Internet shopping is basically a non-contractual agreement, the customer's purchasing behavior has randomness and unpredictability, it is how to remain invincible in this fierce market network,
It should reduce customer churn network as much as possible.
Currently the model used to predict churn rate are:
SVM model, Logistics model, Pareto / NBD model, BG / NBD model and a variety of models of extended, through a combination of classification model assessment method, you can verify the accuracy of the model,
Application of further practical use cases.
Where: Pareto / NBD model description:
Pareto / NBD model:
A: Variable:
ID : User ID
x: specified time period, the number of repeat purchases ( not including the first purchase )
Tx: long last purchase, that is a specified time period, the number of first purchase to buy the last cycle, decimals
T: The first number to buy the last day of the period specified last time, retain the decimal
T_star: prediction time period length
II: 4 parameter estimation:
R code:
Python Code:
Import PANDAS AS PD
from pnbd Import pnbd # develop their own modules
consume_sources = pd.read_excel ( 'Test.xls' )
cal_cbs consume_sources.loc = [:, [ 'X' , 't_x' , 'T_cal' ]]
Fun, X pnbd.EstimateParameters = (cal_cbs, par_start = [. 1,. 1,. 1,. 1], max_param_value = 1000)
Print Fun, X
# 0.4846256 1.4887628 0.6738844 4.4011076 # 150,346.098305 [0.48458758 1.48866284 0.67405456 4.40356461]
As the result of two software running
Three: the user activity prediction of
the params = X
consume_sources [ 'P' ] = consume_sources.apply ( the lambda X:
pnbd.PAlive (the params, X = X [ 'X' ], t_x X = [ 't_x' ], = T_cal X [ 'T_cal' ]), Axis =. 1)
print consume_sources.head(20)
*** thresholding algorithm may choose to select a reasonable threshold
Activity index is calculated:
The percentage of active sample = 3817/22731 = 16.79%
Accuracy accuracy = (2421 + 15342) /22731=78.14%
Sensitivity Coverage = 2421/3817 = 63.43%
Precision hit rate = 2421/5993 = 40.40%
Turnover index is calculated:
Sample loss percentage = 3817/22731 = 83.21%
Accuracy accuracy = (2421 + 15342) /22731=78.14%
Sensitivity Coverage = 15,342 / 18,914 = 81.12%
Precision命中率=15342/16738=91.66%
四：预测未来一个月用户的购买期望次数：
consume_sources['E']=consume_sources.apply(lambda x:
pnbd.ConditionalExpectedTransactions(params,T_star=5,
x=x['x'], t_x=x['t_x'], T_cal=x['T_cal']),axis=1)
consume_sources.to_excel('test.xls',index=False)
Python代码：
pnbd.py
# -*-coding:utf-8-*-
'''
Pareto/NBD模型代码：
仿照R语言：BTYD
params <- c("r", "alpha", "s", "beta")
# 分组求和
pnbd.compress.cbs(cbs, 0)
# 个体客户在时刻T的活跃度模型
pnbd.PAlive(params, 10, 35, 39)
# 客户在时间T后t*时间内发生交易的交易次数的期望模型
pnbd.ConditionalExpectedTransactions(params, T.star=2, x=10, t.x=35, T.cal=39)
# 计算对数极大似然值
pnbd.LL(params, cbs[, "x"], cbs[, "t.x"], cbs[, "T.cal"])
pnbd.cbs.LL(params, cbs)
# 评估4个参数，采用最小方差法
result<-pnbd.EstimateParameters(cal.cbs, par.start = c(1, 1, 1, 1),max.param.value = 100)
'''
from math import lgamma
from scipy.special import gammaln
import math
from scipy.optimize import minimize
import numpy as np
def LL(params, x, t_x, T_cal):
x = np.matrix(x).T
t_x = np.matrix(t_x).T
T_cal = np.matrix(T_cal).T
# z:为数值
def h2f1(a, b, c, z):
lenz = len(z)
j = 0
uj =[1 for i in range(1,lenz+1)]
uj=np.matrix(uj).T
y = uj
lteps = 0
while (lteps < lenz):
lasty = y
j = j + 1
uj = np.multiply(uj , (a + j - 1))
uj = np.multiply(uj,(b + j - 1))
uj = np.multiply(uj,z)
temp=np.multiply((c + j - 1) ,j)
uj = np.multiply(uj,1/temp)
y = y + uj
lteps = sum(y == lasty)
return y
r = params[0]
alpha = params[1]
s = params[2]
beta = params[3]
maxab = max(alpha, beta)
absab = abs(alpha - beta)
param2 = s + 1
if (alpha < beta):
param2 = r + x
part1 = r * np.log(alpha) + s * np.log(beta) - lgamma(r) + gammaln(r +x)
part2 = np.multiply(-(r + x),np.log(alpha + T_cal)) - s * np.log(beta + T_cal)
if (absab == 0):
partF = np.multiply(-(r + s + x),np.log(maxab + t_x))\
+ np.log(1 - np.power(((maxab + t_x) / (maxab + T_cal)),r + s + x))
else:
F1 = h2f1(r + s + x, param2, r + s + x + 1, absab / (maxab +t_x))
F2 = h2f1(r + s + x, param2, r + s + x + 1,absab / (maxab + T_cal))
F2 = np.multiply(F2,np.power((maxab + t_x)/(maxab + T_cal), r + s + x))
partF = np.multiply(-(r + s + x), np.log(maxab + t_x)) + np.log(F1 - F2)
part3 = np.log(s) - np.log(r + s + x) + partF
return (part1 + np.log(np.exp(part2) + np.exp(part3)))
# cbs:DataFrame , params:list
def cbs_LL(params, cal_cbs):
x = cal_cbs['x'].values
t_x = cal_cbs['t_x'].values
T_cal = cal_cbs['T_cal'].values
if 'custs' in cal_cbs.columns:
custs = cal_cbs['custs'].values
else:
custs = [1 for i in range(len(cal_cbs))]
custs = np.matrix(custs).T
ll=sum(np.multiply(custs, LL(params,x,t_x,T_cal)))
return ll[0,0]
# 个体客户在时刻T的活跃度模型
# params=[0.55, 10.56, 0.61, 11.64] PAlive(params, 10, 35, 39)
def PAlive(params, x, t_x, T_cal):
# h2f1： F(a,b,c,z)为高斯超几何函数
def h2f1(a, b, c, z):
j = 0
uj = 1
y = uj
lteps = 0
while (lteps < 1):
lasty = y
j = j + 1
uj = uj * (a + j - 1) * (b + j - 1) / (c + j - 1) * z / j
y = y + uj
if y == lasty:
lteps = lteps + 1
return y
r = params[0]
alpha = params[1]
s = params[2]
beta = params[3]
if (alpha > beta):
F1 = h2f1(r + s + x, s + 1, r + s + x + 1, (alpha - beta) / (alpha + t_x))
F2 = h2f1(r + s + x, s + 1, r + s + x + 1, (alpha - beta) / (alpha + T_cal))
# 与R语言中BTYD.pnbd.PAlive有差异
A0 = F1 / math.pow(alpha+t_x,r+x+s) - F2 / math.pow(alpha + T_cal,r + s + x)
# A0 = F1 / (math.pow(alpha+T_cal,s)*math.pow(alpha + t_x,r+x)) - \
# F2 / math.pow(alpha + T_cal,r + s + x)
elif (alpha < beta):
F1 = h2f1(r + s + x, r + x, r + s + x + 1, (beta - alpha) / (beta + t_x))
F2 = h2f1(r + s + x, r + x, r + s + x + 1, (beta - alpha) / (beta + T_cal))
A0 = F1 / math.pow(beta + t_x,r + s + x) - \
F2 / math.pow(beta + T_cal , r + s + x)
else:
return math.pow(1 + s / (r + s + x) * (math.pow((alpha+T_cal)/(alpha+t_x),r+x+s)-1),-1)
return math.pow(1 + s / (r + s + x) * math.pow(alpha + T_cal,r + x) * math.pow(beta +T_cal,s)* A0,-1)
# 估计4个参数: c("r", "alpha", "s", "beta")
# 所以参数不超过：max_param_value值
# for example:
# EstimateParameters(data_Soures, par_start = [1, 1, 1, 1], max_param_value =100)
def EstimateParameters(cal_cbs, par_start = [1, 1, 1, 1], max_param_value = 10000):
# 对数似然值
def pnbd_ell(params,cal_cbs,max_param_value):
params = np.exp(params)
params[0] = min(params[0], max_param_value)
params[1] = min(params[1], max_param_value)
params[2] = min(params[2], max_param_value)
params[3] = min(params[3], max_param_value)
return -1 * cbs_LL(params=params,cal_cbs=cal_cbs)
logparams = np.log(par_start)
results = minimize(fun=pnbd_ell,x0=logparams,
args=(cal_cbs,max_param_value),
method="L-BFGS-B")
return results['fun'],np.exp(results['x'])
# 单一值
# 客户在时间T后t*时间内发生交易的交易次数的期望模型
def ConditionalExpectedTransactions(params, T_star, x, t_x, T_cal):
r = params[0]
alpha = params[1]
s = params[2]
beta = params[3]
P1 = (r + x) * (beta + T_cal) / ((alpha + T_cal) * (s - 1))
# 与R语言中BTYD.pnbd.ConditionalExpectedTransactions有差异
# P2 < - (1 - ((beta + T.cal) / (beta + T.cal + T.star)) ^ (s - 1))
P2 = (1 -math.pow(((beta + T_cal) / (beta + T_cal + T_star)) , (s - 1)) )
P3 = PAlive(params, x, t_x, T_cal)
return P1 * P2 * P3