AIM-PIbd-31-Razubaev-S-M/Lab7/lab7.ipynb

Лабораторная 7

Информация о диабете индейцев Пима

In [7]:

import pandas as pd
import numpy as np
import skfuzzy as fuzz
import matplotlib.pyplot as plt
from skfuzzy import control as ctrl

df = pd.read_csv(".//scv//diabetes.csv")
print(df.columns)
df

Index(['Pregnancies', 'Glucose', 'BloodPressure', 'SkinThickness', 'Insulin',
       'BMI', 'DiabetesPedigreeFunction', 'Age', 'Outcome'],
      dtype='object')

Out[7]:

	Pregnancies	Glucose	BloodPressure	SkinThickness	Insulin	BMI	DiabetesPedigreeFunction	Age	Outcome
0	6	148	72	35	0	33.6	0.627	50	1
1	1	85	66	29	0	26.6	0.351	31	0
2	8	183	64	0	0	23.3	0.672	32	1
3	1	89	66	23	94	28.1	0.167	21	0
4	0	137	40	35	168	43.1	2.288	33	1
...	...	...	...	...	...	...	...	...	...
763	10	101	76	48	180	32.9	0.171	63	0
764	2	122	70	27	0	36.8	0.340	27	0
765	5	121	72	23	112	26.2	0.245	30	0
766	1	126	60	0	0	30.1	0.349	47	1
767	1	93	70	31	0	30.4	0.315	23	0

768 rows × 9 columns

Создаем лингвистические переменные

Входные: age(возраст) и bmi(ИМТ)

Выходные: glucose(давление)

In [8]:

age = ctrl.Antecedent(np.arange(df["Age"].min(), df["Age"].max() + 1, 1), "age")
bmi = ctrl.Antecedent(np.arange(df["BMI"].min(), df["BMI"].max() + 0.1, 0.1), "bmi")
glucose = ctrl.Consequent(np.arange(df["Glucose"].min(), df["Glucose"].max() + 0.1, 0.1), "glucose")

Настраиваем их

In [15]:

age["young"] = fuzz.zmf(age.universe, 20, 30)
age["middle-aged"] = fuzz.trapmf(age.universe, [18, 30, 45, 60])
age["old"] = fuzz.smf(age.universe, 45, 85)
age.view()


bmi["low"] = fuzz.zmf(bmi.universe, 12, 18)
bmi["normal"] = fuzz.trapmf(bmi.universe, [16, 19, 24, 27])
bmi["high"] = fuzz.smf(bmi.universe, 25, 27)
bmi.view()

glucose["low"] = fuzz.zmf(glucose.universe, 0, 80)
glucose["normal"] = fuzz.trapmf(glucose.universe, [70, 80, 90, 100])
glucose["high"] = fuzz.smf(glucose.universe, 90, 180)
glucose.view()

База нечетких правил:

In [ ]:

import numpy as np
import skfuzzy as fuzz
from skfuzzy import control as ctrl

rule1 = ctrl.Rule(age["young"] & bmi["low"], glucose["low"])
rule2 = ctrl.Rule(age["young"] & bmi["normal"], glucose["normal"])
rule3 = ctrl.Rule(age["young"] & bmi["high"], glucose["normal"])

rule4 = ctrl.Rule(age["middle-aged"] & bmi["low"], glucose["normal"])
rule5 = ctrl.Rule(age["middle-aged"] & bmi["normal"], glucose["normal"])
rule6 = ctrl.Rule(age["middle-aged"] & bmi["high"], glucose["high"])

rule7 = ctrl.Rule(age["old"] & bmi["low"], glucose["low"])
rule8 = ctrl.Rule(age["old"] & bmi["normal"], glucose["normal"])
rule9 = ctrl.Rule(age["old"] & bmi["high"], glucose["high"])

rule1.view()

Out[ ]:

(<Figure size 640x480 with 1 Axes>, <Axes: >)

Создание нечеткой системы и добавление нечетких правил в базу знаний нечеткой системы

In [17]:

glucose_ctrl  = ctrl.ControlSystem(
    [
        rule1,
        rule2,
        rule3,
        rule4,
        rule5,
        rule6,
        rule7,
        rule8,
        rule9,
    ]
)

glucose_simulation = ctrl.ControlSystemSimulation(glucose_ctrl)

glucose_ctrl.view()

d:\5_semester\AIM\rep\AIM-PIbd-31-Razubaev-S-M\.venv\Lib\site-packages\skfuzzy\control\controlsystem.py:135: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  fig.show()

Проверка расчета выходной переменной

In [19]:

glucose_simulation.input["age"] = 31
glucose_simulation.input["bmi"] = 25
glucose_simulation.compute()

glucose_simulation.print_state()
glucose_simulation.output["glucose"]

=============
 Antecedents 
=============
Antecedent: age                     = 31
  - young                           : 0.0
  - middle-aged                     : 1.0
  - old                             : 0.0
Antecedent: bmi                     = 25
  - low                             : 0.0
  - normal                          : 0.6666666666666666
  - high                            : 0.0

=======
 Rules 
=======
RULE #0:
  IF age[young] AND bmi[low] THEN glucose[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[young]                                             : 0.0
  - bmi[low]                                               : 0.0
                                   age[young] AND bmi[low] = 0.0
  Activation (THEN-clause):
                                              glucose[low] : 0.0

RULE #1:
  IF age[young] AND bmi[normal] THEN glucose[normal]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[young]                                             : 0.0
  - bmi[normal]                                            : 0.6666666666666666
                                age[young] AND bmi[normal] = 0.0
  Activation (THEN-clause):
                                           glucose[normal] : 0.0

RULE #2:
  IF age[young] AND bmi[high] THEN glucose[normal]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[young]                                             : 0.0
  - bmi[high]                                              : 0.0
                                  age[young] AND bmi[high] = 0.0
  Activation (THEN-clause):
                                           glucose[normal] : 0.0

RULE #3:
  IF age[middle-aged] AND bmi[low] THEN glucose[normal]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[middle-aged]                                       : 1.0
  - bmi[low]                                               : 0.0
                             age[middle-aged] AND bmi[low] = 0.0
  Activation (THEN-clause):
                                           glucose[normal] : 0.0

RULE #4:
  IF age[middle-aged] AND bmi[normal] THEN glucose[normal]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[middle-aged]                                       : 1.0
  - bmi[normal]                                            : 0.6666666666666666
                          age[middle-aged] AND bmi[normal] = 0.6666666666666666
  Activation (THEN-clause):
                                           glucose[normal] : 0.6666666666666666

RULE #5:
  IF age[middle-aged] AND bmi[high] THEN glucose[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[middle-aged]                                       : 1.0
  - bmi[high]                                              : 0.0
                            age[middle-aged] AND bmi[high] = 0.0
  Activation (THEN-clause):
                                             glucose[high] : 0.0

RULE #6:
  IF age[old] AND bmi[low] THEN glucose[low]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[old]                                               : 0.0
  - bmi[low]                                               : 0.0
                                     age[old] AND bmi[low] = 0.0
  Activation (THEN-clause):
                                              glucose[low] : 0.0

RULE #7:
  IF age[old] AND bmi[normal] THEN glucose[normal]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[old]                                               : 0.0
  - bmi[normal]                                            : 0.6666666666666666
                                  age[old] AND bmi[normal] = 0.0
  Activation (THEN-clause):
                                           glucose[normal] : 0.0

RULE #8:
  IF age[old] AND bmi[high] THEN glucose[high]
	AND aggregation function : fmin
	OR aggregation function  : fmax

  Aggregation (IF-clause):
  - age[old]                                               : 0.0
  - bmi[high]                                              : 0.0
                                    age[old] AND bmi[high] = 0.0
  Activation (THEN-clause):
                                             glucose[high] : 0.0


==============================
 Intermediaries and Conquests 
==============================
Consequent: glucose                  = 85.00000000000001
  low:
    Accumulate using accumulation_max : 0.0
  normal:
    Accumulate using accumulation_max : 0.6666666666666666
  high:
    Accumulate using accumulation_max : 0.0

Out[19]:

np.float64(85.00000000000001)

Визуализации функции принадлежности

In [20]:

glucose.view(sim=glucose_simulation)

d:\5_semester\AIM\rep\AIM-PIbd-31-Razubaev-S-M\.venv\Lib\site-packages\skfuzzy\control\fuzzyvariable.py:125: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  fig.show()

Оценка качества

In [25]:

def fuzzy_pred(row):
    glucose_simulation.input["age"] = row["Age"]
    glucose_simulation.input["bmi"] = row["BMI"]
    glucose_simulation.compute()
    return glucose_simulation.output["glucose"]

result = df.copy()

result["glucose_pred"] = result.apply(fuzzy_pred, axis=1)

result.loc[115:130, ["Age", "BMI", "Glucose", "glucose_pred"]]

Out[25]:

	Age	BMI	Glucose	glucose_pred
115	61	31.2	146	156.076444
116	38	34.0	124	164.363268
117	25	33.7	78	155.611863
118	22	28.2	97	142.749562
119	21	23.2	99	85.000000
120	25	53.2	162	155.611863
121	24	34.2	111	152.260658
122	23	33.6	107	148.066203
123	69	26.8	132	158.239802
124	23	33.3	113	148.066203
125	26	55.0	88	158.305050
126	30	42.9	120	164.363268
127	23	33.3	118	148.066203
128	40	34.5	117	164.363268
129	62	27.9	105	156.763261
130	33	29.7	173	164.363268

In [29]:

import math
from sklearn import metrics

rmetrics = {}
rmetrics["RMSE"] = math.sqrt(
    metrics.mean_squared_error(result["Glucose"], result["glucose_pred"])
)
rmetrics["RMAE"] = math.sqrt(
    metrics.mean_absolute_error(result["Glucose"], result["glucose_pred"])
)
rmetrics["R2"] = metrics.r2_score(
    result["Glucose"], result["glucose_pred"]
)
rmetrics

Out[29]:

{'RMSE': 44.436073098835, 'RMAE': 6.078634343122391, 'R2': -0.9341083419845992}

Вывод: данные прогнозируются с низкой точностью и допускается множество ошибок