
#Read csv file with features of substance
import pandas as pd

directory = 'INSERT DIRECTORY'

#First column is for indexes
features = pd.read_csv(directory, sep="\t", index_col=0)


#Exclude temperature & humidity sensor and information about the day
features = features.drop('Temperature', axis=1)
features = features.drop('Humidity Difference', axis=1)
features = features.drop('Day', axis=1)


#Display the 62 features for all measurements
features


'''
#only for Isobutanol, the highest concentration was not used as it was too high
values = [0,1000,2000,250,500]
features = features.loc[features.iloc[:,-1].isin(values)]
features = features.reset_index(drop=True)
'''

'\n#only for Isobutanol\nvalues = [0,1000,2000,250,500]\nfeatures = features.loc[features.iloc[:,-1].isin(values)]\nfeatures = features.reset_index(drop=True)\n'


#Standardize features with z-scores
normalized_features = features.copy()
normalized_features.iloc[:,:-1] = (normalized_features.iloc[:,:-1]-normalized_features.iloc[:,:-1].mean())/normalized_features.iloc[:,:-1].std()


#Look at the concentration levels and number of samples per level
normalized_features.iloc[:,-1].value_counts()

0.0        16
500.0      13
6000.0     13
1000.0     12
4000.0     12
2000.0     11
9000.0     10
12000.0     9
15000.0     9
Name: Concentration, dtype: int64


#Calculation of the effective leverage

#number of samples
n = len(features)

#effective leverage calculation
cmean = normalized_features.iloc[:,-1].mean()
sumres = 0
#calculate the sum of the residuals
for c in normalized_features.iloc[:,-1]:
    res = (c-cmean)**2
    sumres = sumres+res

leverage = (cmean**2)/sumres
leverage = leverage+(1/n) #1/n added to the leverage to get the effective leverage


#get an idea of the PC1 vs. concentration plot
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt

#fit PCA
pca_ = PCA(n_components=2)
principalComponents_ = pca_.fit_transform(normalized_features.iloc[:,:-1])
principal_Df = pd.DataFrame(data = principalComponents_, columns = ['principal component 1', 'principal component 2'])

#plot error bars
principal_Df["Concentration"] = normalized_features.iloc[:,-1]
plt.errorbar(principal_Df.groupby('Concentration').mean().index, principal_Df.groupby('Concentration').mean().iloc[:,0], yerr=principal_Df.groupby('Concentration').std().iloc[:,0], marker='o', capsize=3, markersize="4", color='black', ls='none', linewidth=0.5)


# display plot
plt.xlabel('Concentration [ppm]')
plt.ylabel('PC1')
plt.show()

#Print the explained variance of the first component
print("Explained variance of first PC: ", pca_.explained_variance_ratio_[0])

Explained variance of first PC:  0.9346590025991751


#define the k for the LOD estiamtion

#set kLOD to 3.3 (or to 2*t(1-α,v) for smaller number of samples)
kLOD = 3.72 
#kLOD = 4.03 #for Diacetyl due to smaller sample size
#kLOD = 10 #for LOQ


############################## Methods based on pseudo univariate calculation with PCA ##############################
import numpy as np
from scipy import stats
from sklearn.metrics import mean_squared_error
import math

#calculation of yLOD

#Only consider the components of the samples with a concentration of zero
values = [0]

#calculate the mean and standard deviation of the first principal component for the blanks
meanblank = principal_Df[normalized_features.iloc[:,-1].isin(values)]["principal component 1"].mean()
stdblank = principal_Df[normalized_features.iloc[:,-1].isin(values)]["principal component 1"].std()

yLOD = meanblank+(kLOD*stdblank)
print("yLOD for PC1 vs. concentration plot: ", yLOD)
#calculate the mean PC-value of every concentration level
new_df = pd.DataFrame()
new_df["PC1"] = principal_Df["principal component 1"]
new_df["Concentration"] = normalized_features.iloc[:,-1]
print(new_df.groupby(new_df.iloc[:,-1]).mean())

#Calculate the calibration curve and plot the function
y = principal_Df.loc[:, 'principal component 1']
x = normalized_features.iloc[:,-1]
slope, intercept, r, p, std_err = stats.linregress(x, y)

def myfunc(x):
  return slope * x + intercept

mymodel = list(map(myfunc, x))
plt.xlabel('Concentration [ppm]')
plt.ylabel('PC1')

#plot the error bars
principal_Df["Concentration"] = normalized_features.iloc[:,-1]
plt.errorbar(principal_Df.groupby('Concentration').mean().index, principal_Df.groupby('Concentration').mean().iloc[:,0], yerr=principal_Df.groupby('Concentration').std().iloc[:,0], marker='o', capsize=3, markersize="4", color='black', ls='none', linewidth=0.5)
plt.plot(x, mymodel, linewidth=0.5)
plt.show() 
plt.close()

#calculation of cLOD

#The slope of the calibration curve
m = slope

#First use the function of the sklearn library to calculate the RMSE
#remark: classical calibration is used (the LOD was NOT determined using inverse calibration)
y_true = principal_Df.loc[:, 'principal component 1']
y_pred = list(map(myfunc, x))
rmse = mean_squared_error(y_true, y_pred, squared=False)

#calculation of cLOD including also the leverage and RMSE

cLOD = (kLOD*rmse*math.sqrt(1+leverage))/m
print("cLOD for PC1 vs. concentration plot with RMSE and leverage: ",cLOD)

#calculation of cLOD including also the leverage and stdblank

cLOD = (kLOD*stdblank*math.sqrt(1+leverage))/m
print("cLOD for PC1 vs. concentration plot with STDblank and leverage: ",cLOD)

yLOD for PC1 vs. concentration plot:  -0.3215183587656165
                     PC1  Concentration
Concentration                          
0.0            -7.344232            0.0
500.0          -5.570894          500.0
1000.0         -5.404290         1000.0
2000.0         -5.150209         2000.0
4000.0         -0.712469         4000.0
6000.0          3.107914         6000.0
9000.0         10.798600         9000.0
12000.0         5.671004        12000.0
15000.0        13.394979        15000.0

cLOD for PC1 vs. concentration plot with RMSE and leverage:  9984.204246604699
cLOD for PC1 vs. concentration plot with STDblank and leverage:  5178.195007887557


############################## Methods based on PLSR and PCR ##############################


#PCR

from sklearn.model_selection import StratifiedKFold
from sklearn.linear_model import LinearRegression
import math
import statistics

#list for number of components that yielded to the minimum R2/RMSE
numcomp = []
#copy of the feature DataFrame
ff = features.copy()
#to apply stratified k-fold method from sklearn
ff.iloc[:,-1] = ff.iloc[:,-1].astype("string")

#repeat the stratified k-fold validation 10 times with shuffled data
for c in range(0,11):
    ff = ff.sample(frac=1).reset_index(drop=True)
    X = ff.iloc[:,:-1]
    y = ff.iloc[:,-1]

    loo = StratifiedKFold(n_splits=5)

    loo.get_n_splits(X,y)

    r2list = []
    rmselist = []

    #repeat stratified k-fold for different number of components
    for n in range(1,20):

        pca = PCA(n_components=n)
        regr = LinearRegression()
        r2mean = 0
        rmsemean = 0

        for i, (train_index, test_index) in enumerate(loo.split(X,y)):

            #first normalize the features of the training set
            norm_features = X.iloc[train_index,:].copy()
            mean = norm_features.iloc[:,:].mean()
            std = norm_features.iloc[:,:].std()
            norm_features.iloc[:,:] = (norm_features.iloc[:,:]-mean)/std
            norm_features_test = X.iloc[test_index,:].copy()
            norm_features_test.iloc[:,:] = (norm_features_test.iloc[:,:]-mean)/std

            #first fit on training data and the transform test data
            principalComponentstrain = pca.fit_transform(norm_features.iloc[:,:])
            principalComponentstest = pca.transform(norm_features_test.iloc[:,:])

            #build regression model on PCA components
            reg = regr.fit(principalComponentstrain, y.iloc[train_index])

            #calculate R2 and rmse
            r2 = reg.score(principalComponentstest, y.iloc[test_index]) #Q2
            y_pred = reg.predict(principalComponentstest)
            rmse = mean_squared_error(y.iloc[test_index], y_pred, squared=False) #squared=False --> RMSE
            r2mean += r2
            rmsemean += rmse
        r2mean=(r2mean/5)
        rmsemean=(rmsemean/5)
        r2list.append(r2mean)
        rmselist.append(rmsemean)

    xs = [x for x in range(1,len(r2list)+1)]

    #plot the R2 for the different number of components
    plt.plot(xs, r2list)
    plt.ylabel('Q2 (i.e., R2 Prediction)')
    plt.xlabel('Number of Components')
    plt.show()
    plt.close()

    #Minimum number of components for smallest RMSE
    comp1 = rmselist.index(min(rmselist))+1
    print("Minimum number of components for smallest RMSE:", comp1, "(For RMSE of:", min(rmselist), ")")
    numcomp.append(comp1)

    #Minimum number of components for greatest Q2
    comp2 = r2list.index(max(r2list))+1
    print("Minimum number of components for greatest Q2:", comp2, "(For Q2 of:", max(r2list), ")")
    numcomp.append(comp2)

#Calculation of LOD
pcr = LinearRegression()
#use the number of components previously determined
pca = PCA(n_components=round(statistics.median(numcomp)))
print("Number of components:",round(statistics.median(numcomp)))
components = pca.fit_transform(normalized_features.iloc[:,:-1])

pcr.fit(components, normalized_features.iloc[:,-1])

#get R2 and RMSE of the fitted model
r2 = pcr.score(components, normalized_features.iloc[:,-1])
y_pred = pcr.predict(components)
rmse = mean_squared_error(normalized_features.iloc[:,-1], y_pred, squared=False)
print("R2:",r2,"RMSE:",rmse)

plt.figure(figsize=(5,5))
predicted = pcr.predict(components)
actual = normalized_features.iloc[:,-1]
plt.scatter(actual, predicted, c='crimson', s=3)
plt.xlabel('True Values (Concentration [ppm])')#, fontsize=15)
plt.ylabel('Predictions (Concentration [ppm])')#, fontsize=15)
plt.axis('equal')
plt.show()
plt.close()

#calculation of cLOD including also the leverage and STDblank/RMSE of predicted vs actual
rmse = mean_squared_error(actual, predicted, squared=False)

#use the slope of the "predicted=actual"-line
m = 1

cLOD = (kLOD*rmse*math.sqrt(1+leverage))/m
print("cLOD for PCR with leverage and RMSE:",cLOD)

#calculation of cLOD including also the leverage and stdblank of predicted vs actual
stdblank = predicted[actual[actual == 0].index].std()

cLOD = (kLOD*stdblank*math.sqrt(1+leverage))/m
print("cLOD for PCR with leverage and STDblank:",cLOD)

Minimum number of components for smallest RMSE: 17 (For RMSE of: 1017.254524824771 )
Minimum number of components for greatest Q2: 17 (For Q2 of: 0.9556899884007674 )

Minimum number of components for smallest RMSE: 15 (For RMSE of: 972.1091050285643 )
Minimum number of components for greatest Q2: 15 (For Q2 of: 0.9588500013620938 )

Minimum number of components for smallest RMSE: 19 (For RMSE of: 966.9406524559408 )
Minimum number of components for greatest Q2: 19 (For Q2 of: 0.9575595311532688 )

Minimum number of components for smallest RMSE: 14 (For RMSE of: 1013.5557494951447 )
Minimum number of components for greatest Q2: 14 (For Q2 of: 0.9547137188950258 )

Minimum number of components for smallest RMSE: 19 (For RMSE of: 995.2864201773116 )
Minimum number of components for greatest Q2: 19 (For Q2 of: 0.9574235322599588 )

Minimum number of components for smallest RMSE: 15 (For RMSE of: 1011.2227035995593 )
Minimum number of components for greatest Q2: 15 (For Q2 of: 0.956084344839805 )

Minimum number of components for smallest RMSE: 15 (For RMSE of: 1030.752163771012 )
Minimum number of components for greatest Q2: 15 (For Q2 of: 0.9531868578506302 )

Minimum number of components for smallest RMSE: 16 (For RMSE of: 1103.722804352346 )
Minimum number of components for greatest Q2: 14 (For Q2 of: 0.9472624207090492 )

Minimum number of components for smallest RMSE: 15 (For RMSE of: 1018.8097132877522 )
Minimum number of components for greatest Q2: 15 (For Q2 of: 0.9534738247765512 )

Minimum number of components for smallest RMSE: 14 (For RMSE of: 1033.5580980405541 )
Minimum number of components for greatest Q2: 14 (For Q2 of: 0.9531480000378642 )


#PLSR

from sklearn.model_selection import StratifiedKFold
from sklearn.cross_decomposition import PLSRegression

numcomp = []
ff = features.copy()
#Change datatype to string to apply StratifiedKFold-Method
ff.iloc[:,-1] = ff.iloc[:,-1].astype("string")

for c in range(0,11):
    ff = ff.sample(frac=1).reset_index(drop=True)
    X = ff.iloc[:,:-1]
    y = ff.iloc[:,-1]

    loo = StratifiedKFold(n_splits=5)
    loo.get_n_splits(X,y)

    r2list = []
    rmselist = []

    for n in range(1,20):

        pls33 = PLSRegression(n_components=n)
        r2mean = 0
        rmsemean = 0

        for i, (train_index, test_index) in enumerate(loo.split(X,y)):

            norm_features = X.iloc[train_index,:].copy()
            mean = norm_features.iloc[:,:].mean()
            std = norm_features.iloc[:,:].std()
            norm_features.iloc[:,:] = (norm_features.iloc[:,:]-mean)/std
            norm_features_test = X.iloc[test_index,:].copy()
            norm_features_test.iloc[:,:] = (norm_features_test.iloc[:,:]-mean)/std
            
            pls33.fit(norm_features.iloc[:,:], y.iloc[train_index])
            r2 = pls33.score(norm_features_test.iloc[:,:], y.iloc[test_index]) #Q2
            y_pred = pls33.predict(norm_features_test.iloc[:,:])
            rmse = mean_squared_error(y.iloc[test_index], y_pred, squared=False) #squared=False --> RMSE
            r2mean += r2 
            rmsemean += rmse
        r2mean=(r2mean/5)
        rmsemean=(rmsemean/5)
        r2list.append(r2mean)
        rmselist.append(rmsemean)

    xs = [x for x in range(1,len(r2list)+1)]

    plt.plot(xs, rmselist)
    plt.ylabel('RMSE')
    plt.xlabel('Number of Components')
    plt.show()
    plt.close()

    #Minimum number of components for smallest RMSE
    comp1 = rmselist.index(min(rmselist))+1
    print("Minimum number of components for smallest RMSE:", comp1, "(For RMSE of:", min(rmselist), ")")
    numcomp.append(comp1)

    #Minimum number of components for greatest Q2
    comp2 = r2list.index(max(r2list))+1
    print("Minimum number of components for greatest Q2:", comp2, "(For Q2 of:", max(r2list), ")")
    numcomp.append(comp2)

#Now calculation of LOD
plsr = PLSRegression(n_components=round(statistics.median(numcomp)))
print("Number of components:",round(statistics.median(numcomp)))
plsr.fit(normalized_features.iloc[:,:-1], normalized_features.iloc[:,-1])

r2 = plsr.score(normalized_features.iloc[:,:-1], normalized_features.iloc[:,-1])
y_pred = plsr.predict(normalized_features.iloc[:,:-1])
rmse = mean_squared_error(normalized_features.iloc[:,-1], y_pred, squared=False)
print("R2:",r2,"RMSE:",rmse)

plt.figure(figsize=(5,5))
predicted = plsr.predict(normalized_features.iloc[:,:-1])
actual = normalized_features.iloc[:,-1]
plt.scatter(actual, predicted, c='crimson', s=3)
plt.xlabel('True Values (Concentration [ppm])')
plt.ylabel('Predictions (Concentration [ppm])')
plt.axis('equal')
plt.show()
plt.close()

#calculation of cLOD including also the leverage and RMSE of predicted vs actual

rmse = mean_squared_error(actual, predicted, squared=False)

m = 1

cLOD = (kLOD*rmse*math.sqrt(1+leverage))/m
print("cLOD for PLSR with leverage and RMSE:",cLOD)

#calculation of cLOD including also the leverage and stdblank of predicted vs actual
stdblank = predicted[actual[actual == 0].index].std()

cLOD = (kLOD*stdblank*math.sqrt(1+leverage))/m
print("cLOD for PLSR with leverage and STDblank:",cLOD)

Minimum number of components for smallest RMSE: 9 (For RMSE of: 978.3016137398643 )
Minimum number of components for greatest Q2: 9 (For Q2 of: 0.9590800257507379 )

Minimum number of components for smallest RMSE: 9 (For RMSE of: 894.5610534164946 )
Minimum number of components for greatest Q2: 9 (For Q2 of: 0.9657846529758096 )

Minimum number of components for smallest RMSE: 9 (For RMSE of: 903.1105820856301 )
Minimum number of components for greatest Q2: 9 (For Q2 of: 0.9645957545790521 )

Minimum number of components for smallest RMSE: 8 (For RMSE of: 1028.5024590805592 )
Minimum number of components for greatest Q2: 8 (For Q2 of: 0.9532923160423854 )

Minimum number of components for smallest RMSE: 10 (For RMSE of: 899.6413151996783 )
Minimum number of components for greatest Q2: 10 (For Q2 of: 0.9637563551334839 )

Minimum number of components for smallest RMSE: 8 (For RMSE of: 1009.975521904152 )
Minimum number of components for greatest Q2: 8 (For Q2 of: 0.9550832223781317 )

Minimum number of components for smallest RMSE: 8 (For RMSE of: 967.8999135391465 )
Minimum number of components for greatest Q2: 8 (For Q2 of: 0.9588651410874952 )

Minimum number of components for smallest RMSE: 10 (For RMSE of: 923.489717040013 )
Minimum number of components for greatest Q2: 10 (For Q2 of: 0.9632934487487855 )

Minimum number of components for smallest RMSE: 8 (For RMSE of: 979.6255059138417 )
Minimum number of components for greatest Q2: 8 (For Q2 of: 0.9586915915404639 )

Minimum number of components for smallest RMSE: 8 (For RMSE of: 954.9681448986385 )
Minimum number of components for greatest Q2: 8 (For Q2 of: 0.9601352812556208 )

	0	1	2	3	4	5	6	7	8	9	...	53	54	55	56	57	58	59	60	61	Concentration
0	-15414.933333	-18689.766667	-6075.133333	-6299.7	-5185.333333	-5543.366667	2357.166667	1999.166667	-5240.633333	-3232.966667	...	-15054.666667	-17127.766667	-14964.366667	-15731.800000	-14458.333333	-12710.933333	-14868.000000	2.031147e+04	1.199987e+04	1000.0
1	-31579.133333	-30115.766667	-10357.233333	-10122.9	-10448.633333	-10742.266667	-2068.933333	-2118.633333	-8679.833333	-5463.166667	...	-22324.466667	-25981.166667	-27234.866667	-23750.800000	-22456.433333	-27059.333333	-26662.500000	-4.810843e+04	-3.533303e+04	1000.0
2	-35462.333333	-35657.466667	-11825.733333	-11338.1	-11443.133333	-11851.566667	-2666.933333	-1340.233333	-8159.233333	-5319.566667	...	-23017.466667	-29283.866667	-26761.666667	-21870.900000	-28322.133333	-31144.833333	-23881.900000	-2.981833e+03	-6.346483e+04	1000.0
3	-23613.333333	-26278.966667	-8468.233333	-9287.7	-3791.033333	-3512.666667	10541.666667	10696.866667	-1945.333333	-368.766667	...	-10073.966667	-9204.966667	-8459.366667	-9199.400000	-10403.933333	-6885.933333	-5762.400000	1.098370e+05	9.511247e+04	2000.0
4	-28928.533333	-31346.566667	-10811.933333	-11041.2	-7952.033333	-9997.366667	4355.566667	4067.866667	-6547.433333	-2876.566667	...	-22255.766667	-22931.966667	-22609.966667	-21363.300000	-21685.033333	-21836.433333	-22170.600000	4.585537e+04	5.037567e+04	2000.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
100	145203.933333	148993.466667	27564.666667	31059.7	56307.566667	58206.166667	72561.866667	72951.933333	29806.800000	31767.100000	...	99756.000000	94635.833333	93545.333333	88659.966667	87896.233333	108120.533333	107247.033333	1.290786e+06	1.353217e+06	9000.0
101	129621.533333	132768.766667	22773.966667	23577.4	49836.866667	48231.166667	67353.166667	66695.633333	27091.000000	25483.200000	...	78886.400000	73234.433333	73072.333333	66713.366667	66039.433333	86519.433333	83760.533333	1.200376e+06	1.276475e+06	9000.0
102	6887.433333	6045.666667	4565.066667	4845.8	6077.366667	6784.766667	5651.966667	4163.033333	3838.800000	4432.000000	...	16623.900000	18093.733333	17403.333333	18711.766667	18745.833333	20696.833333	22963.233333	1.249697e+04	9.307600e+03	0.0
103	766.333333	-1595.833333	-680.033333	-476.9	-235.333333	-2282.833333	-1103.633333	202.033333	-120.900000	-145.000000	...	-2813.300000	-1834.966667	-2259.266667	-1822.733333	-1568.566667	-1535.866667	-2754.666667	1.427217e+04	-3.416400e+03	0.0
104	-7653.766667	-4449.833333	-3885.033333	-4368.9	-5842.033333	-4501.933333	-4548.333333	-4365.066667	-3717.900000	-4287.000000	...	-13810.600000	-16258.766667	-15144.066667	-16889.033333	-17177.266667	-19160.966667	-20208.566667	-2.676913e+04	-5.891200e+03	0.0