DL4J中函数拟合程序的结构

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#神经网络

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本文以DL4J库为例，详细介绍了如何使用神经网络进行函数拟合。从数据生成、网络配置、训练过程到结果输出，逐步讲解了整个程序的结构，并提出后续将探讨Nd4j矩阵计算、多层网络结构和训练策略等主题。

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下面以函数拟合为例，说明DL4J的程序结构。参考源代码：

org.deeplearning4j.examples.feedforward.regression.RegressionMathFunctions

1.生成数据

1.1自变量

//生成一维向量，共nSamples个值，范围在区间[-10, 10]中
//nSamples 为样本数量，官方例子中默认1000
final INDArray x = Nd4j.linspace(-10,10,nSamples).reshape(nSamples, 1);

1.2因变量

//计算sin(x)，fn=sin(x)
final DataSetIterator iterator = getTrainingData(x,fn,batchSize,rng)

//函数getTrainingData()定义如下：
/** Create a DataSetIterator for training
 * @param x X values
 * @param function Function to evaluate
 * @param batchSize Batch size (number of examples for every call of DataSetIterator.next())
 * @param rng Random number generator (for repeatability)
 */
private static DataSetIterator getTrainingData(final INDArray x, final MathFunction function, final int batchSize, final Random rng) {
    final INDArray y = function.getFunctionValues(x);
    final DataSet allData = new DataSet(x,y);
    final List<DataSet> list = allData.asList();
    Collections.shuffle(list,rng);
    return new ListDataSetIterator(list,batchSize);
}

2.配置神经网络

//在主函数创建多层神经网络
final MultiLayerNetwork net = new MultiLayerNetwork(conf);
net.init();
net.setListeners(new ScoreIterationListener(1));

private static MultiLayerConfiguration getDeepDenseLayerNetworkConfiguration() {
    final int numHiddenNodes = 50;
    return new NeuralNetConfiguration.Builder()
        .seed(seed)
        .iterations(iterations)
        .optimizationAlgo(OptimizationAlgorithm.STOCHASTIC_GRADIENT_DESCENT)
        .learningRate(learningRate)
        .weightInit(WeightInit.XAVIER)
        .updater(Updater.NESTEROVS).momentum(0.9)
        .list()
        .layer(0, new DenseLayer.Builder().nIn(numInputs).nOut(numHiddenNodes)
            .activation(Activation.TANH).build())
        .layer(1, new DenseLayer.Builder().nIn(numHiddenNodes).nOut(numHiddenNodes)
            .activation(Activation.TANH).build())
        .layer(2, new OutputLayer.Builder(LossFunctions.LossFunction.MSE)
            .activation(Activation.IDENTITY)
            .nIn(numHiddenNodes).nOut(numOutputs).build())
        .pretrain(false).backprop(true).build();
}

3.训练测试

//在主函数中执行以下代码
final INDArray[] networkPredictions = new INDArray[nEpochs/ plotFrequency];
for( int i=0; i<nEpochs; i++ ){
    iterator.reset();
    net.fit(iterator);
    if((i+1) % plotFrequency == 0) {
        networkPredictions[i/ plotFrequency] = net.output(x, false);
    }
}

4.输出结果

//在主函数中执行以下代码
plot(fn,x,fn.getFunctionValues(x),networkPredictions);

//定义作图函数plot()
private static void plot(final MathFunction function, final INDArray x, final INDArray y, final INDArray... predicted) {
    final XYSeriesCollection dataSet = new XYSeriesCollection();
    addSeries(dataSet,x,y,"True Function (Labels)");
    for( int i=0; i<predicted.length; i++ ){
        addSeries(dataSet,x,predicted[i],String.valueOf(i));
    }
    final JFreeChart chart = ChartFactory.createXYLineChart(
        "Regression Example - " + function.getName(),     // chart title
        "X",                    // x axis label
        function.getName() + "(X)", // y axis label
        dataSet,                  // data
        PlotOrientation.VERTICAL,
        true,                     // include legend
        true,                      // tooltips
        false                      // urls
    );
    final ChartPanel panel = new ChartPanel(chart);
    final JFrame f = new JFrame();
    f.add(panel);
    f.setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
    f.pack();
    f.setVisible(true);
}