PM2.5预测

课程链接：李宏毅课程-机器学习

数据集介绍

• 本次作业使用丰原站的观测记录，分成 train set 跟 test set，train set 是丰原站每个月的前 20 天所有资料。test set 则是从丰原站剩下的资料中取样出来。
• train.csv: 每个月前 20 天的完整资料。
• test.csv : 从剩下的资料当中取样出连续的 10 小时为一笔，前九小时的所有观测数据当作 feature，第十小时的 PM2.5 当作 answer。一共取出 240 笔不重複的 test data，请根据 feature 预测这 240 笔的 PM2.5。
• Data 含有 18 项观测数据 AMB_TEMP, CH4, CO, NHMC, NO, NO2, NOx, O3, PM10, PM2.5, RAINFALL, RH, SO2, THC, WD_HR, WIND_DIREC, WIND_SPEED, WS_HR。

1.数据分析

import os
import pandas as pd
import numpy as np

data=pd.read_csv("work/hw1_data/train.csv", encoding="big5")

1.1观察数据

data.head(20)

	日期	測站	測項	0	1	2	3	4	5	6	...	14	15	16	17	18	19	20	21	22	23
0	2014/1/1	豐原	AMB_TEMP	14	14	14	13	12	12	12	...	22	22	21	19	17	16	15	15	15	15
1	2014/1/1	豐原	CH4	1.8	1.8	1.8	1.8	1.8	1.8	1.8	...	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8
2	2014/1/1	豐原	CO	0.51	0.41	0.39	0.37	0.35	0.3	0.37	...	0.37	0.37	0.47	0.69	0.56	0.45	0.38	0.35	0.36	0.32
3	2014/1/1	豐原	NMHC	0.2	0.15	0.13	0.12	0.11	0.06	0.1	...	0.1	0.13	0.14	0.23	0.18	0.12	0.1	0.09	0.1	0.08
4	2014/1/1	豐原	NO	0.9	0.6	0.5	1.7	1.8	1.5	1.9	...	2.5	2.2	2.5	2.3	2.1	1.9	1.5	1.6	1.8	1.5
5	2014/1/1	豐原	NO2	16	9.2	8.2	6.9	6.8	3.8	6.9	...	11	11	22	28	19	12	8.1	7	6.9	6
6	2014/1/1	豐原	NOx	17	9.8	8.7	8.6	8.5	5.3	8.8	...	14	13	25	30	21	13	9.7	8.6	8.7	7.5
7	2014/1/1	豐原	O3	16	30	27	23	24	28	24	...	65	64	51	34	33	34	37	38	38	36
8	2014/1/1	豐原	PM10	56	50	48	35	25	12	4	...	52	51	66	85	85	63	46	36	42	42
9	2014/1/1	豐原	PM2.5	26	39	36	35	31	28	25	...	36	45	42	49	45	44	41	30	24	13
10	2014/1/1	豐原	RAINFALL	NR	NR	NR	NR	NR	NR	NR	...	NR	NR	NR	NR	NR	NR	NR	NR	NR	NR
11	2014/1/1	豐原	RH	77	68	67	74	72	73	74	...	47	49	56	67	72	69	70	70	70	69
12	2014/1/1	豐原	SO2	1.8	2	1.7	1.6	1.9	1.4	1.5	...	3.9	4.4	9.9	5.1	3.4	2.3	2	1.9	1.9	1.9
13	2014/1/1	豐原	THC	2	2	2	1.9	1.9	1.8	1.9	...	1.9	1.9	1.9	2.1	2	1.9	1.9	1.9	1.9	1.9
14	2014/1/1	豐原	WD_HR	37	80	57	76	110	106	101	...	307	304	307	124	118	121	113	112	106	110
15	2014/1/1	豐原	WIND_DIREC	35	79	2.4	55	94	116	106	...	313	305	291	124	119	118	114	108	102	111
16	2014/1/1	豐原	WIND_SPEED	1.4	1.8	1	0.6	1.7	2.5	2.5	...	2.5	2.2	1.4	2.2	2.8	3	2.6	2.7	2.1	2.1
17	2014/1/1	豐原	WS_HR	0.5	0.9	0.6	0.3	0.6	1.9	2	...	2.1	2.1	1.9	1	2.5	2.5	2.8	2.6	2.4	2.3
18	2014/1/2	豐原	AMB_TEMP	16	15	15	14	14	15	16	...	24	24	23	21	20	19	18	18	18	18
19	2014/1/2	豐原	CH4	1.8	1.8	1.8	1.8	1.8	1.8	1.8	...	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8

20 rows × 27 columns

data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 4320 entries, 0 to 4319
Data columns (total 27 columns):
 #   Column  Non-Null Count  Dtype 
---  ------  --------------  ----- 
 0   日期      4320 non-null   object
 1   測站      4320 non-null   object
 2   測項      4320 non-null   object
 3   0       4320 non-null   object
 4   1       4320 non-null   object
 5   2       4320 non-null   object
 6   3       4320 non-null   object
 7   4       4320 non-null   object
 8   5       4320 non-null   object
 9   6       4320 non-null   object
 10  7       4320 non-null   object
 11  8       4320 non-null   object
 12  9       4320 non-null   object
 13  10      4320 non-null   object
 14  11      4320 non-null   object
 15  12      4320 non-null   object
 16  13      4320 non-null   object
 17  14      4320 non-null   object
 18  15      4320 non-null   object
 19  16      4320 non-null   object
 20  17      4320 non-null   object
 21  18      4320 non-null   object
 22  19      4320 non-null   object
 23  20      4320 non-null   object
 24  21      4320 non-null   object
 25  22      4320 non-null   object
 26  23      4320 non-null   object
dtypes: object(27)
memory usage: 911.4+ KB

data.describe()

	日期	測站	測項	0	1	2	3	4	5	6	...	14	15	16	17	18	19	20	21	22	23
count	4320	4320	4320	4320	4320	4320	4320	4320	4320	4320	...	4320	4320	4320	4320	4320	4320	4320	4320	4320	4320
unique	240	1	18	369	361	351	355	353	342	356	...	423	411	409	423	405	374	366	374	382	370
top	2014/1/20	豐原	WIND_SPEED	NR	NR	NR	NR	NR	NR	NR	...	NR	NR	NR	NR	NR	NR	NR	NR	NR	NR
freq	18	4320	240	221	225	229	226	229	230	226	...	220	219	221	221	222	223	225	224	226	224

4 rows × 27 columns

1.1特征抽取

# rainfall补零,截取第四列一直到结束
data=data.iloc[:,3:]
data[data=='NR']=0
numpy_data=data.to_numpy()

# 可见雨全0
data.head(18)

	0	1	2	3	4	5	6	7	8	9	...	14	15	16	17	18	19	20	21	22	23
0	14	14	14	13	12	12	12	12	15	17	...	22	22	21	19	17	16	15	15	15	15
1	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	...	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8	1.8
2	0.51	0.41	0.39	0.37	0.35	0.3	0.37	0.47	0.78	0.74	...	0.37	0.37	0.47	0.69	0.56	0.45	0.38	0.35	0.36	0.32
3	0.2	0.15	0.13	0.12	0.11	0.06	0.1	0.13	0.26	0.23	...	0.1	0.13	0.14	0.23	0.18	0.12	0.1	0.09	0.1	0.08
4	0.9	0.6	0.5	1.7	1.8	1.5	1.9	2.2	6.6	7.9	...	2.5	2.2	2.5	2.3	2.1	1.9	1.5	1.6	1.8	1.5
5	16	9.2	8.2	6.9	6.8	3.8	6.9	7.8	15	21	...	11	11	22	28	19	12	8.1	7	6.9	6
6	17	9.8	8.7	8.6	8.5	5.3	8.8	9.9	22	29	...	14	13	25	30	21	13	9.7	8.6	8.7	7.5
7	16	30	27	23	24	28	24	22	21	29	...	65	64	51	34	33	34	37	38	38	36
8	56	50	48	35	25	12	4	2	11	38	...	52	51	66	85	85	63	46	36	42	42
9	26	39	36	35	31	28	25	20	19	30	...	36	45	42	49	45	44	41	30	24	13
10	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
11	77	68	67	74	72	73	74	73	66	56	...	47	49	56	67	72	69	70	70	70	69
12	1.8	2	1.7	1.6	1.9	1.4	1.5	1.6	5.1	15	...	3.9	4.4	9.9	5.1	3.4	2.3	2	1.9	1.9	1.9
13	2	2	2	1.9	1.9	1.8	1.9	1.9	2.1	2	...	1.9	1.9	1.9	2.1	2	1.9	1.9	1.9	1.9	1.9
14	37	80	57	76	110	106	101	104	124	46	...	307	304	307	124	118	121	113	112	106	110
15	35	79	2.4	55	94	116	106	94	232	153	...	313	305	291	124	119	118	114	108	102	111
16	1.4	1.8	1	0.6	1.7	2.5	2.5	2	0.6	0.8	...	2.5	2.2	1.4	2.2	2.8	3	2.6	2.7	2.1	2.1
17	0.5	0.9	0.6	0.3	0.6	1.9	2	2	0.5	0.3	...	2.1	2.1	1.9	1	2.5	2.5	2.8	2.6	2.4	2.3

18 rows × 24 columns

# RangeIndex: 4320 entries, 0 to 4319 24列(小时),18个特征
# 4320  18= 12月  18   480每月小时数...os
month_data={}
for month in range(12):
    # 每月数据量
    sample=np.empty([18,480])
    # 每天数据量
    for day in range(20):
        # 每天24小时，对应这个18个*24小时个数据
        sample[:, day*24:(day+1)*24]=numpy_data[18*(20*month +day): 18*(20*month +day+1),:]
    month_data[month]=sample

1.1数据分析

# 数据
x=np.empty([12*471,18*9],dtype=float)
# pm2.5
y=np.empty([12*471,1],dtype=float)
for month in range(12):
    for day in range(20):
        for hour in range(24):
            # 如果是最后一天，最后一个包结束，则返回
            if day==19 and hour>14:
                continue
            # 每个小时的18项数据
            x[month*471+day*24+hour,:]=month_data[month][:,day*24+hour:day*24+hour+9].reshape(1,-1)
            # pm值
            y[month*471+day*24+hour,0]=month_data[month][9,day*24+hour+9]
print(x)
print(y)

[[14.  14.  14.  ...  2.   2.   0.5]
 [14.  14.  13.  ...  2.   0.5  0.3]
 [14.  13.  12.  ...  0.5  0.3  0.8]
 ...
 [17.  18.  19.  ...  1.1  1.4  1.3]
 [18.  19.  18.  ...  1.4  1.3  1.6]
 [19.  18.  17.  ...  1.3  1.6  1.8]]
[[30.]
 [41.]
 [44.]
 ...
 [17.]
 [24.]
 [29.]]

1.1归一化

mean_x = np.mean(x, axis = 0) #18 * 9 
std_x = np.std(x, axis = 0) #18 * 9 
for i in range(len(x)): #12 * 471
    for j in range(len(x[0])): #18 * 9 
        if std_x[j] != 0:
            x[i][j] = (x[i][j] - mean_x[j]) / std_x[j]

import math
x_train_set = x[: math.floor(len(x) * 0.8), :]
y_train_set = y[: math.floor(len(y) * 0.8), :]
x_validation = x[math.floor(len(x) * 0.8): , :]
y_validation = y[math.floor(len(y) * 0.8): , :]
print(x_train_set)
print(y_train_set)
print(x_validation)
print(y_validation)
print(len(x_train_set))
print(len(y_train_set))
print(len(x_validation))
print(len(y_validation))

[[-1.35825331 -1.35883937 -1.359222   ...  0.26650729  0.2656797
  -1.14082131]
 [-1.35825331 -1.35883937 -1.51819928 ...  0.26650729 -1.13963133
  -1.32832904]
 [-1.35825331 -1.51789368 -1.67717656 ... -1.13923451 -1.32700613
  -0.85955971]
 ...
 [ 0.86929969  0.70886668  0.38952809 ...  1.39110073  0.2656797
  -0.39079039]
 [ 0.71018876  0.39075806  0.07157353 ...  0.26650729 -0.39013211
  -0.39079039]
 [ 0.3919669   0.07264944  0.07157353 ... -0.38950555 -0.39013211
  -0.85955971]]
[[30.]
 [41.]
 [44.]
 ...
 [ 7.]
 [ 5.]
 [14.]]
[[ 0.07374504  0.07264944  0.07157353 ... -0.38950555 -0.85856912
  -0.57829812]
 [ 0.07374504  0.07264944  0.23055081 ... -0.85808615 -0.57750692
   0.54674825]
 [ 0.07374504  0.23170375  0.23055081 ... -0.57693779  0.54674191
  -0.1095288 ]
 ...
 [-0.88092053 -0.72262212 -0.56433559 ... -0.57693779 -0.29644471
  -0.39079039]
 [-0.7218096  -0.56356781 -0.72331287 ... -0.29578943 -0.39013211
  -0.1095288 ]
 [-0.56269867 -0.72262212 -0.88229015 ... -0.38950555 -0.10906991
   0.07797893]]
[[13.]
 [24.]
 [22.]
 ...
 [17.]
 [24.]
 [29.]]
4521
4521
1131
1131

2.训练

# 1为常数项
dim = 18 * 9 + 1
w = np.zeros([dim, 1])
x = np.concatenate((np.ones([12 * 471, 1]), x), axis = 1).astype(float)
learning_rate = 100
iter_time = 3000
adagrad = np.zeros([dim, 1])
# 防止被除数为0
eps = 0.0000000001
for t in range(iter_time):
    # 平方差
    loss = np.sqrt(np.sum(np.power(np.dot(x, w) - y, 2))/471/12)#rmse
    # 每100次输出一次
    if(t%100==0):
        print(str(t) + ":" + str(loss))
    # 梯度
    gradient = 2 * np.dot(x.transpose(), np.dot(x, w) - y) #dim*1
    adagrad += gradient ** 2
    w = w - learning_rate * gradient / np.sqrt(adagrad + eps)
np.save('weight.npy', w)

0:27.071214829194115
100:33.78905859777454
200:19.913751298197102
300:13.531068193689693
400:10.645466158446172
500:9.277353455475067
600:8.518042045956506
700:8.014061987588427
800:7.636756824775698
900:7.336563740371129
1000:7.090968643947224
1100:6.887311480324104
1200:6.717116295730699
1300:6.574102121171872
1400:6.453381172520272
1500:6.351062466046938
1600:6.264012287766374
1700:6.18968838345321
1800:6.126016764546809
1900:6.071297135545992
2000:6.024129170225593
2100:5.98335455636348
2200:5.94801117011856
2300:5.9172966606664765
2400:5.890539375339805
2500:5.867175036840055
2600:5.846727947724756
2700:5.82879577424176
2800:5.8130371731415105
2900:5.799161687153943

3.测试

test_data=pd.read_csv("work/hw1_data/test.csv",header=None, encoding="big5")

test_data.head()

	0	1	2	3	4	5	6	7	8	9	10
0	id_0	AMB_TEMP	21	21	20	20	19	19	19	18	17
1	id_0	CH4	1.7	1.7	1.7	1.7	1.7	1.7	1.7	1.7	1.8
2	id_0	CO	0.39	0.36	0.36	0.4	0.53	0.55	0.34	0.31	0.23
3	id_0	NMHC	0.16	0.24	0.22	0.27	0.27	0.26	0.27	0.29	0.1
4	id_0	NO	1.3	1.3	1.3	1.3	1.4	1.6	1.2	1.1	0.9

test_data=test_data.iloc[:,2:]

test_data.head(18)

	2	3	4	5	6	7	8	9	10
0	21	21	20	20	19	19	19	18	17
1	1.7	1.7	1.7	1.7	1.7	1.7	1.7	1.7	1.8
2	0.39	0.36	0.36	0.4	0.53	0.55	0.34	0.31	0.23
3	0.16	0.24	0.22	0.27	0.27	0.26	0.27	0.29	0.1
4	1.3	1.3	1.3	1.3	1.4	1.6	1.2	1.1	0.9
5	17	14	13	14	18	21	8.9	9.4	5
6	18	16	14	15	20	23	10	10	5.8
7	32	31	31	26	16	12	27	20	26
8	62	50	44	39	38	32	48	36	25
9	33	39	39	25	18	18	17	9	4
10	NR	NR	NR	NR	NR	NR	NR	NR	NR
11	83	85	87	87	86	85	78	81	80
12	2	1.8	1.8	1.8	2.1	2.6	2	2.3	2.4
13	1.8	1.9	1.9	2	2	2	2	2	1.9
14	58	53	67	59	59	73	79	82	104
15	57	44	73	44	56	115	45	107	103
16	1.4	1.3	1.5	1.4	1.6	1.6	1.2	1.8	2.3
17	1	0.9	0.9	0.9	1.2	0.7	1	0.6	1.8

# 雨置0
test_data[test_data == 'NR'] = 0

test_data=test_data.to_numpy()
# 240个记录,18*9
test_x=np.empty([240,18*9], dtype=float)
for i in range(240):
    test_x[i, :] = test_data[18 * i: 18* (i + 1), :].reshape(1, -1)
# 归一化
for i in range(len(test_x)):
    for j in range(len(test_x[0])):
        if std_x[j] != 0:
            test_x[i][j] = (test_x[i][j] - mean_x[j]) / std_x[j]
test_x = np.concatenate((np.ones([240, 1]), test_x), axis = 1).astype(float)

4.预测

w=np.load("weight.npy")
ans_y=np.dot(test_x,w)

5.保存

import csv
with open("submit.csv", mode="w",newline='') as submit_file:
    csv_writer=csv.writer(submit_file)
    header=['id','value']
    csv_writer.writerow(header)
    for i in range(240):
        row=["id_" +str (i), ans_y[i][0]]
        csv_writer.writerow(row)
        print(row)

['id_0', 6.664170072810432]
['id_1', 18.06982655390777]
['id_2', 22.749942554291376]
['id_3', 8.180003749823934]
['id_4', 27.299558542667313]
['id_5', 21.792597812878892]
['id_6', 23.292841352717286]
['id_7', 30.78108127047032]
['id_8', 16.586402887372365]
['id_9', 60.38550637230346]
['id_10', 12.993646232319968]
['id_11', 10.70200092475075]
['id_12', 65.64215329134743]
['id_13', 52.053427445578166]
['id_14', 21.375482365639467]
['id_15', 11.574783938138383]
['id_16', 32.25504500615686]
['id_17', 67.31566462493525]
['id_18', -0.6161598259829901]
['id_19', 17.665748375976165]
['id_20', 40.895099614627014]
['id_21', 72.26013598885945]
['id_22', 9.638987238738466]
['id_23', 17.84024484244622]
['id_24', 15.127968656872923]
['id_25', 36.92049576207732]
['id_26', 15.646177020329155]
['id_27', 72.87300224422786]
['id_28', 8.418221455802819]
['id_29', 55.413280515043375]
['id_30', 24.051900611720047]
['id_31', 7.595635842604071]
['id_32', 2.80866765727627]
['id_33', 20.849380390807408]
['id_34', 28.71170267153394]
['id_35', 37.875874390298236]
['id_36', 44.1847957487677]
['id_37', 30.146475294376234]
['id_38', 42.03786649980424]
['id_39', 34.65230321491354]
['id_40', 7.9113030707433]
['id_41', 41.395781258982645]
['id_42', 31.05374516132014]
['id_43', 50.00315759679335]
['id_44', 17.211685655310127]
['id_45', 35.19296162566461]
['id_46', 25.11387615254853]
['id_47', 9.720234223141482]
['id_48', 24.515130798666405]
['id_49', 31.47494455467578]
['id_50', 19.730949751475126]
['id_51', 8.913291561410212]
['id_52', 20.08798021632116]
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