,0.584,6.833,94.3,2.0882,24,666,20.2,81.33,19.69,14.1 6.44405,0,18.1,0,0.584,6.425,74.8,2.2004,24,666,20.2,97.95,12.03,16.1 5.58107,0,18.1,0,0.713,6.436,87.9,2.3158,24,666,20.2,100.19,16.22,14.3 13.9134,0,18.1,0,0.713,6.208,95,2.2222,24,666,20.2,100.63,15.17,11.7 11.1604,0,18.1,0,0.74,6.629,94.6,2.1247,24,666,20.2,109.85,23.27,13.4 14.4208,0,18.1,0,0.74,6.461,93.3,2.0026,24,666,20.2,27.49,18.05,9.6 15.1772,0,18.1,0,0.74,6.152,100,1.9142,24,666,20.2,9.32,26.45,8.7 13.6781,0,18.1,0,0.74,5.935,87.9,1.8206,24,666,20.2,68.95,34.02,8.4 9.39063,0,18.1,0,0.74,5.627,93.9,1.8172,24,666,20.2,396.9,22.88,12.8 22.0511,0,18.1,0,0.74,5.818,92.4,1.8662,24,666,20.2,391.45,22.11,10.5 9.72418,0,18.1,0,0.74,6.406,97.2,2.0651,24,666,20.2,385.96,19.52,17.1 5.66637,0,18.1,0,0.74,6.219,100,2.0048,24,666,20.2,395.69,16.59,18.4 9.96654,0,18.1,0,0.74,6.485,100,1.9784,24,666,20.2,386.73,18.85,15.4 12.8023,0,18.1,0,0.74,5.854,96.6,1.8956,24,666,20.2,240.52,23.79,10.8 10.6718,0,18.1,0,0.74,6.459,94.8,1.9879,24,666,20.2,43.06,23.98,11.8 6.28807,0,18.1,0,0.74,6.341,96.4,2.072,24,666,20.2,318.01,17.79,14.9 9.92485,0,18.1,0,0.74,6.251,96.6,2.198,24,666,20.2,388.52,16.44,12.6 9.32909,0,18.1,0,0.713,6.185,98.7,2.2616,24,666,20.2,396.9,18.13,14.1 7.52601,0,18.1,0,0.713,6.417,98.3,2.185,24,666,20.2,304.21,19.31,13 6.71772,0,18.1,0,0.713,6.749,92.6,2.3236,24,666,20.2,0.32,17.44,13.4 5.44114,0,18.1,0,0.713,6.655,98.2,2.3552,24,666,20.2,355.29,17.73,15.2 5.09017,0,18.1,0,0.713,6.297,91.8,2.3682,24,666,20.2,385.09,17.27,16.1 8.24809,0,18.1,0,0.713,7.393,99.3,2.4527,24,666,20.2,375.87,16.74,17.8 9.51363,0,18.1,0,0.713,6.728,94.1,2.4961,24,666,20.2,6.68,18.71,14.9 4.75237,0,18.1,0,0.713,6.525,86.5,2.4358,24,666,20.2,50.92,18.13,14.1 4.66883,0,18.1,0,0.713,5.976,87.9,2.5806,24,666,20.2,10.48,19.01,12.7 8.20058,0,18.1,0,0.713,5.936,80.3,2.7792,24,666,20.2,3.5,16.94,13.5 7.75223,0,18.1,0,0.713,6.301,83.7,2.7831,24,666,20.2,272.21,16.23,14.9 6.80117,0,18.1,0,0.713,6.081,84.4,2.7175,24,666,20.2,396.9,14.7,20 4.81213,0,18.1,0,0.713,6.701,90,2.5975,24,666,20.2,255.23,16.42,16.4 3.69311,0,18.1,0,0.713,6.376,88.4,2.5671,24,666,20.2,391.43,14.65,17.7 6.65492,0,18.1,0,0.713,6.317,83,2.7344,24,666,20.2,396.9,13.99,19.5 5.82115,0,18.1,0,0.713,6.513,89.9,2.8016,24,666,20.2,393.82,10.29,20.2 7.83932,0,18.1,0,0.655,6.209,65.4,2.9634,24,666,20.2,396.9,13.22,21.4 3.1636,0,18.1,0,0.655,5.759,48.2,3.0665,24,666,20.2,334.4,14.13,19.9 3.77498,0,18.1,0,0.655,5.952,84.7,2.8715,24,666,20.2,22.01,17.15,19 4.42228,0,18.1,0,0.584,6.003,94.5,2.5403,24,666,20.2,331.29,21.32,19.1 15.5757,0,18.1,0,0.58,5.926,71,2.9084,24,666,20.2,368.74,18.13,19.1 13.0751,0,18.1,0,0.58,5.713,56.7,2.8237,24,666,20.2,396.9,14.76,20.1 4.34879,0,18.1,0,0.58,6.167,84,3.0334,24,666,20.2,396.9,16.29,19.9 4.03841,0,18.1,0,0.532,6.229,90.7,3.0993,24,666,20.2,395.33,12.87,19.6 3.56868,0,18.1,0,0.58,6.437,75,2.8965,24,666,20.2,393.37,14.36,23.2 4.64689,0,18.1,0,0.614,6.98,67.6,2.5329,24,666,20.2,374.68,11.66,29.8 8.05579,0,18.1,0,0.584,5.427,95.4,2.4298,24,666,20.2,352.58,18.14,13.8 6.39312,0,18.1,0,0.584,6.162,97.4,2.206,24,666,20.2,302.76,24.1,13.3 4.87141,0,18.1,0,0.614,6.484,93.6,2.3053,24,666,20.2,396.21,18.68,16.7 15.0234,0,18.1,0,0.614,5.304,97.3,2.1007,24,666,20.2,349.48,24.91,12 10.233,0,18.1,0,0.614,6.185,96.7,2.1705,24,666,20.2,379.7,18.03,14.6 14.3337,0,18.1,0,0.614,6.229,88,1.9512,24,666,20.2,383.32,13.11,21.4 5.82401,0,18.1,0,0.532,6.242,64.7,3.4242,24,666,20.2,396.9,10.74,23 5.70818,0,18.1,0,0.532,6.75,74.9,3.3317,24,666,20.2,393.07,7.74,23.7 5.73116,0,18.1,0,0.532,7.061,77,3.4106,24,666,20.2,395.28,7.01,25 2.81838,0,18.1,0,0.532,5.762,40.3,4.0983,24,666,20.2,392.92,10.42,21.8 2.37857,0,18.1,0,0.583,5.871,41.9,3.724,24,666,20.2,370.73,13.34,20.6 3.67367,0,18.1,0,0.583,6.312,51.9,3.9917,24,666,20.2,388.62,10.58,21.2 5.69175,0,18.1,0,0.583,6.114,79.8,3.5459,24,666,20.2,392.68,14.98,19.1 4.83567,0,18.1,0,0.583,5.905,53.2,3.1523,24,666,20.2,388.22,11.45,20.6 0.15086,0,27.74,0,0.609,5.454,92.7,1.8209,4,711,20.1,395.09,18.06,15.2 0.18337,0,27.74,0,0.609,5.414,98.3,1.7554,4,711,20.1,344.05,23.97,7 0.20746,0,27.74,0,0.609,5.093,98,1.8226,4,711,20.1,318.43,29.68,8.1 0.10574,0,27.74,0,0.609,5.983,98.8,1.8681,4,711,20.1,390.11,18.07,13.6 0.11132,0,27.74,0,0.609,5.983,83.5,2.1099,4,711,20.1,396.9,13.35,20.1 0.17331,0,9.69,0,0.585,5.707,54,2.3817,6,391,19.2,396.9,12.01,21.8 0.27957,0,9.69,0,0.585,5.926,42.6,2.3817,6,391,19.2,396.9,13.59,24.5 0.17899,0,9.69,0,0.585,5.67,28.8,2.7986,6,391,19.2,393.29,17.6,23.1 0.2896,0,9.69,0,0.585,5.39,72.9,2.7986,6,391,19.2,396.9,21.14,19.7 0.26838,0,9.69,0,0.585,5.794,70.6,2.8927,6,391,19.2,396.9,14.1,18.3 0.23912,0,9.69,0,0.585,6.019,65.3,2.4091,6,391,19.2,396.9,12.92,21.2 0.17783,0,9.69,0,0.585,5.569,73.5,2.3999,6,391,19.2,395.77,15.1,17.5 0.22438,0,9.69,0,0.585,6.027,79.7,2.4982,6,391,19.2,396.9,14.33,16.8 0.06263,0,11.93,0,0.573,6.593,69.1,2.4786,1,273,21,391.99,9.67,22.4 0.04527,0,11.93,0,0.573,6.12,76.7,2.2875,1,273,21,396.9,9.08,20.6 0.06076,0,11.93,0,0.573,6.976,91,2.1675,1,273,21,396.9,5.64,23.9 0.10959,0,11.93,0,0.573,6.794,89.3,2.3889,1,273,21,393.45,6.48,22 0.04741,0,11.93,0,0.573,6.03,80.8,2.505,1,273,21,396.9,7.88,11.9
代码:
import org.apache.spark.ml.feature.LabeledPoint import org.apache.spark.ml.linalg.Vectors import org.apache.spark.ml.regression.{LinearRegression, LinearRegressionModel} import org.apache.spark.sql.{Dataset, SparkSession} import scala.collection.immutable object LinearRegression2 { def main(args: Array[String]) { val spark = SparkSession .builder .master("local") .appName("LinearRegression") .getOrCreate() import spark.implicits._ //读取样本数据 val data_path1 = "house_data.csv" val data1: Dataset[String] = spark.read.textFile(data_path1) val data2: Dataset[LabeledPoint] = data1.map { line => val parts = line.split(',') //取特征值.. val features: immutable.Seq[String] = for(i <- 0 until 12) yield parts(i) LabeledPoint(parts(13).toDouble, Vectors.dense(features.map(_.toDouble).toArray)) } //1 为随机种子 val train2TestData: Array[Dataset[LabeledPoint]] = data2.randomSplit(Array(0.8, 0.2), 2) // 迭代次数 val numIterations = 10 val lr = new LinearRegression() .setFeaturesCol("features") .setLabelCol("label") //收敛的值，越小结果越精确，但迭代次数也越大，花费更多时间 .setTol(1E-6) //迭代次数 .setMaxIter(numIterations) //是否需要截距，默认true .setFitIntercept(true) val startTime = System.nanoTime() val model: LinearRegressionModel = lr.fit(train2TestData(0)) //训练模型所消耗的时间 val elapsedTime = (System.nanoTime() - startTime) / 1e9 println("Training time: " + elapsedTime +"seconds") //权重. println("Weights: " + model.coefficients) //截距. println("Intercept:" + model.intercept) //用测试集数据去评估模型，得到一个评估结果。 val summary = model.evaluate(train2TestData(1)) //打印测试结果 summary.predictions.show() //平均绝对误差，预测数据和原始数据对应点误差绝对值和的均值 println("平均绝对值误差: " + summary.meanAbsoluteError) //均方差，预测数据和原始数据对应点误差的平方和的均值 println("均方差: " + summary.meanSquaredError) //测试集的数据条目 println(summary.numInstances) /** * 训练完之后，可以将模型进行保存.. * model.save("model/lir.model") * 模型训练完毕后，以后用的时候可以直接加载模型，无需再训练 * val model = LinearRegressionModel.load("model/lir.model") */ spark.stop() } }执行结果
+-----+--------------------+-------------------+ |label| features| prediction| +-----+--------------------+-------------------+ | 7.2|[14.2362,0.0,18.1...| 19.292308597104586| | 8.1|[0.20746,0.0,27.7...| 7.5416548482414925| | 8.8|[73.5341,0.0,18.1...|-1.4905770946035553| | 10.4|[25.9406,0.0,18.1...| 7.108399199583843| | 10.5|[24.3938,0.0,18.1...| 7.463918272363248| | 11.3|[9.18702,0.0,18.1...| 15.51902740402609| | 12.0|[15.0234,0.0,18.1...| 13.096727831614949| | 12.1|[9.59571,0.0,18.1...| 20.150862207690054| | 12.8|[9.39063,0.0,18.1...| 15.209771092515677| | 13.1|[23.6482,0.0,18.1...| 18.46433759809537| | 13.4|[3.32105,0.0,19.5...| 19.258501533378304| | 13.4|[7.05042,0.0,18.1...| 14.344269743723242| | 13.8|[2.37934,0.0,19.5...| 16.417589029617595| | 14.1|[4.75237,0.0,18.1...| 15.531296234009563| | 14.3|[0.88125,0.0,21.8...| 13.989579508751198| | 14.6|[10.233,0.0,18.1,...| 19.59835602444984| | 15.0|[51.1358,0.0,18.1...| 3.8196651665200996| | 15.2|[1.23247,0.0,8.14...| 17.927575362206746| | 16.1|[6.44405,0.0,18.1...| 18.70165812465354| | 16.6|[0.22927,0.0,6.91...| 20.527508513580685| +-----+--------------------+-------------------+ only showing top 20 rows 平均绝对值误差: 3.5772891666288342 均方差: 25.93492056582901 93