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【Tutorial】運用KNN演算法進行室內定位(Part 1)

作者:Ches拔(Sco Lin

最近看了一些論文,發現愈來愈多人開始用Machine Learning來做室內定位,不看還好,一看驚為天人,決定花點時間學習一下,並且決定這次以週刊專欄或是科技新聞那樣專業的方式寫寫看!

Machine Learning,眾人以ML簡之,Big Data、Machine Learning、Deep Learning即是以AI著稱。機器訓練得宜,則學術深博。常言道,得AI者,得天下。今,吾以KNN首试。KNN為何?Wiki曰明於此,例參Github而來,Python語句。

假設,今有四點如圖:

a1a2A類,b1b2B類,此時入c如下:

要怎麼能辨別c為B類?有興趣者可參考程式碼:

程式碼

 from matplotlib import pyplot as plt

import numpy as np

a1 = np.array([1, 1])

a2 = np.array([5, 1])

b1 = np.array([1, 5])

b2 = np.array([5, 5])

b3 = np.array([3, 5])

c = np.array([3, 4])

X1, Y1 = a1

X2, Y2 = a2

X3, Y3 = b1

X4, Y4 = b2

X5, Y5 = b3

X6, Y6 = c

plt.title(‘show data’)

plt.scatter(X1, Y1, color=”blue”, label=”a1″)

plt.scatter(X2, Y2, color=”blue”, label=”a2″)

plt.scatter(X3, Y3, color=”red”, label=”b1″)

plt.scatter(X4, Y4, color=”red”, label=”b2″)

plt.scatter(X5, Y5, color=”red”, label=”b3″)

plt.scatter(X6, Y6, color=”red”, label=”c”)

plt.legend(loc=’upper left’)

plt.annotate(r’a1(1,1)’, xy=(X1, Y1), xycoords=’data’, xytext=(+10, +30), textcoords=’offset points’, fontsize=16, arrowprops=dict(arrowstyle=”->”, connectionstyle=”arc3,rad=.2″))

plt.annotate(r’a2(5,1)’, xy=(X2, Y2), xycoords=’data’, xytext=(+10, +30), textcoords=’offset points’, fontsize=16, arrowprops=dict(arrowstyle=”->”, connectionstyle=”arc3,rad=.2″))

plt.annotate(r’b1(1,5)’, xy=(X3, Y3), xycoords=’data’, xytext=(+10, +30), textcoords=’offset points’, fontsize=16, arrowprops=dict(arrowstyle=”->”, connectionstyle=”arc3,rad=.2″))

plt.annotate(r’b2(5,5)’, xy=(X4, Y4), xycoords=’data’, xytext=(+10, +30), textcoords=’offset points’, fontsize=16, arrowprops=dict(arrowstyle=”->”, connectionstyle=”arc3,rad=.2″))

plt.annotate(r’b3(3,5)’, xy=(X5, Y5), xycoords=’data’, xytext=(+10, +30), textcoords=’offset points’, fontsize=16, arrowprops=dict(arrowstyle=”->”, connectionstyle=”arc3,rad=.2″))

plt.annotate(r’c(3,4)’, xy=(X6, Y6), xycoords=’data’, xytext=(+10, +30), textcoords=’offset points’, fontsize=16, arrowprops=dict(arrowstyle=”->”, connectionstyle=”arc3,rad=.2″))

plt.show()

KNN例1程式碼如下,設k為3(見式3),為取3點極近xy數組。

例1程式碼

 from matplotlib import pyplot as plt

import numpy as np

import math

def Euclidean(vec1, vec2): #Euclidean間距算法

npvec1, npvec2 = np.array(vec1), np.array(vec2)

return math.sqrt(((npvec1-npvec2)**2).sum())

def Cosine(vec1, vec2): #Cosine間距算法

npvec1, npvec2 = np.array(vec1), np.array(vec2)

return npvec1.dot(npvec2)/(math.sqrt((npvec1**2).sum()) * math.sqrt((npvec2**2).sum()))

def create_trainset():

trainset_tf = dict()

trainset_tf[u’X1, Y1′] = np.array([1, 1])

trainset_tf[u’X2, Y2′] = np.array([5, 1])

trainset_tf[u’X3, Y3′] = np.array([1, 5])

trainset_tf[u’X4, Y4′] = np.array([5, 5])

trainset_tf[u’X5, Y5′] = np.array([3, 5])

trainset_class = dict()

trainset_class[u’X1, Y1′] = ‘A’

trainset_class[u’X2, Y2′] = ‘A’

trainset_class[u’X3, Y3′] = ‘B’

trainset_class[u’X4, Y4′] = ‘B’

trainset_class[u’X5, Y5′] = ‘B’

return trainset_tf, trainset_class

def knn_classify(input_tf, trainset_tf, trainset_class, k):

xy = np.array([0, 0])

tf_distance = dict()

print ‘(1) 各點之遙’

for place in trainset_tf.keys():

tf_distance[place] = Euclidean(trainset_tf.get(place), input_tf)

print ‘\tTF(%s) = %f’ % (place, tf_distance.get(place))

class_count = dict()

print ‘(2) 得K個鄰為類, k = %d’ % k

for i, place in enumerate(sorted(tf_distance, key=tf_distance.get, reverse=False)):

current_class = trainset_class.get(place)

print ‘\tTF(%s) = %f, class = %s’ % (place, tf_distance.get(place), current_class)

class_count[current_class] = class_count.get(current_class, 0) + 1

xy = xy + trainset_tf[place]

if (i + 1) >= k:

break

print ‘(3) K鄰均等之x與y –>’ #式3

finalx=float(xy[0])/k

finaly=float(xy[1])/k

print ‘\tx = %f’ % finalx, ‘, y = %f’% finaly

print ‘(4) K個鄰累計,最高者任其終類’

input_class = ”

for i, c in enumerate(sorted(class_count, key=class_count.get, reverse=True)):

if i == 0:

input_class = c

print ‘\t%s類, 現%d次’ % (c, class_count.get(c))

print ‘(5) 結果 = %s’ % input_class

input_tf = np.array([3, 4])

trainset_tf, trainset_class = create_trainset()

knn_classify(input_tf, trainset_tf, trainset_class, k=3)

結果如下:

見結果,x於3,y於5。在程式碼中設input_tf = np.array([3, 4]),表x於3,y於4,y於實測與預測相差1,頗為接近!心喜!信心大增!

故例2,我設定實測集合於下:

例2實測集合

def create_trainset():

trainset_tf = dict()

trainset_tf[u’T1, U1, V1, W1, X1, Y1, Z1′] = np.array([-55, -65, -65, -75, -85, 1, 1])

trainset_tf[u’T2, U2, V2, W2, X2, Y2, Z2′] = np.array([-65, -55, -85, -75, -65, 5, 1])

trainset_tf[u’T3, U3, V3, W3, X3, Y3, Z3′] = np.array([-65, -85, -55, -60, -65, 1, 5])

trainset_tf[u’T4, U4, V4, W4, X4, Y4, Z4′] = np.array([-75, -75, -60, -55, -60, 5, 5])

trainset_tf[u’T5, U5, V5, W5, X5, Y5, Z5′] = np.array([-85, -65, -65, -59, -55, 3, 5])

以[-55, -65, -65, -75, -85, 1, 1]為例,-55表示手環在第一個接收器的位置,-85離最遠,於空間內置放5個接收器,手環於5個地點發射,故5個接收器的強度都不同。

5個負數代表5個接收器收到的RSSI,後面2個值(1,1)代表xy軸。LinkIt 7697一秒可以送出多筆資料,但這只是模擬數據,實做是要用洗資料的方式,而現在建立的這個資料集是代表實測出來的建模,要給機器去學習比對,找出使用者目前位置。

例2

trainset_class = dict()

trainset_class[u’T1, U1, V1, W1, X1, Y1, Z1′] = ‘A’

trainset_class[u’T2, U2, V2, W2, X2, Y2, Z2′] = ‘A’

trainset_class[u’T3, U3, V3, W3, X3, Y3, Z3′] = ‘B’

trainset_class[u’T4, U4, V4, W4, X4, Y4, Z4′] = ‘B’

trainset_class[u’T5, U5, V5, W5, X5, Y5, Z5′] = ‘B’

return trainset_tf, trainset_class

此時,若有人戴手環入室,input_tf代表這人的室內數據。負數為各LinkIt 7697所得RSSI,設xy數分別為零,將由ML算之,設集如下: input_tf = np.array([-72, -72, -63, -53, -63, 0, 0])

ML得x為3, y為5,倒果為因,同上例1之xy得數,由此可看出Machine Learning之強大,何況Deep Learning乎?

例2程式碼

from matplotlib import pyplot as plt

import numpy as np

import math

 

def Euclidean(vec1, vec2): #Euclidean間距算法

npvec1, npvec2 = np.array(vec1), np.array(vec2)

return math.sqrt(((npvec1-npvec2)**2).sum())

 

def Cosine(vec1, vec2): #Cosine間距算法

npvec1, npvec2 = np.array(vec1), np.array(vec2)

return npvec1.dot(npvec2)/(math.sqrt((npvec1**2).sum()) * math.sqrt((npvec2**2).sum()))

def create_trainset():

trainset_tf = dict()

trainset_tf[u’T1, U1, V1, W1, X1, Y1, Z1′] = np.array([-55, -65, -65, -75, -85, 1, 1])

trainset_tf[u’T2, U2, V2, W2, X2, Y2, Z2′] = np.array([-65, -55, -85, -75, -65, 5, 1])

trainset_tf[u’T3, U3, V3, W3, X3, Y3, Z3′] = np.array([-65, -85, -55, -60, -65, 1, 5])

trainset_tf[u’T4, U4, V4, W4, X4, Y4, Z4′] = np.array([-75, -75, -60, -55, -60, 5, 5])

trainset_tf[u’T5, U5, V5, W5, X5, Y5, Z5′] = np.array([-85, -65, -65, -59, -55, 3, 5])

trainset_class = dict()

trainset_class[u’T1, U1, V1, W1, X1, Y1, Z1′] = ‘A’

trainset_class[u’T2, U2, V2, W2, X2, Y2, Z2′] = ‘A’

trainset_class[u’T3, U3, V3, W3, X3, Y3, Z3′] = ‘B’

trainset_class[u’T4, U4, V4, W4, X4, Y4, Z4′] = ‘B’

trainset_class[u’T5, U5, V5, W5, X5, Y5, Z5′] = ‘B’

return trainset_tf, trainset_class

def knn_classify(input_tf, trainset_tf, trainset_class, k):

xy = np.array([0, 0])

tf_distance = dict()

print ‘(1) 各點之遙’

for place in trainset_tf.keys():

tf_distance[place] = Euclidean(trainset_tf.get(place), input_tf)

print ‘\tTF(%s) = %f’ % (place, tf_distance.get(place))

class_count = dict()

print ‘(2) 得K個鄰為類 k = %d’ % k

for i, place in enumerate(sorted(tf_distance, key=tf_distance.get, reverse=False)):

current_class = trainset_class.get(place)

print ‘\tTF(%s) = %f, class = %s’ % (place, tf_distance.get(place), current_class)

class_count[current_class] = class_count.get(current_class, 0) + 1

xy = [(xy[0] + trainset_tf[place][5]),(xy[1] + trainset_tf[place][6])]

if (i + 1) >= k:

break

print ‘(3) K鄰均等之x與y –>’

finalx=float(xy[0])/k

finaly=float(xy[1])/k

print ‘\tx = %f’ % finalx, ‘, y = %f’% finaly

print ‘(4) K個鄰累計,最高者任其終類’

input_class = ”

for i, c in enumerate(sorted(class_count, key=class_count.get, reverse=True)): #擇小排序之

if i == 0:

input_class = c

print ‘\t%s類, 現%d次’ % (c, class_count.get(c))

print ‘(5) 結果 = %s’ % input_class

input_tf = np.array([-72, -72, -63, -53, -63, 0, 0])

trainset_tf, trainset_class = create_trainset()

knn_classify(input_tf, trainset_tf, trainset_class, k=3)

結果如下:

此為現實定位模擬數值,接著將有實測之文,ML系列文將以不同風貌展現!

(本文同步發表於作者部落格 — 物聯網學習筆記文章連結;責任編輯:廖庭儀。)

(編按:本文原作為文言文體,風格特殊,有興趣者不妨連回原作拜讀~)

Ches拔(Sco Lin)

Ches拔(Sco Lin)

兩個男孩的爸爸、下班變身孩子王、衝浪閱讀與coding、PM擔當RD魂。
Ches拔(Sco Lin)

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