分类算法（决策树、逻辑回归、线性SVC、SVC）模型的耗时测试

初学数据挖掘算法时，在具体工作中常常不清楚如何选择算法，本文将从耗时的角度进行测试，选择的基础算法有DecisionClassifier、LogisticRegression、LinearSVC、SVC（高斯核函数）。并没有再用SVC(kernel = linear)作对比，LinearSVC就够了。

数据集使用的是sklearn.datasets中的make_moons，下图中数据加入10%噪声。就分类效果来说，对于这种非线性分类来说，逻辑回归和线性svc肯定不会很好，但这次测试主要针对耗费时间所以暂时不讨论分类效果。

先贴代码说明过程：

import numpy as np
import pandas as pd
from sklearn.datasets import make_moons
import time

from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.svm import LinearSVC
from sklearn.svm import SVC

from sklearn.metrics import accuracy_score
from sklearn.metrics import recall_score

n_samples = np.linspace(10000, 1000000, 100)
#n_features = np.linspace(10, 100, 10)

k = 0
list_DecisionTreeClassifier = []
list_LogisticRegression = []
list_LinearSVC = []
list_SVC = []
for n_sample in n_samples:
#    for n_feature in n_features:
    start = time.clock()
    data = make_moons(n_samples = int(n_sample), noise = 0.2, random_state = 42)
    x = data[0]
    y = data[1]
    x_train, x_test, y_train, y_test = train_test_split(x, y, random_state=42)
    tree_clf = DecisionTreeClassifier()
    log_clf = LogisticRegression()
    linearsvc_clf = LinearSVC()
    svc_clf = SVC()
    for clf in [tree_clf, log_clf, linearsvc_clf, svc_clf]:
        clf.fit(x_train, y_train)
        y_pred = clf.predict(x_test)
        k = k + 1
        print(clf.__class__.__name__, '  n_sample =', int(n_sample),
              '\ntrain_score: ', clf.score(x_train, y_train), 'test_score: ', clf.score(x_test, y_test),
              '\naccuracy_score: ', accuracy_score(y_test, y_pred),
              '\nrecall_score: ', recall_score(y_test, y_pred, average = 'micro'),
              '\ntime: ', time.clock() - start, 
              '\nk =', k,
              '\n---------------------------------------------------------------')
        if clf == tree_clf:
            list_DecisionTreeClassifier.append(time.clock() - start)
        elif clf == log_clf:
            list_LogisticRegression.append(time.clock() - start)
        elif clf == linearsvc_clf:
            list_LinearSVC.append(time.clock() - start)
        elif clf == svc_clf:
            list_SVC.append(time.clock() - start)
            
            
print(list_DecisionTreeClassifier)
print(list_LogisticRegression)
print(list_LinearSVC)
print(list_SVC)

数据如下：

第一行是样本数量，从10k到1000k，也就是百万，所有样本均为两个特征。

一共跑了20.24小时，其中决策树0.047h、逻辑回归0.065h、LinearSVC 0.387h、SVC（高斯核函数） 19.74h。

n_samples(k)	DecisionClassifier	LogisticRegression	LinearSVC	SVC
10	0.02883747	0.049836921	0.078581678	0.327533809
20	0.058209357	0.072491098	0.12397223	0.959392353
30	0.055744011	0.076332479	0.152550657	2.102193433
40	0.075380437	0.102246571	0.203200135	3.242318279
50	0.096630075	0.12982895	0.268338368	4.742749603
60	0.123576192	0.163956345	0.328781705	6.687300061
70	0.168099112	0.213670662	0.441686996	9.074958383
80	0.168602809	0.220825094	0.428130358	11.48451644
90	0.211460762	0.272062956	0.523074432	14.64752711
100	0.24415954	0.313279468	0.654271114	17.69263482
110	0.244321442	0.325576588	0.778064836	20.76720159
120	0.27956278	0.378553588	0.935907076	49.65587547
130	0.32607641	0.460912716	1.16475368	29.29933011
140	0.346625301	0.48400057	1.315402189	34.02656613
150	0.372370017	0.586220849	1.584742415	40.06493316
160	0.423706959	0.646293885	1.848321679	44.7496937
170	0.440558938	0.63655953	1.787725574	49.81503784
180	0.486027535	0.673445079	2.250058327	58.382703
190	0.557732921	0.834294278	2.64545725	96.63282664
200	0.55375261	0.852491846	2.658757889	94.75976404
210	0.660044253	0.941345617	2.768064517	80.91920565
220	0.626086788	0.966818007	3.005038905	86.18817032
230	0.670140606	0.993128967	3.212830983	122.7775426
240	0.73641105	1.067132817	3.021734793	98.89337542
250	0.692669689	0.992732375	3.949486686	104.3569378
260	0.706089611	0.998963824	3.100860021	113.7740898
270	0.793118174	1.090411634	4.163498036	124.1380248
280	0.812848696	1.137654793	3.530820015	134.5863551
290	0.840621207	1.202555292	3.611334561	165.7891099
300	0.820008109	1.187318188	3.697400011	180.7568949
310	0.915756437	1.289138554	3.965521402	227.2264197
320	0.938713664	1.328560853	4.29018248	202.5930091
330	0.984258369	1.357701372	4.529406067	188.1415734
340	1.0649243	1.481109295	4.639771011	252.7613858
350	1.041193263	1.430132414	4.824420714	247.1732288
360	1.123670843	1.524292161	5.725227875	264.2904282
370	1.152559513	1.615813865	6.322684206	247.99097
380	1.142039723	1.637767849	8.954775502	266.9802446
390	1.190608269	1.66227408	5.425929867	319.2140473
400	1.214198991	1.729258832	9.016491641	321.7064201
410	1.26459413	1.793089668	6.083544475	299.8074605
420	1.319481026	1.837493583	8.346132674	319.218243
430	1.341065817	1.880541944	6.638102447	329.2450695
440	1.359091242	1.96505313	7.579508121	349.2920359
450	1.430822091	2.01616922	10.7825815	377.9132338
460	1.481463267	2.074451365	7.030453175	562.6923841
470	1.524301847	2.081178761	8.532552788	480.4078591
480	1.549834016	2.171983666	10.97452927	495.310479
490	1.605759025	2.22234255	9.559583592	440.4521703
500	1.6389734	2.281242692	9.421958412	465.9535545
510	1.591427192	2.251642757	10.1713034	481.42287
520	1.688606351	2.307748213	9.904361544	511.5490605
530	1.736909211	2.396495156	10.64585661	546.4557019
540	1.689089291	2.347317468	10.10210958	599.3554054
550	1.716026275	2.431734004	10.73117288	640.8862102
560	1.843366078	2.547667842	11.00812391	656.5034435
570	1.864082683	2.600270391	12.9047205	605.5532614
580	1.906778458	2.62118294	14.64065912	697.0465515
590	1.878746626	2.672614256	15.51130785	663.513101
600	1.947375588	2.750074517	13.53774197	675.039494
610	2.027375089	2.838580405	12.67999563	710.3224443
620	2.033808294	2.862703883	13.61235801	898.6646633
630	2.067229959	2.814968374	15.87992865	835.0988546
640	2.076654347	2.791250898	14.76721681	764.5906833
650	2.131187271	2.987456843	14.93312678	810.0983294
660	2.241519836	3.128689821	16.9502807	1130.963952
670	2.239337611	3.057659719	16.46323553	845.722558
680	2.275467891	3.105867099	18.35621547	1154.157348
690	2.291907503	3.190526626	16.15837223	991.0283706
700	2.3328265	3.260851552	16.92598729	1060.819834
710	2.489256729	3.366372152	17.3391335	977.3716089
720	2.55171679	3.479403092	17.81736425	1005.078345
730	2.540897272	3.498850215	17.90919011	1069.855728
740	2.612989841	3.515815386	22.03596312	1944.74973
750	2.620192428	3.612667973	22.28870128	1642.03376
760	2.628637376	3.509083839	25.85574401	1309.324554
770	2.795656584	3.805254498	27.374286	1723.238744
780	2.739056842	3.651658533	26.68898966	1251.787643
790	2.700334737	3.697969576	23.75833155	1300.57802
800	2.851554748	3.932474465	30.10339926	1288.789001
810	2.840837354	3.897600937	22.98218657	1345.440995
820	2.874908843	3.907148204	27.86596795	1301.799378
830	2.902940953	3.994063297	24.41901289	1361.743071
840	2.98235124	4.111643837	26.81874638	1404.069808
850	3.030584081	4.174068749	30.87201563	1454.968759
860	3.107563339	4.081504226	27.35487237	1490.286797
870	3.122779963	4.183902183	28.26201365	1696.073407
880	3.063565703	4.260023773	35.9357651	1633.272899
890	3.217063697	4.306676612	30.60561677	1660.043353
900	3.180678247	4.403967858	29.99422963	1621.002932
910	3.347478541	4.560222623	44.98514177	1696.784396
920	3.366416156	4.629918758	34.08945046	1743.880592
930	3.472418035	4.718100011	32.78220483	1740.061516
940	3.459947942	4.658998114	34.14549835	1863.307061
950	3.541337038	4.823270514	36.36540129	1887.806115
960	3.608922629	4.856454168	47.56512038	1925.553855
970	3.689194182	5.011694898	37.64121789	1994.018002
980	3.640454324	4.900210474	49.82976018	2009.114227
990	3.63392038	4.985876288	40.58021385	1957.2254
1000	3.665191647	5.039182628	46.99966042	2033.99081

一目了然，折线图不太好画，SVC实在多太多。

顺便拟合了各自样本量为自变量、时间为因变量的函数：

DecisionClassifier：                         R² = 0.9937

LogisticRegression：                       R² = 0.9953

LinearSVC：          R² = 0.9639

SVC：                            R² = 0.9675

决策树和逻辑回归都是一次函数，拟合模型耗费时间和样本量成正比。

俩支持向量机就厉害了，都是二次函数，但也有差别，二次函数的斜率是导数 ，SVC的a比Linear两个数量级。

还是再贴一个100万样本时各自的模拟精度：

对于非线性数据，逻辑回归和线性支持向量机的效果都是相对较差的，而决策树和SVC(高斯核函数)分类效果较好。

 

由此可以得出在选择模型时的一些方法：

1、如果决定先尝试，优先选择逻辑回归和决策树；

2、当数据为非线性时，应该避免选择逻辑回归等线性模型（但可尝试多项式逻辑回归）；

3、当样本和特征数量都较少时，花费时间相近，可以尝试多种模型来选择一个效果较好的；

4、样本或特征较多并且不想等太久的时候，一定不要选择SVM！！！即使要用也尽量选择LinearSVM；

5、使用集成算法之前应该根据base_model对拟合时间有一个预估；

6、一个关于SVM的小经验：通过随机森林的方式抽样拟合模型，当单个模型处理的数据变小总体时间会少很多，并且可以做并行计算，比全部样本拟合一个模型花的时间少得多。