位置指紋法中最常用的演算法是k最近鄰（kNN）。本文的目的學習一下python機器學習scikit-learn的使用，嘗試了各種常見的機器學習分類器，比較它們在位置指紋法中的定位效果。

匯入資料

# 匯入資料
import numpy as np
import scipy.io as scio
offline_data = scio.loadmat('offline_data_random.mat')
online_data = scio.loadmat('online_data.mat')
offline_location, offline_rss = offline_data['offline_location'], offline_data['offline_rss']
trace, rss = online_data['trace'][0:1000, :], online_data['rss'][0:1000, :]
del offline_data
del online_data
 

# 定位準確度定義
def accuracy(predictions, labels):
    return np.mean(np.sqrt(np.sum((predictions - labels)**2, 1)))

knn迴歸

# knn迴歸
from sklearn import neighbors
knn_reg = neighbors.KNeighborsRegressor(40, weights='uniform', metric='euclidean')
%time knn_reg.fit(offline_rss, offline_location)
%time predictions = knn_reg.predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, "m"
 

Wall time: 92 ms
Wall time: 182 ms
accuracy:  2.24421479398 m

Logistic regression （邏輯斯蒂迴歸）

# 邏輯斯蒂迴歸是用來分類的
labels = np.round(offline_location[:, 0]/100.0) * 100 + np.round(offline_location[:, 1]/100.0)
from sklearn.linear_model import LogisticRegressionCV
clf_l2_LR_cv = LogisticRegressionCV(Cs=20, penalty='l2', tol=0.001)
predict_labels = clf_l2_LR.fit(offline_rss, labels).predict(rss)
x = np.floor(predict_labels/100.0)
y = predict_labels - x * 100
predictions = np.column_stack((x, y)) * 100
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'
 

accuracy:  3.08581348591 m

Support Vector Machine for Regression （支援向量機）

from sklearn import svm
clf_x = svm.SVR(C=1000, gamma=0.01)
clf_y = svm.SVR(C=1000, gamma=0.01)
%time clf_x.fit(offline_rss, offline_location[:, 0])
%time clf_y.fit(offline_rss, offline_location[:, 1])
%time x = clf_x.predict(rss)
%time y = clf_y.predict(rss)
predictions = np.column_stack((x, y))
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, "m"

Wall time: 9min 27s
Wall time: 12min 42s
Wall time: 1.06 s
Wall time: 1.05 s
accuracy:  2.2468400825 m

Support Vector Machine for Classification （支援向量機）

from sklearn import svm
labels = np.round(offline_location[:, 0]/100.0) * 100 + np.round(offline_location[:, 1]/100.0)
clf_svc = svm.SVC(C=1000, tol=0.01, gamma=0.001)
%time clf_svc.fit(offline_rss, labels)
%time predict_labels = clf_svc.predict(rss)
x = np.floor(predict_labels/100.0)
y = predict_labels - x * 100
predictions = np.column_stack((x, y)) * 100
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

Wall time: 1min 16s
Wall time: 15 s
accuracy:  2.50931890608 m

random forest regressor （隨機森林）

from sklearn.ensemble import RandomForestRegressor
estimator = RandomForestRegressor(n_estimators=150)
%time estimator.fit(offline_rss, offline_location)
%time predictions = estimator.predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

Wall time: 58.6 s
Wall time: 196 ms
accuracy:  2.20778352008 m

random forest classifier （隨機森林）

from sklearn.ensemble import RandomForestClassifier
labels = np.round(offline_location[:, 0]/100.0) * 100 + np.round(offline_location[:, 1]/100.0)
estimator = RandomForestClassifier(n_estimators=20, max_features=None, max_depth=20) # 記憶體受限，tree的數量有點少
%time estimator.fit(offline_rss, labels)
%time predict_labels = estimator.predict(rss)
x = np.floor(predict_labels/100.0)
y = predict_labels - x * 100
predictions = np.column_stack((x, y)) * 100
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

Wall time: 39.6 s
Wall time: 113 ms
accuracy:  2.56860790666 m

Linear Regression （線性迴歸）

from sklearn.linear_model import LinearRegression
predictions = LinearRegression().fit(offline_rss, offline_location).predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

accuracy:  3.83239841667 m

Ridge Regression （嶺迴歸）

from sklearn.linear_model import RidgeCV
clf = RidgeCV(alphas=np.logspace(-4, 4, 10))
predictions = clf.fit(offline_rss, offline_location).predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

accuracy:  3.83255676918 m

Lasso迴歸

from sklearn.linear_model import MultiTaskLassoCV
clf = MultiTaskLassoCV(alphas=np.logspace(-4, 4, 10))
predictions = clf.fit(offline_rss, offline_location).predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

accuracy:  3.83244688001 m

Elastic Net （彈性網迴歸）

from sklearn.linear_model import MultiTaskElasticNetCV
clf = MultiTaskElasticNetCV(alphas=np.logspace(-4, 4, 10))
predictions = clf.fit(offline_rss, offline_location).predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, 'm'

accuracy:  3.832486036 m

Bayesian Ridge Regression （貝葉斯嶺迴歸）

from sklearn.linear_model import BayesianRidge
from sklearn.multioutput import MultiOutputRegressor
clf = MultiOutputRegressor(BayesianRidge())
predictions = clf.fit(offline_rss, offline_location).predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, "m"

accuracy:  3.83243319129 m

Gradient Boosting for regression （梯度提升）

from sklearn import ensemble
from sklearn.multioutput import MultiOutputRegressor
clf = MultiOutputRegressor(ensemble.GradientBoostingRegressor(n_estimators=100, max_depth=10))
%time clf.fit(offline_rss, offline_location)
%time predictions = clf.predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, "m"

Wall time: 43.4 s
Wall time: 17 ms
accuracy:  2.22100945095 m

Multi-layer Perceptron regressor （神經網路多層感知器）

from sklearn.neural_network import MLPRegressor
clf = MLPRegressor(hidden_layer_sizes=(100, 100))
%time clf.fit(offline_rss, offline_location)
%time predictions = clf.predict(rss)
acc = accuracy(predictions, trace)
print "accuracy: ", acc/100, "m"

Wall time: 1min 1s
Wall time: 6 ms
accuracy:  2.4517504109 m

總結

上面的幾個線性迴歸模型顯然效果太差，這裡彙總一下其他的一些迴歸模型：

從大致的定位精度上看，KNN、SVM、RF、GBDT這四個模型比較好（上面很多演算法並沒有仔細地調引數，這個結果也比較粗略，神經網路完全不知道怎麼去調...）。此外要注意的是，SVM訓練速度慢，調參太麻煩，KNN進行預測時的時間複雜度應該是和訓練資料量成正比的，從定位的實時性上應該不如RF和GBDT。

作者：rubbninja
出處：http://www.cnblogs.com/rubbninja/
關於作者：目前主要研究領域為機器學習與無線定位技術，歡迎討論與指正！
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