交通流量预测在智能交通(ITS)系统中占有重要地位，是实现交通诱导的前提。准确实时的短时交通流预测有助于更好的分析路网交通状况，对路网交通规划和交通优化控制有非常重要的作用。随着交通数据采集技术的不断发展，及时获取路网中实时的交通数据已成为可能，大量的交通信息为基于深度学习的预测模型提供了数据保障。
基于神经网络的交通流预测的相关研究如下列论文所示。由于与我的研究方向相关，在本文中我实现了基于SAEs、RNN的交通流量预测模型。

Paper：
Traffic Flow Prediction With Big Data: A Deep Learning Approach
Using LSTM and GRU neural network methods for traffic flow prediction

Github：https://github.com/xiaochus/TrafficFlowPrediction

环境

• Python 3.5
• Tensorflow-gpu 1.2.0
• Keras 2.1.3
• scikit-learn 0.18

数据处理

实验数据是从Caltrans Performance Measurement System (PeMS)获取的。原始的流量数据是一个长度为n的一维数据。我们首先使用训练集的数据实现一个标准化对象scaler，然后使用scaler分别对训练集与测试集进行标准化。
由于时序预测任务需要使用历史数据对未来数据进行预测，我们使用时滞变量lags对数据进行划分，最后获得大小为(samples, lags)的数据集。
划分好的数据集在排列顺序上依旧带有时序特性，虽然keras在训练时可以选择对数据进行混洗，但是其执行顺序是先对val数据进行采样再进行混洗，采样过程依旧是按照顺序来的。因此我们事先使用np.random.shuffle对数据进行混洗，打乱数据的顺序。

def process_data(train, test, lags):
    """Process data
    Reshape and split train\test data.

    # Arguments
        train: String, name of .csv train file.
        test: String, name of .csv test file.
        lags: integer, time lag.
    # Returns
        X_train: ndarray.
        y_train: ndarray.
        X_test: ndarray.
        y_test: ndarray.
        scaler: StandardScaler.
    """
    attr = 'Lane 1 Flow (Veh/5 Minutes)'
    df1 = pd.read_csv(train, encoding='utf-8').fillna(0)
    df2 = pd.read_csv(test, encoding='utf-8').fillna(0)

    # scaler = StandardScaler().fit(df1[attr].values)
    scaler = MinMaxScaler(feature_range=(0, 1)).fit(df1[attr].values)
    flow1 = scaler.transform(df1[attr].values)
    flow2 = scaler.transform(df2[attr].values)

    train, test = [], []
    for i in range(lags, len(flow1)):
        train.append(flow1[i - lags: i + 1])
    for i in range(lags, len(flow2)):
        test.append(flow2[i - lags: i + 1])

    train = np.array(train)
    test = np.array(test)
    np.random.shuffle(train)

    X_train = train[:, :-1]
    y_train = train[:, -1]
    X_test = test[:, :-1]
    y_test = test[:, -1]

    return X_train, y_train, X_test, y_test, scaler

模型

LSTM

2隐层LSTM网络。

LSTM.png

def get_lstm(units):
    """LSTM(Long Short-Term Memory)
    Build LSTM Model.

    # Arguments
        units: List(int), number of input, output and hidden units.
    # Returns
        model: Model, nn model.
    """

    model = Sequential()
    model.add(LSTM(units[1], input_shape=(units[0], 1), return_sequences=True))
    model.add(LSTM(units[2]))
    model.add(Dropout(0.2))
    model.add(Dense(units[3], activation='linear'))

    return model

GRU

2隐层GRU网络。

GRU.png

def get_gru(units):
    """GRU(Gated Recurrent Unit)
    Build GRU Model.

    # Arguments
        units: List(int), number of input, output and hidden units.
    # Returns
        model: Model, nn model.
    """

    model = Sequential()
    model.add(GRU(units[1], input_shape=(units[0], 1), return_sequences=True))
    model.add(GRU(units[2]))
    model.add(Dropout(0.2))
    model.add(Dense(units[3], activation='linear'))

    return model

SAEs

SAEs.png

Auto-Encoders的原理是先通过一个encode层对输入进行编码，这个编码就是特征，然后利用encode乘第2层参数（也可以是encode层的参数的转置乘特征并加偏执），重构（解码）输入，然后用重构的输入和实际输入的损失训练参数。
这里我们构建了三个单独的自动编码器，并按照相同的隐层结构构建了一个三层的SAEs。

def _get_sae(inputs, hidden, output):
    """SAE(Auto-Encoders)
    Build SAE Model.

    # Arguments
        inputs: Integer, number of input units.
        hidden: Integer, number of hidden units.
        output: Integer, number of output units.
    # Returns
        model: Model, nn model.
    """

    model = Sequential()
    model.add(Dense(hidden, input_dim=inputs, name='hidden'))
    model.add(Activation('sigmoid'))
    model.add(Dropout(0.2))
    model.add(Dense(output))

    return model


def get_saes(layers):
    """SAEs(Stacked Auto-Encoders)
    Build SAEs Model.

    # Arguments
        layers: List(int), number of input, output and hidden units.
    # Returns
        models: List(Model), List of SAE and SAEs.
    """
    sae1 = _get_sae(layers[0], layers[1], layers[-1])
    sae2 = _get_sae(layers[1], layers[2], layers[-1])
    sae3 = _get_sae(layers[2], layers[3], layers[-1])

    saes = Sequential()
    saes.add(Dense(layers[1], input_dim=layers[0], name='hidden1'))
    saes.add(Activation('sigmoid'))
    saes.add(Dense(layers[2], name='hidden2'))
    saes.add(Activation('sigmoid'))
    saes.add(Dense(layers[3], name='hidden3'))
    saes.add(Activation('sigmoid'))
    saes.add(Dropout(0.2))
    saes.add(Dense(layers[4]))

    models = [sae1, sae2, sae3, saes]

    return models

训练

LSTM、GRU按照正常的RNN网络进行训练。使用train_model()函数训练。
SAEs的训练过程：多个SAE分别训练，第一个SAE训练完之后，其encode的输出作为第二个SAE的输入，接着训练。最后训练完后，将所有SAE的中间隐层连接起来组成一个SAEs网络，使用之前的权值作为初始化权值，再对整个网络进行fine-tune。使用train_seas()函数训练。

使用RMSprop(lr=0.001, rho=0.9, epsilon=1e-06)作为优化器，batch_szie为256，lags为12(即时滞长度为一个小时)。

def train_model(model, X_train, y_train, name, config):
    """train
    train a single model.

    # Arguments
        model: Model, NN model to train.
        X_train: ndarray(number, lags), Input data for train.
        y_train: ndarray(number, ), result data for train.
        name: String, name of model.
        config: Dict, parameter for train.
    """

    model.compile(loss="mse", optimizer="rmsprop", metrics=['mape'])
    # early = EarlyStopping(monitor='val_loss', patience=30, verbose=0, mode='auto')
    hist = model.fit(
        X_train, y_train,
        batch_size=config["batch"],
        epochs=config["epochs"],
        validation_split=0.05)

    model.save('model/' + name + '.h5')
    df = pd.DataFrame.from_dict(hist.history)
    df.to_csv('model/' + name + ' loss.csv', encoding='utf-8', index=False)


def train_seas(models, X_train, y_train, name, config):
    """train
    train the SAEs model.

    # Arguments
        models: List, list of SAE model.
        X_train: ndarray(number, lags), Input data for train.
        y_train: ndarray(number, ), result data for train.
        name: String, name of model.
        config: Dict, parameter for train.
    """

    temp = X_train
    # early = EarlyStopping(monitor='val_loss', patience=30, verbose=0, mode='auto')

    for i in range(len(models) - 1):
        if i > 0:
            p = models[i - 1]
            hidden_layer_model = Model(input=p.input,
                                       output=p.get_layer('hidden').output)
            temp = hidden_layer_model.predict(temp)

        m = models[i]
        m.compile(loss="mse", optimizer="rmsprop", metrics=['mape'])
        m.fit(temp, y_train, batch_size=config["batch"],
              epochs=config["epochs"],
              validation_split=0.05)

        models[i] = m

    saes = models[-1]
    for i in range(len(models) - 1):
        weights = models[i].get_layer('hidden').get_weights()
        saes.get_layer('hidden%d' % (i + 1)).set_weights(weights)

    train_model(saes, X_train, y_train, name, config)

实验

评估

在这里使用MAE、MSE、RMSE、MAPE、R2、explained_variance_score几个指标对回归预测结果进行评估。

def MAPE(y_true, y_pred):
    """Mean Absolute Percentage Error
    Calculate the mape.

    # Arguments
        y_true: List/ndarray, ture data.
        y_pred: List/ndarray, predicted data.
    # Returns
        mape: Double, result data for train.
    """

    y = [x for x in y_true if x > 0]
    y_pred = [y_pred[i] for i in range(len(y_true)) if y_true[i] > 0]

    num = len(y_pred)
    sums = 0

    for i in range(num):
        tmp = abs(y[i] - y_pred[i]) / y[i]
        sums += tmp

    mape = sums * (100 / num)

    return mape


def eva_regress(y_true, y_pred):
    """Evaluation
    evaluate the predicted resul.

    # Arguments
        y_true: List/ndarray, ture data.
        y_pred: List/ndarray, predicted data.
    """

    mape = MAPE(y_true, y_pred)
    vs = metrics.explained_variance_score(y_true, y_pred)
    mae = metrics.mean_absolute_error(y_true, y_pred)
    mse = metrics.mean_squared_error(y_true, y_pred)
    r2 = metrics.r2_score(y_true, y_pred)
    print('explained_variance_score:%f' % vs)
    print('mape:%f%%' % mape)
    print('mae:%f' % mae)
    print('mse:%f' % mse)
    print('rmse:%f' % math.sqrt(mse))
    print('r2:%f' % r2)

预测

我们使用训练好的模型对测试集进行预测。

def main():
    lstm = load_model('model/lstm.h5')
    gru = load_model('model/gru.h5')
    saes = load_model('model/saes.h5')
    models = [lstm, gru, saes]
    names = ['LSTM', 'GRU', 'SAEs']

    lag = 12
    file1 = 'data/train.csv'
    file2 = 'data/test.csv'
    _, _, X_test, y_test, scaler = process_data(file1, file2, lag)
    y_test = scaler.inverse_transform(y_test)

    y_preds = []
    for name, model in zip(names, models):
        if name == 'SAEs':
            X_test = np.reshape(X_test, (X_test.shape[0], X_test.shape[1]))
        else:
            X_test = np.reshape(X_test, (X_test.shape[0], X_test.shape[1], 1))
        file = 'images/' + name + '.png'
        plot_model(model, to_file=file, show_shapes=True)
        predicted = model.predict(X_test)
        predicted = scaler.inverse_transform(predicted)
        y_preds.append(predicted[:300])
        print(name)
        eva_regress(y_test, predicted)

    plot_results(y_test[: 300], y_preds, names)

预测精度对比如下所示：

预测结果对比如下所示：

eva.png