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"TSNE" （机器学习方法）

详细信息和子选项

  • "TSNE" 代表 t 分布随机邻域嵌入，是一种非线性非参数降维方法. 该方法尝试学习数据的低维表示，以保留数据的局部结构.
  • "TSNE" 适用于具有非线性流形的数据集，特别适用于高维数据集的可视化； 但是，对于具有大量特征和大量示例的数据集进行训练则很慢.
  • 下面显示了 "TSNE" 方法应用于基准数据集 Fisher's Irises、MNIST 和 FashionMNIST 的学习的二维嵌入：
  • 给定原始空间中数据点 (xi, xj) 的相似矩阵 p_(ij)，"TSNE" 尝试找到低维嵌入 ，使得低维空间中的 q_(ij) 与 p_(ij) 相匹配.
  • 原始空间中的相似性由 给出，其中 对应于邻域半径. 低维空间中的相似性由 给出.
  • 低维嵌入 通过最小化嵌入成本 计算.
  • 参数 由一个困惑度参数间接控制. 困惑度越大，聚类越少，反之亦然.
  • 可以给出以下子选项：
  • "Perplexity" Automatic半径 ϵ
    "LinearPrereduction" False在运行 t-SNE 方法之前是否执行线性缩减

范例

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基本范例  (1)

使用 "TSNE" 方法降低一些图像的维度：

Wolfram Language code: fmnist = {[image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image]}; reduced = DimensionReduce[fmnist, 2, Method -> "TSNE"];

可视化图像的二维表示：

Wolfram Language code: ListPlot[MapThread[Labeled[#1, #2]&, {reduced, fmnist}], ...]

选项  (2)

"Perplexity"  (1)

从 ExampleData 加载 Fisher Iris 数据集：

Wolfram Language code: iris = ExampleData[{"MachineLearning", "FisherIris"}, "Data"];
Wolfram Language code: RandomSample[iris, 5]

使用 "TSNE" 方法生成降维函数：

Wolfram Language code: diris = DimensionReduction[iris[[All, 1]], 2, Method -> "TSNE"]

按物种对示例进行分组：

Wolfram Language code: byspecies = GroupBy[iris, Last -> First];

降低特征的维度：

Wolfram Language code: byspecies = diris /@ byspecies;

可视化降维后的数据集：

Wolfram Language code: ListPlot[Values[byspecies], PlotLegends -> Keys[byspecies]]

使用不同的困惑值执行相同的操作：

Wolfram Language code: diris = DimensionReduction[iris[[All, 1]], 2, Method -> {"TSNE", "Perplexity" -> 100}]
Wolfram Language code: byspecies = GroupBy[iris, Last -> First]; byspecies = diris /@ byspecies; ListPlot[Values[byspecies], PlotLegends -> Keys[byspecies]]

"LinearPrereduction"  (1)

从 "MNIST" 数据集中加载样本：

Wolfram Language code: mnist = RandomSample[ResourceData["MNIST"][[All, 1]], 200];

使用 "TSNE" 降低图像的维度：

Wolfram Language code: features = DimensionReduce[mnist, Method -> "TSNE"];

在使用 "LinearPrereduction" 子选项运行 t-SNE 方法之前，通过执行线性缩减来查找特征：

Wolfram Language code: features2 = DimensionReduce[mnist, Method -> {"TSNE", "LinearPrereduction" -> True}];

可视化得到的特征并比较结果：

Wolfram Language code: ListPlot[List /@ features, ...] ListPlot[List /@ features2, ...]

应用  (1)

数据可视化  (1)

使用 "TSNE" 方法降低一些图像的维度：

Wolfram Language code: flowers = {[image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image], [image]}; reduced = DimensionReduce[flowers, 2, Method -> {"TSNE", "LinearPrereduction" -> True}];

可视化图像的二维表示：

Wolfram Language code: ListPlot[MapThread[Labeled[#1, #2]&, {reduced, flowers}]]