geoman模型基于编解码网络及分层注意力机制设计而成，可以对多源时间序列进行预测。在编码端，引入局部及全局注意力，并将传感器之间的距离作为全局注意力的一部分；在解码端，引入时间注意力，用于挖掘时间上的依赖关系。该模型相关代码可以在github上找到，但是缺少数据处理的部分，本文介绍其数据处理部分，数据集下载地址为http://urban-computing.com/index-40.htm。相关代码如下：

# load data of beijing
    data_path = './data'
    air_quality_data = pd.read_csv('{}/airquality.csv'.format(data_path), nrows=278023)

    # remove data from 1022 that with lot of null data
    air_quality_data = air_quality_data[air_quality_data['station_id'] != 1022]
    columns = ['PM25_Concentration', 'PM10_Concentration',
               'NO2_Concentration', 'CO_Concentration',
               'O3_Concentration', 'SO2_Concentration']
    # pivot the data
    pivot_air_data = air_quality_data.pivot(index='time', columns='station_id', values=columns)
    # linear interpolate to fill the loss value
    pivot_air_data1 = pivot_air_data.interpolate(method='linear').dropna()

    air_quality_data = pivot_air_data1.stack(level=1).reset_index().sort_values(by=['station_id', 'time'])
    # feature normalization
    temp_data = air_quality_data.values
    temp_data1 = temp_data[:, 2:].astype('float32')
    scaler = MinMaxScaler(feature_range=(0, 1))
    scaled = scaler.fit_transform(temp_data1)
    temp_data[:, 2:] = scaled
    air_quality_data = pd.DataFrame(temp_data, columns=['time', 'station_id'] + columns)

    # select the 1001 point as the local input
    local_input = air_quality_data[air_quality_data.station_id == 1001].drop(['station_id', 'time'], axis=1).values
    # transform time series to supervised
    time_length = local_input.shape[0]
    local_data = []
    label = []
    for i in range(hps.n_steps_encoder, time_length - hps.n_steps_decoder):
        local_data.append(scaled[i - hps.n_steps_encoder:i, :])
        label.append(scaled[i:i + hps.n_steps_decoder, 0])  # take pm2.5 as the target series
    local_data = np.array(local_data)
    label = np.array(label)
    length = local_data.shape[0]
    global_attn_index = np.arange(0, length, 1)
    global_inp_index = np.arange(0, length, 1)
    split_ratio = int(length / 10)

    # split the data into train/valid/test with the ratio of 8:1:1
    training_data = [local_data[:8 * split_ratio],
                     global_attn_index[:8 * split_ratio],
                     global_inp_index[:8 * split_ratio],
                     label.reshape(label.shape[0], label.shape[1], 1)[:8 * split_ratio],
                     label[:8 * split_ratio]]
    valid_data = [local_data[8 * split_ratio:9 * split_ratio],
                  global_attn_index[8 * split_ratio:9 * split_ratio],
                  global_inp_index[8 * split_ratio:9 * split_ratio],
                  label.reshape(label.shape[0], label.shape[1], 1)[8 * split_ratio:9 * split_ratio],
                  label[8 * split_ratio:9 * split_ratio]]
    test_data = [local_data[9 * split_ratio:],
                 global_attn_index[9 * split_ratio:],
                 global_inp_index[9 * split_ratio:],
                 label.reshape(label.shape[0], label.shape[1], 1)[9 * split_ratio:],
                 label[9 * split_ratio:]]
    # construct global_input data
    pivot_df = air_quality_data.pivot(index='time', columns='station_id', values=columns)
    global_inputs = pivot_df['PM25_Concentration'].values.astype('float32')
    points = np.arange(1001, 1037, 1).tolist()
    points.remove(1022)
    global_attn_states = []
    for station_id in points:
        id_df = air_quality_data[air_quality_data.station_id == station_id].drop(['station_id', 'time'], axis=1)
        factor_agg = []
        for factor in columns:
            id_fac_df = id_df[factor]
            lags, cols = list(), list()
            for i in range(hps.n_steps_encoder - 1, -1, -1):
                lags.append(id_fac_df.shift(i))
                cols.append('{}(t-{})'.format(factor, i))
            agg = pd.concat(lags, axis=1).dropna()
            agg.columns = cols
            factor_agg.append(agg)
        global_attn_states.append(pd.concat(factor_agg, axis=1).values)
    global_attn_states = np.concatenate(global_attn_states, axis=1)
    time_len = global_attn_states.shape[0]
    global_attn_states = global_attn_states.reshape(time_len, len(points), 6, hps.n_steps_encoder)

    # measure sensor geospatial similarity
    sensors = pd.read_csv('{}/station.csv'.format(data_path), nrows=36).drop(index=21)
    # lat and lng of sensors
    lat = sensors['latitude'].values
    lng = sensors['longitude'].values
    end_lats, start_lngs = np.meshgrid(lat, lng)
    start_lats = end_lats.T
    end_lngs = start_lngs.T
    distance = get_distance_hav(start_lngs, start_lats, end_lngs, end_lats)
    sensor_sim = 1 / (distance + 1)
    # normalization
    min_sim = np.min(sensor_sim)
    max_sim = np.max(sensor_sim)
    sensor_sim_nor = (sensor_sim - min_sim) / (max_sim - min_sim)
    sensor_sim_nor = sensor_sim_nor[0, :]

模型结果如下：

rmse=23.8