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"LogisticRegression" （机器学习方法）

  • Classify 的方法.
  • 通过特征线性组合的逻辑斯蒂函数模拟类别概率.

详细信息与子选项

  • "LogisticRegression" 通过数值特征 , 的线性组合模拟各个类别的对数概率，其中 对应于类别 k 的参数. 参数矩阵 的估计通过最小化损失函数 sum_(i=1)^m-log(P_(theta)(class=y_i|x_i))+lambda_1 sum_(i=1)^nTemplateBox[{{theta, _, i}}, Abs]+(lambda_2)/2 sum_(i=1)^ntheta_i^2 得到.
  • 可以给出下列选项：
  • "L1Regularization" 0损失函数中 的值
    "L2Regularization" Automatic损失函数中 的值
    "OptimizationMethod" Automatic使用什么方法
  • "OptimizationMethod" 的可能设置包括：
  • "LBFGS"Broyden–Fletcher–Goldfarb–Shanno 算法的有限内存
    "StochasticGradientDescent"随机梯度法
    "Newton"牛顿法

范例

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基本范例  (2)

在标记的示例上训练分类器函数：

Wolfram Language code: c = Classify[{1, 2, 3, 4} -> {1, 1, 2, 2}, Method -> "LogisticRegression"]

获取关于分类器的信息：

Wolfram Language code: Information[c]

对新范例分类：

Wolfram Language code: c[1.3]

生成一些正态分布的数据：

Wolfram Language code: sampledata[center_] := RandomVariate[MultinormalDistribution[center, IdentityMatrix[2]], 200];
Wolfram Language code: clusters = sampledata /@ {{1.5, 1}, {-1.5, 1}, {0, -3}};

可视化：

Wolfram Language code: ListPlot[clusters, PlotStyle -> Darker@{Yellow, Blue, Green}]

在此数据集上训练分类器：

Wolfram Language code: c = Classify[<|Yellow -> clusters[[1]], Blue -> clusters[[2]], Green -> clusters[[3]]|>, Method -> "LogisticRegression"]

将各个类别作为特征的函数，绘制各个类别的训练集和概率分布：

Wolfram Language code: Show[ Plot3D[{ c[{x, y}, "Probability" -> Yellow], c[{x, y}, "Probability" -> Blue], c[{x, y}, "Probability" -> Green]}, {x, -4, 4}, {y, -5, 4}, Exclusions -> None], ListPointPlot3D[Map[Append[#, 1]&, clusters, {2}], PlotStyle -> {Yellow, Blue, Green}]]

选项  (6)

"L1Regularization"  (2)

使用 "L1Regularization" 选项训练分类器：

Wolfram Language code: c = Classify[<|1 -> {1, 23, 1.3, 4}, 2 -> {-4, -3.2, -4, -5}|>, Method -> {"LogisticRegression", "L1Regularization" -> 3}]

生成一些数据，并进行可视化：

Wolfram Language code: colors = {RGBColor[1, 0, 0], RGBColor[0, 0, 1], RGBColor[0, 1, 0], RGBColor[1., 0.77, 0.]}; clusters = Table[RandomVariate[BinormalDistribution[ RandomReal[{-3, 3}, 2], RandomReal[{0.5, 2}, 2], RandomReal[{0.2, 0.8}]], RandomInteger[{30, 40}]], {4}]; plot = ListPlot[clusters, PlotStyle -> Darker[colors, 0.1], ImageSize -> 200, PlotRange -> {{-5, 5}, {-5, 5}}, Frame -> True, AspectRatio -> 1, PlotLabel -> "data"]
Wolfram Language code: line = Range[-5, 5, 0.25]; points = Tuples[line, 2];
Wolfram Language code: makecolormap[probs_] := Transpose @ Partition[ Map[Blend[Keys[#], Values[#]]&, probs], Length[line]];

使用不同的值作为 "L1Regularization" 训练或干分类器，并比较结果：

Wolfram Language code: data = AssociationThread[colors, clusters]; Table[ ArrayPlot[ makecolormap @ Classify[data, points, "Probabilities", Method -> {"LogisticRegression", "L1Regularization" -> λ}], PlotLabel -> ("L1Regularization" -> λ), DataReversed -> True, ImageSize -> 150], {λ, {0, 3, 5, 10}}]~Multicolumn~2 ~Legended~plot

"L2Regularization"  (2)

使用 "L2Regularization" 选项训练分类器：

Wolfram Language code: c = Classify[<|1 -> {1, 23, 1.3, 4}, 2 -> {-4, -3.2, -4, -5}|>, Method -> {"LogisticRegression", "L2Regularization" -> 3}]

生成一些数据，并进行可视化：

Wolfram Language code: colors = {RGBColor[1, 0, 0], RGBColor[0, 0, 1], RGBColor[0, 1, 0], RGBColor[1., 0.77, 0.]}; clusters = Table[RandomVariate[BinormalDistribution[ RandomReal[{-4, 3}, 2], RandomReal[{0.5, 2}, 2], RandomReal[{0.2, 0.8}]], RandomInteger[{30, 40}]], {4}]; plot = ListPlot[clusters, PlotStyle -> Darker[colors, 0.1], ImageSize -> 200, PlotRange -> {{-5, 5}, {-5, 5}}, Frame -> True, AspectRatio -> 1, PlotLabel -> "data"]
Wolfram Language code: line = Range[-5, 5, 0.25]; points = Tuples[line, 2];

使用不同的值作为 "L2Regularization" 训练或干分类器，并比较结果：

Wolfram Language code: makecolormap[probs_] := Transpose @ Partition[ Map[Blend[Keys[#], Values[#]]&, probs], Length[line]];
Wolfram Language code: data = AssociationThread[colors, clusters]; Table[ ArrayPlot[ makecolormap @ Classify[data, points, "Probabilities", Method -> {"LogisticRegression", "L2Regularization" -> λ}], PlotLabel -> ("L2Regularization" -> λ), DataReversed -> True, ImageSize -> 150], {λ, {0, 3, 5, 10}}]~Multicolumn~2 ~Legended~plot

"OptimizationMethod"  (2)

使用特定的 "OptimizationMethod" 训练分类器：

Wolfram Language code: c = Classify[<|1 -> {1, 23, 1.3, 4}, 2 -> {-4, -3.2, -4, -5}|>, Method -> {"LogisticRegression", "OptimizationMethod" -> "StochasticGradientDescent"}]

使用 "Newton" 方法训练分类器：

Wolfram Language code: trainingset = {[image] -> 2, [image] -> 5, [image] -> 8, [image] -> 0, [image] -> 2, [image] -> 7, [image] -> 5, [image] -> 1, [image] -> 3, [image] -> 0, [image] -> 3, [image] -> 9, [image] -> 6, [image] -> 2, [image] -> 8, [image] -> 2, [image] -> 0, [image] -> 6, [image] -> 6, [image] -> 1, [image] -> 1, [image] -> 7, [image] -> 8, [image] -> 5, [image] -> 0, [image] -> 4, [image] -> 7, [image] -> 6, [image] -> 0, [image] -> 2, [image] -> 5, [image] -> 3, [image] -> 1, [image] -> 5, [image] -> 6, [image] -> 7, [image] -> 5, [image] -> 4, [image] -> 1, [image] -> 9, [image] -> 3, [image] -> 6, [image] -> 8, [image] -> 0, [image] -> 9, [image] -> 3, [image] -> 0, [image] -> 3, [image] -> 7, [image] -> 4, [image] -> 4, [image] -> 3, [image] -> 8, [image] -> 0, [image] -> 4, [image] -> 1, [image] -> 3, [image] -> 7, [image] -> 6, [image] -> 4, [image] -> 7, [image] -> 2, [image] -> 7, [image] -> 2, [image] -> 5, [image] -> 2, [image] -> 0, [image] -> 9, [image] -> 8, [image] -> 9, [image] -> 8, [image] -> 1, [image] -> 6, [image] -> 4, [image] -> 8, [image] -> 5, [image] -> 8, [image] -> 0, [image] -> 6, [image] -> 7, [image] -> 4, [image] -> 5, [image] -> 8, [image] -> 4, [image] -> 3, [image] -> 1, [image] -> 5, [image] -> 1, [image] -> 9, [image] -> 9, [image] -> 9, [image] -> 2, [image] -> 4, [image] -> 7, [image] -> 3, [image] -> 1, [image] -> 9, [image] -> 2, [image] -> 9, [image] -> 6};
Wolfram Language code: logistic = Classify[trainingset, Method -> {"LogisticRegression", "OptimizationMethod" -> "Newton"}]

使用 "StochasticGradientDescent" 方法训练分类器：

Wolfram Language code: logistic2 = Classify[trainingset, Method -> {"LogisticRegression", "OptimizationMethod" -> "StochasticGradientDescent"}]

比较相应的训练时间：

Wolfram Language code: Information[logistic, "TrainingTime"] Information[logistic2, "TrainingTime"]