简介

前面涉及到的都是二分类的逻辑回归问题，只要输出一个概率就可以对数据集进行二分类，但在实际生活中，对图片进行分类等

鸢尾花(iris)分类

详情

根据鸢尾花花萼和花瓣的长度和宽度对其进行分类。鸢尾属约有 300 个品种，但我们的程序将仅对下列三个品种进行分类：

  • 山鸢尾
  • 维吉尼亚鸢尾
  • 变色鸢尾

维基百科

操作步骤

1、加载IRIS数据集(训练集和验证集)

  1. /**
  2.  * @license
  3.  * Copyright 2018 Google LLC. All Rights Reserved.
  4.  * Licensed under the Apache License, Version 2.0 (the "License");
  5.  * you may not use this file except in compliance with the License.
  6.  * You may obtain a copy of the License at
  7.  *
  8.  * http://www.apache.org/licenses/LICENSE-2.0
  9.  *
  10.  * Unless required by applicable law or agreed to in writing, software
  11.  * distributed under the License is distributed on an "AS IS" BASIS,
  12.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  13.  * See the License for the specific language governing permissions and
  14.  * limitations under the License.
  15.  * =============================================================================
  16.  */
  18. import * as tf from '@tensorflow/tfjs';
  20. export const IRIS_CLASSES =
  21.     ['山鸢尾', '变色鸢尾', '维吉尼亚鸢尾'];
  22. export const IRIS_NUM_CLASSES = IRIS_CLASSES.length;
  24. // Iris flowers data. Source:
  25. //   https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data
  26. const IRIS_DATA = [
  27.   [5.1, 3.5, 1.4, 0.2, 0], [4.9, 3.0, 1.4, 0.2, 0], [4.7, 3.2, 1.3, 0.2, 0],
  28.   [4.6, 3.1, 1.5, 0.2, 0], [5.0, 3.6, 1.4, 0.2, 0], [5.4, 3.9, 1.7, 0.4, 0],
  29.   [4.6, 3.4, 1.4, 0.3, 0], [5.0, 3.4, 1.5, 0.2, 0], [4.4, 2.9, 1.4, 0.2, 0],
  30.   [4.9, 3.1, 1.5, 0.1, 0], [5.4, 3.7, 1.5, 0.2, 0], [4.8, 3.4, 1.6, 0.2, 0],
  31.   [4.8, 3.0, 1.4, 0.1, 0], [4.3, 3.0, 1.1, 0.1, 0], [5.8, 4.0, 1.2, 0.2, 0],
  32.   [5.7, 4.4, 1.5, 0.4, 0], [5.4, 3.9, 1.3, 0.4, 0], [5.1, 3.5, 1.4, 0.3, 0],
  33.   [5.7, 3.8, 1.7, 0.3, 0], [5.1, 3.8, 1.5, 0.3, 0], [5.4, 3.4, 1.7, 0.2, 0],
  34.   [5.1, 3.7, 1.5, 0.4, 0], [4.6, 3.6, 1.0, 0.2, 0], [5.1, 3.3, 1.7, 0.5, 0],
  35.   [4.8, 3.4, 1.9, 0.2, 0], [5.0, 3.0, 1.6, 0.2, 0], [5.0, 3.4, 1.6, 0.4, 0],
  36.   [5.2, 3.5, 1.5, 0.2, 0], [5.2, 3.4, 1.4, 0.2, 0], [4.7, 3.2, 1.6, 0.2, 0],
  37.   [4.8, 3.1, 1.6, 0.2, 0], [5.4, 3.4, 1.5, 0.4, 0], [5.2, 4.1, 1.5, 0.1, 0],
  38.   [5.5, 4.2, 1.4, 0.2, 0], [4.9, 3.1, 1.5, 0.1, 0], [5.0, 3.2, 1.2, 0.2, 0],
  39.   [5.5, 3.5, 1.3, 0.2, 0], [4.9, 3.1, 1.5, 0.1, 0], [4.4, 3.0, 1.3, 0.2, 0],
  40.   [5.1, 3.4, 1.5, 0.2, 0], [5.0, 3.5, 1.3, 0.3, 0], [4.5, 2.3, 1.3, 0.3, 0],
  41.   [4.4, 3.2, 1.3, 0.2, 0], [5.0, 3.5, 1.6, 0.6, 0], [5.1, 3.8, 1.9, 0.4, 0],
  42.   [4.8, 3.0, 1.4, 0.3, 0], [5.1, 3.8, 1.6, 0.2, 0], [4.6, 3.2, 1.4, 0.2, 0],
  43.   [5.3, 3.7, 1.5, 0.2, 0], [5.0, 3.3, 1.4, 0.2, 0], [7.0, 3.2, 4.7, 1.4, 1],
  44.   [6.4, 3.2, 4.5, 1.5, 1], [6.9, 3.1, 4.9, 1.5, 1], [5.5, 2.3, 4.0, 1.3, 1],
  45.   [6.5, 2.8, 4.6, 1.5, 1], [5.7, 2.8, 4.5, 1.3, 1], [6.3, 3.3, 4.7, 1.6, 1],
  46.   [4.9, 2.4, 3.3, 1.0, 1], [6.6, 2.9, 4.6, 1.3, 1], [5.2, 2.7, 3.9, 1.4, 1],
  47.   [5.0, 2.0, 3.5, 1.0, 1], [5.9, 3.0, 4.2, 1.5, 1], [6.0, 2.2, 4.0, 1.0, 1],
  48.   [6.1, 2.9, 4.7, 1.4, 1], [5.6, 2.9, 3.6, 1.3, 1], [6.7, 3.1, 4.4, 1.4, 1],
  49.   [5.6, 3.0, 4.5, 1.5, 1], [5.8, 2.7, 4.1, 1.0, 1], [6.2, 2.2, 4.5, 1.5, 1],
  50.   [5.6, 2.5, 3.9, 1.1, 1], [5.9, 3.2, 4.8, 1.8, 1], [6.1, 2.8, 4.0, 1.3, 1],
  51.   [6.3, 2.5, 4.9, 1.5, 1], [6.1, 2.8, 4.7, 1.2, 1], [6.4, 2.9, 4.3, 1.3, 1],
  52.   [6.6, 3.0, 4.4, 1.4, 1], [6.8, 2.8, 4.8, 1.4, 1], [6.7, 3.0, 5.0, 1.7, 1],
  53.   [6.0, 2.9, 4.5, 1.5, 1], [5.7, 2.6, 3.5, 1.0, 1], [5.5, 2.4, 3.8, 1.1, 1],
  54.   [5.5, 2.4, 3.7, 1.0, 1], [5.8, 2.7, 3.9, 1.2, 1], [6.0, 2.7, 5.1, 1.6, 1],
  55.   [5.4, 3.0, 4.5, 1.5, 1], [6.0, 3.4, 4.5, 1.6, 1], [6.7, 3.1, 4.7, 1.5, 1],
  56.   [6.3, 2.3, 4.4, 1.3, 1], [5.6, 3.0, 4.1, 1.3, 1], [5.5, 2.5, 4.0, 1.3, 1],
  57.   [5.5, 2.6, 4.4, 1.2, 1], [6.1, 3.0, 4.6, 1.4, 1], [5.8, 2.6, 4.0, 1.2, 1],
  58.   [5.0, 2.3, 3.3, 1.0, 1], [5.6, 2.7, 4.2, 1.3, 1], [5.7, 3.0, 4.2, 1.2, 1],
  59.   [5.7, 2.9, 4.2, 1.3, 1], [6.2, 2.9, 4.3, 1.3, 1], [5.1, 2.5, 3.0, 1.1, 1],
  60.   [5.7, 2.8, 4.1, 1.3, 1], [6.3, 3.3, 6.0, 2.5, 2], [5.8, 2.7, 5.1, 1.9, 2],
  61.   [7.1, 3.0, 5.9, 2.1, 2], [6.3, 2.9, 5.6, 1.8, 2], [6.5, 3.0, 5.8, 2.2, 2],
  62.   [7.6, 3.0, 6.6, 2.1, 2], [4.9, 2.5, 4.5, 1.7, 2], [7.3, 2.9, 6.3, 1.8, 2],
  63.   [6.7, 2.5, 5.8, 1.8, 2], [7.2, 3.6, 6.1, 2.5, 2], [6.5, 3.2, 5.1, 2.0, 2],
  64.   [6.4, 2.7, 5.3, 1.9, 2], [6.8, 3.0, 5.5, 2.1, 2], [5.7, 2.5, 5.0, 2.0, 2],
  65.   [5.8, 2.8, 5.1, 2.4, 2], [6.4, 3.2, 5.3, 2.3, 2], [6.5, 3.0, 5.5, 1.8, 2],
  66.   [7.7, 3.8, 6.7, 2.2, 2], [7.7, 2.6, 6.9, 2.3, 2], [6.0, 2.2, 5.0, 1.5, 2],
  67.   [6.9, 3.2, 5.7, 2.3, 2], [5.6, 2.8, 4.9, 2.0, 2], [7.7, 2.8, 6.7, 2.0, 2],
  68.   [6.3, 2.7, 4.9, 1.8, 2], [6.7, 3.3, 5.7, 2.1, 2], [7.2, 3.2, 6.0, 1.8, 2],
  69.   [6.2, 2.8, 4.8, 1.8, 2], [6.1, 3.0, 4.9, 1.8, 2], [6.4, 2.8, 5.6, 2.1, 2],
  70.   [7.2, 3.0, 5.8, 1.6, 2], [7.4, 2.8, 6.1, 1.9, 2], [7.9, 3.8, 6.4, 2.0, 2],
  71.   [6.4, 2.8, 5.6, 2.2, 2], [6.3, 2.8, 5.1, 1.5, 2], [6.1, 2.6, 5.6, 1.4, 2],
  72.   [7.7, 3.0, 6.1, 2.3, 2], [6.3, 3.4, 5.6, 2.4, 2], [6.4, 3.1, 5.5, 1.8, 2],
  73.   [6.0, 3.0, 4.8, 1.8, 2], [6.9, 3.1, 5.4, 2.1, 2], [6.7, 3.1, 5.6, 2.4, 2],
  74.   [6.9, 3.1, 5.1, 2.3, 2], [5.8, 2.7, 5.1, 1.9, 2], [6.8, 3.2, 5.9, 2.3, 2],
  75.   [6.7, 3.3, 5.7, 2.5, 2], [6.7, 3.0, 5.2, 2.3, 2], [6.3, 2.5, 5.0, 1.9, 2],
  76.   [6.5, 3.0, 5.2, 2.0, 2], [6.2, 3.4, 5.4, 2.3, 2], [5.9, 3.0, 5.1, 1.8, 2],
  77. ];
  79. /**
  80.  * Convert Iris data arrays to `tf.Tensor`s.
  81.  *
  82.  * @param data The Iris input feature data, an `Array` of `Array`s, each element
  83.  *   of which is assumed to be a length-4 `Array` (for petal length, petal
  84.  *   width, sepal length, sepal width).
  85.  * @param targets An `Array` of numbers, with values from the set {0, 1, 2}:
  86.  *   representing the true category of the Iris flower. Assumed to have the same
  87.  *   array length as `data`.
  88.  * @param testSplit Fraction of the data at the end to split as test data: a
  89.  *   number between 0 and 1.
  90.  * @return A length-4 `Array`, with
  91.  *   - training data as `tf.Tensor` of shape [numTrainExapmles, 4].
  92.  *   - training one-hot labels as a `tf.Tensor` of shape [numTrainExamples, 3]
  93.  *   - test data as `tf.Tensor` of shape [numTestExamples, 4].
  94.  *   - test one-hot labels as a `tf.Tensor` of shape [numTestExamples, 3]
  95.  */
  96. function convertToTensors(data, targets, testSplit) {
  97.   const numExamples = data.length;
  98.   if (numExamples !== targets.length) {
  99.     throw new Error('data and split have different numbers of examples');
  100.   }
  102.   // Randomly shuffle `data` and `targets`.
  103.   const indices = [];
  104.   for (let i = 0; i < numExamples; ++i) {
  105.     indices.push(i);
  106.   }
  107.   tf.util.shuffle(indices);
  109.   const shuffledData = [];
  110.   const shuffledTargets = [];
  111.   for (let i = 0; i < numExamples; ++i) {
  112.     shuffledData.push(data[indices[i]]);
  113.     shuffledTargets.push(targets[indices[i]]);
  114.   }
  116.   // Split the data into a training set and a tet set, based on `testSplit`.
  117.   const numTestExamples = Math.round(numExamples * testSplit);
  118.   const numTrainExamples = numExamples - numTestExamples;
  120.   const xDims = shuffledData[0].length;
  122.   // Create a 2D `tf.Tensor` to hold the feature data.
  123.   const xs = tf.tensor2d(shuffledData, [numExamples, xDims]);
  125.   // Create a 1D `tf.Tensor` to hold the labels, and convert the number label
  126.   // from the set {0, 1, 2} into one-hot encoding (.e.g., 0 --> [1, 0, 0]).
  127.   const ys = tf.oneHot(tf.tensor1d(shuffledTargets).toInt(), IRIS_NUM_CLASSES);
  129.   // Split the data into training and test sets, using `slice`.
  130.   const xTrain = xs.slice([0, 0], [numTrainExamples, xDims]);
  131.   const xTest = xs.slice([numTrainExamples, 0], [numTestExamples, xDims]);
  132.   const yTrain = ys.slice([0, 0], [numTrainExamples, IRIS_NUM_CLASSES]);
  133.   const yTest = ys.slice([0, 0], [numTestExamples, IRIS_NUM_CLASSES]);
  134.   return [xTrain, yTrain, xTest, yTest];
  135. }
  137. /**
  138.  * Obtains Iris data, split into training and test sets.
  139.  *
  140.  * @param testSplit Fraction of the data at the end to split as test data: a
  141.  *   number between 0 and 1.
  142.  *
  143.  * @param return A length-4 `Array`, with
  144.  *   - training data as an `Array` of length-4 `Array` of numbers.
  145.  *   - training labels as an `Array` of numbers, with the same length as the
  146.  *     return training data above. Each element of the `Array` is from the set
  147.  *     {0, 1, 2}.
  148.  *   - test data as an `Array` of length-4 `Array` of numbers.
  149.  *   - test labels as an `Array` of numbers, with the same length as the
  150.  *     return test data above. Each element of the `Array` is from the set
  151.  *     {0, 1, 2}.
  152.  */
  153. export function getIrisData(testSplit) {
  154.   return tf.tidy(() => {
  155.     const dataByClass = [];
  156.     const targetsByClass = [];
  157.     for (let i = 0; i < IRIS_CLASSES.length; ++i) {
  158.       dataByClass.push([]);
  159.       targetsByClass.push([]);
  160.     }
  161.     for (const example of IRIS_DATA) {
  162.       const target = example[example.length - 1];
  163.       const data = example.slice(0, example.length - 1);
  164.       dataByClass[target].push(data);
  165.       targetsByClass[target].push(target);
  166.     }
  168.     const xTrains = [];
  169.     const yTrains = [];
  170.     const xTests = [];
  171.     const yTests = [];
  172.     for (let i = 0; i < IRIS_CLASSES.length; ++i) {
  173.       const [xTrain, yTrain, xTest, yTest] =
  174.           convertToTensors(dataByClass[i], targetsByClass[i], testSplit);
  175.       xTrains.push(xTrain);
  176.       yTrains.push(yTrain);
  177.       xTests.push(xTest);
  178.       yTests.push(yTest);
  179.     }
  181.     const concatAxis = 0;
  182.     return [
  183.       tf.concat(xTrains, concatAxis), tf.concat(yTrains, concatAxis),
  184.       tf.concat(xTests, concatAxis), tf.concat(yTests, concatAxis)
  185.     ];
  186.   });
  187. }

2、定义模型结构

带有 softmax(将输出压缩为和为1的概率)的神经网络

3、训练模型并预测

相比之前损失函数，会增加准确度、训练时损失、训练集和验证集准确度等度量单位
见图：训练集损失/测试集损失 and 训练集准确度/测试集准确度 基本拟合，说明这是有效的训练
WechatIMG447.jpeg

  1. import * as tf from '@tensorflow/tfjs'
  2. import * as tfvis from '@tensorflow/tfjs-vis'
  3. import { getIrisData, IRIS_CLASSES } from './data';
  4. console.log('IRIS_CLASSES', IRIS_CLASSES)
  5. window.onload = async () => {
  6.     const [xTrain, yTrain, xTest, yTest] = getIrisData(0.15);
  7.     console.log('ssss', getIrisData(0.15))
  9.     // 初始化模型
  10.     const model = tf.sequential()
  11.     model.add(tf.layers.dense({
  12.         units: 10,
  13.         inputShape: xTrain.shape[1] , // 或 4
  14.         activation: 'sigmoid'
  15.     }))
  16.     model.add(tf.layers.dense({
  17.         units: 3, // 因为需要输出3个概率，所以这里是3
  18.         activation: 'softmax'
  19.     }))
  20.     // 准确度度量
  21.     model.compile({
  22.         loss: 'categoricalCrossentropy', // 交叉熵损失函数(解决多分类问题)
  23.         optimizer: tf.train.adam(0.1),
  24.         metrics: ['accuracy'] // 准确度
  25.     })
  27.     await model.fit(xTrain, yTrain, {
  28.         epochs: 100,
  29.         validationData: [xTrain, yTrain], // 验证集
  30.         callbacks: tfvis.show.fitCallbacks(
  31.        {
  32.             name: '训练效果'
  33.         }, 
  34.         ['loss', 'val_loss', 'acc', 'val_acc'],
  35.         {
  36.             callbacks: ['onEpochEnd']
  37.         }
  38.         )
  39.     })
  40.     window.predict = (form) => {
  41.         const input = tf.tensor([[
  42.             form.a.value * 1, // 花萼长度
  43.             form.b.value * 1, // 花萼宽度
  44.             form.c.value * 1, // 花瓣长度
  45.             form.d.value * 1, // 花瓣宽度
  46.         ]]);
  47.         const pred = model.predict(input); // pred.argMax(数据维度） 输出概率中的最高值
  48.         alert(`预测结果：${IRIS_CLASSES[pred.argMax(1).dataSync(0)]}`);
  49.     };
  50. }