Every few months I implement a logistic regression (binary classification) model using raw Python (or some other language). The idea is that coding is a skill that must be practiced. One rainy Pacific Northwest afternoon, I zapped out logistic regression for the Banknote Authentication (BA) problem.

The goal of the BA problem is to predict if a banknote (think euro or dollar bill) is real/authentic (class 0) or fake/forgery (class 1). The raw data is available in several places on the Internet and looks like:

3.6216, 8.6661, -2.8073, -0.44699, 0
4.5459, 8.1674, -2.4586, -1.4621, 0
. . . 
-3.5637, -8.3827, 12.393, -1.2823, 1
-2.5419, -0.65804, 2.6842, 1.1952, 1

There are 1,372 data items. There are four predictor variables derived from a digital image of each banknote: variance, skewness, kurtosis, entropy. I broke the dataset into a 1,000-item set for training and a 372-item set by testing. I normalized all predictor values by dividing each by 20.0 so that the normalized values are all between 0.0 and 1.0 and replaced comma delimiters with tabs. The normalized data looks like:

-0.177550    0.094775   0.009325   -0.122045   1
 0.065570    0.227310   0.114675    0.011271   0
-0.200865   -0.415615   0.622735   -0.071875   1
. . . 

There are many design possibilities for logistic regression. I opted for simplicity and just maintained an array of weights (one for each predictor) and a bias value. Therefore, creating the LR model is:

print("Creating logistic regression model ")
wts = np.zeros(4)  # one wt per predictor
lo = -0.01; hi = 0.01
for i in range(len(wts)):
  wts[i] = (hi - lo) * np.random.random() + lo
bias = 0.00

I implemented a compute_outpute() function as:

def compute_output(w, b, x):
  # input x using weights w and bias b
  z = 0.0
  for i in range(len(w)):
    z += w[i] * x[i]
  z += b
  p = 1.0 / (1.0 + np.exp(-z))  # logistic sigmoid
  return p

Anyway, it was a fun exercise and, as always, I gained some new insights into the details of logistic regression.

Some fake upscale brand watches are very difficult to distinguish from authentic. But some fakes are easy to identify. Left: This Rolex is creative but not convincing. Center: I strongly suspect that Ghetto University is not legit. Right: An Apple watch — pretty punny.

Demo code: (replace “lt”, “gt”, lte”, “gte” with Boolean operator symbols — my blog editor chokes on them)

# banknote_logreg.py

# predict real (0) or forgery (1) from
# variance, skewness, kurtosis, entropy (all div by 20.0)
# data:
# -0.177550  0.094775  0.009325  -0.122045   1
#  0.065570  0.227310  0.114675   0.011271   0

# Anaconda3-2020.02  Python 3.7.6
# Windows 10/11

import numpy as np

# -----------------------------------------------------------

def compute_output(w, b, x):
  # input x using weights w and bias b
  z = 0.0
  for i in range(len(w)):
    z += w[i] * x[i]
  z += b
  p = 1.0 / (1.0 + np.exp(-z))  # logistic sigmoid
  return p

# -----------------------------------------------------------

def accuracy(w, b, data_x, data_y):
  n_correct = 0; n_wrong = 0
  for i in range(len(data_x)):
    x = data_x[i]  # inputs
    y = int(data_y[i])  # target 0 or 1
    p = compute_output(w, b, x)
    if (y == 0 and p = 0.5):
      n_correct += 1
    else:
      n_wrong += 1
  acc = (n_correct * 1.0) / (n_correct + n_wrong)
  return acc

# -----------------------------------------------------------

def mse_loss(w, b, data_x, data_y):
  sum = 0.0
  for i in range(len(data_x)):
    x = data_x[i]  # inputs
    y = int(data_y[i])  # target 0 or 1
    p = compute_output(w, b, x)
    sum += (y - p) * (y - p)
  mse = sum / len(data_x)
  return mse

# -----------------------------------------------------------

def main():
  # 0. get ready
  print("\nBegin logistic regression with raw Python demo ")
  np.random.seed(1)

  # 1. load data
  print("\nLoading Banknote train and test data to memory ")
  # variance, skewness, kurtosis, entropy (all div by 20.0)
  # 0 = real, 1 = forgery
  # -0.177550  0.094775  0.009325  -0.122045   1
  #  0.065570  0.227310  0.114675   0.011271   0

  train_file = ".\\Data\\banknote_train.txt"
  train_xy = np.loadtxt(train_file, usecols=range(0,5),
    delimiter="\t", comments="#",  dtype=np.float32) 
  train_x = train_xy[:,0:4]
  train_y = train_xy[:,4]

  test_file = ".\\Data\\banknote_test.txt"
  test_xy = np.loadtxt(test_file, usecols=range(0,5),
    delimiter="\t", comments="#", dtype=np.float32)
  test_x = test_xy[:,0:4]
  test_y = test_xy[:,4]

# -----------------------------------------------------------

  # 2. create model
  print("\nCreating logistic regression model ")
  wts = np.zeros(4)  # one wt per predictor
  lo = -0.01; hi = 0.01
  for i in range(len(wts)):
    wts[i] = (hi - lo) * np.random.random() + lo
  bias = 0.00

# -----------------------------------------------------------

  # 3. train model
  lrn_rate = 0.01
  max_epochs = 100
  indices = np.arange(len(train_x))  # [0, 1, .. 999]
  print("\nTraining using SGD with lrn_rate = %0.4f " % lrn_rate)
  for epoch in range(max_epochs):
    np.random.shuffle(indices)
    for i in indices:
      x = train_x[i]  # inputs
      y = train_y[i]  # target 0.0 or 1.0
      p = compute_output(wts, bias, x)

      # update all wts and the bias
      for j in range(len(wts)):
        wts[j] += lrn_rate * x[j] * (y - p)  # target - oupt
      bias += lrn_rate * (y - p)
    if epoch % 10 == 0:
      loss = mse_loss(wts, bias, train_x, train_y)
      print("epoch = %5d  |  loss = %9.4f " % (epoch, loss))
  print("Done ")

# -----------------------------------------------------------

  # 4. evaluate model
  print("\nEvaluating trained model ")
  acc_train = accuracy(wts, bias, train_x, train_y)
  print("Accuracy on train data: %0.4f " % acc_train)
  acc_test = accuracy(wts, bias, test_x, test_y)
  print("Accuracy on test data: %0.4f " % acc_test)

  # 5. use model
  print("\nPrediction for [0.2, 0.3, 0.5, 0.7] banknote: ")
  x = np.array([0.2, 0.3, 0.5, 0.7], dtype=np.float32)
  p = compute_output(wts, bias, x)
  print("%0.8f " % p)
  if p "lt" 0.5:  # replace here
    print("class 0 (real) ")
  else:
    print("class 1 (forgery) ") 

  # 6. TODO: save trained weights and bias to file

  print("\nEnd Banknote logistic regression demo ")

if __name__ == "__main__":
  main()

Training data. You might lose the tabs if you copy-paste.

# banknote_train.txt
# 1,000 items
# variance, skewness, kurtosis, entropy (all div by 20.0)
# 0 = real, 1 = forgery
#
-0.177550	0.094775	0.009325	-0.122045	1
0.065570	0.227310	0.114675	0.011271	0
-0.200865	-0.415615	0.622735	-0.071875	1
-0.255950	0.332430	-0.002499	-0.326030	1
0.181445	0.040661	0.081385	0.038814	0
0.051175	0.345050	-0.100310	-0.135625	0
0.232320	0.526630	-0.229260	-0.210300	0
0.188955	0.128810	0.065490	0.028275	0
0.222745	0.124880	0.051565	0.048447	0
0.219230	-0.243970	0.168310	-0.001466	0
-0.059020	0.575465	0.007783	-0.340970	0
-0.272070	0.361815	0.005469	-0.378210	1
0.084245	0.437445	-0.063205	-0.069290	0
-0.087945	-0.323120	0.423865	0.015991	1
-0.114300	-0.272420	0.290195	0.044116	1
0.140165	0.454310	-0.168340	-0.051120	0
0.287280	0.509040	-0.239285	-0.216830	0
0.036126	-0.002691	0.283515	-0.067545	0
0.207125	-0.183960	0.191405	0.081485	0
-0.066370	0.474900	0.122040	-0.263445	0
-0.034539	-0.025039	-0.017709	0.023749	1
0.155300	0.477070	-0.212680	-0.200150	0
0.195510	0.303250	-0.122670	-0.034117	0
-0.020429	0.154885	-0.148035	-0.134460	1
0.079050	0.043455	-0.115690	0.041206	1
-0.167910	-0.362020	0.572095	-0.028557	1
0.198300	0.196065	0.035287	0.016831	0
0.162925	-0.223070	0.190120	-0.007544	0
-0.091935	-0.315050	0.282530	0.009784	1
0.172830	0.476140	-0.200560	-0.179720	0
-0.076110	0.542045	0.139135	-0.204870	0
0.262115	0.551360	-0.217650	-0.205065	0
-0.218865	-0.275835	0.546950	-0.020410	1
-0.188735	0.125810	0.041671	-0.015497	1
0.151645	0.114740	0.105675	0.017542	0
-0.090380	-0.440655	0.435430	-0.010841	1
-0.252385	-0.290115	0.562200	-0.019505	1
0.032749	0.259075	0.053365	-0.021057	0
-0.014929	0.123845	-0.147560	-0.033083	1
0.203160	0.179200	0.036273	0.019741	0
0.032148	0.355090	0.017465	-0.020669	0
-0.005892	-0.078945	0.401500	-0.001402	0
0.201075	-0.135020	0.124785	0.018318	0
0.212390	0.384780	-0.138480	-0.053835	0
0.072505	0.180335	-0.202785	-0.079830	1
-0.048663	-0.320840	0.280130	0.051615	1
0.144400	0.022348	0.229535	-0.012199	0
0.130520	0.400405	-0.011796	-0.088040	0
0.133030	0.158405	0.098095	0.009331	0
-0.175300	-0.628335	0.758030	-0.037608	1
0.018990	0.035490	0.037860	-0.022220	0
0.040678	0.457830	-0.107460	-0.209070	0
-0.132030	-0.220795	0.299150	-0.006962	1
0.122635	0.148265	0.010011	-0.002824	0
-0.047962	0.004552	0.311020	-0.074140	0
-0.187515	-0.672930	0.879660	-0.138855	1
-0.135140	0.081635	0.041799	-0.004570	1
0.000864	0.434650	0.069945	-0.198340	0
0.029418	0.538635	-0.069420	-0.216380	0
-0.233825	-0.283180	0.548450	-0.016725	1
-0.144950	-0.030212	0.130225	0.068880	1
-0.128250	-0.289495	0.300610	0.002348	1
-0.228850	0.172575	0.033360	-0.047371	1
0.011216	-0.026074	-0.020193	0.060085	1
-0.274505	0.455240	-0.019379	-0.298815	1
-0.034940	-0.168855	0.206055	0.075215	1
0.047366	-0.028557	0.359515	-0.033794	0
-0.027678	-0.396165	0.335780	0.037197	1
-0.156830	0.021106	0.131125	-0.003212	1
0.190585	0.507285	-0.202315	-0.228145	0
0.128490	-0.220380	0.299280	0.003900	0
-0.144165	0.088565	0.034473	-0.023190	1
-0.062120	-0.085875	-0.026277	-0.010518	1
0.097145	0.319805	0.004612	0.029051	0
-0.131430	0.009001	0.089780	0.048641	1
0.251485	-0.248520	0.175125	-0.011876	0
0.077390	0.459070	-0.081630	-0.086875	0
0.015902	-0.049663	0.054735	0.044310	1
0.025900	0.012933	-0.042043	0.048059	1
0.148595	0.341845	-0.013510	0.035646	0
-0.019194	-0.052355	0.402570	0.024784	0
0.168780	-0.204755	0.218350	0.053490	0
-0.175900	0.143815	0.007740	-0.060430	1
-0.091955	-0.454415	0.462080	-0.005216	1
0.167915	0.517835	-0.186505	-0.184955	0
0.227985	-0.121055	0.132065	0.080840	0
0.016783	0.341845	0.034859	-0.027846	0
0.001511	-0.052560	0.070120	0.038685	1
0.010489	-0.023073	0.386335	0.045473	0
0.205985	-0.139780	0.103535	0.033706	0
0.047113	0.292805	0.093810	-0.016272	0
0.038082	0.291045	0.059795	-0.032307	0
-0.141335	-0.452035	0.453470	-0.049117	1
0.119585	0.227825	-0.249440	-0.144935	1
-0.042355	0.156645	-0.150560	-0.146940	1
-0.212200	-0.653170	0.855580	-0.140085	1
-0.124705	0.177235	-0.068605	-0.142415	1
-0.021470	-0.007347	0.002213	-0.007803	1
0.178805	0.488765	-0.198975	-0.173190	0
-0.191015	-0.652755	0.847915	-0.115260	1
-0.048035	0.134815	-0.156130	-0.065605	1
-0.017405	-0.019348	-0.023921	0.031314	1
0.246470	0.013864	0.010396	0.016831	0
-0.073905	0.007139	-0.058110	-0.024290	1
0.046485	-0.189855	0.232145	-0.014785	0
0.099090	0.463105	-0.176050	-0.093600	0
0.174925	0.158195	0.011339	-0.008255	0
0.067830	0.211790	0.106705	0.016055	0
0.133240	0.537700	-0.169970	-0.208425	0
0.200130	-0.179715	0.177865	0.013405	0
0.126835	0.129950	0.104690	0.010043	0
0.040792	0.242000	-0.263065	-0.304115	1
-0.352105	0.460000	0.012967	-0.234160	1
0.097860	-0.255765	0.430635	-0.071485	0
-0.186500	-0.648615	0.649085	-0.134200	1
0.075900	0.284730	0.004741	-0.001337	0
0.025975	-0.163165	0.154475	-0.049245	0
0.022063	0.147435	0.216125	0.035775	0
-0.069425	0.625130	0.034559	-0.377435	0
0.171230	-0.007347	0.040171	0.014568	0
0.074480	0.171440	-0.201545	-0.071295	1
0.182910	0.284320	-0.085785	-0.011876	0
-0.050580	-0.009519	-0.045299	0.000150	1
-0.000745	-0.051215	-0.047012	0.032478	1
0.258655	0.198030	-0.099150	0.020387	0
-0.337630	0.440860	-0.003099	-0.186250	1
-0.220090	-0.646855	0.782795	-0.084030	1
-0.179665	0.011484	0.035630	-0.016660	1
-0.126865	-0.347950	0.440270	0.076445	1
-0.078105	-0.110605	0.212955	0.013986	1
-0.163890	0.090115	0.009025	-0.119655	1
0.118645	0.523630	-0.150435	-0.160065	0
0.173335	-0.203620	0.214410	0.077090	0
-0.151325	-0.003104	0.034302	-0.002759	1
0.218170	0.023176	0.071405	0.101010	0
0.180385	0.342880	-0.058110	0.014116	0
0.126655	0.145675	-0.041100	-0.006122	0
-0.046794	-0.255040	0.226835	0.069330	1
0.154320	-0.129225	0.111545	0.015474	0
0.053035	0.122710	0.125940	-0.008514	0
-0.088485	0.171645	-0.060720	-0.118945	1
0.115330	0.176820	0.028776	0.020969	0
0.196460	-0.145780	0.110645	0.015409	0
0.028530	-0.001240	0.062105	-0.028105	0
-0.132395	0.506870	-0.066550	-0.273535	0
-0.056955	0.090635	0.345720	0.035064	0
-0.052775	0.039730	-0.084840	-0.023384	1
0.183510	0.149710	0.042571	0.015344	0
0.141045	0.365540	-0.040929	-0.093920	0
-0.210550	-0.623680	0.748520	-0.069420	1
0.072535	0.439515	-0.111620	-0.032630	0
-0.117050	0.618920	0.035202	-0.379180	0
0.068770	0.443965	-0.095680	-0.026876	0
-0.106665	0.078425	-0.004213	-0.087265	1
0.043101	0.134815	0.214540	0.027370	0
0.179310	-0.154785	0.140465	0.012241	0
-0.069975	-0.095810	0.125770	0.029956	1
-0.083385	-0.357675	0.394645	0.048383	1
-0.157115	-0.651825	0.783865	-0.033083	1
0.173210	0.534390	-0.170355	-0.205450	0
0.141305	0.470035	-0.165170	-0.052545	0
-0.262030	0.331290	-0.009954	-0.343035	1
0.263100	0.199170	-0.077860	0.050515	0
0.005870	0.313805	-0.077475	-0.123730	0
0.132315	-0.240760	0.317745	0.000150	0
-0.144145	0.194820	-0.009440	-0.058360	1
-0.014348	0.158920	-0.178835	-0.159480	1
0.021695	0.276975	0.101650	-0.020216	0
0.057150	0.041696	0.272760	-0.028492	0
-0.083185	0.164405	-0.113505	-0.111120	1
0.223410	0.114535	0.047883	0.041529	0
-0.167765	0.017796	0.132365	-0.018923	1
0.197300	0.342570	-0.077215	-0.027910	0
0.208680	0.166680	-0.071220	0.030215	0
0.201075	-0.109570	0.123240	0.057045	0
0.202230	0.558705	-0.217910	-0.237005	0
-0.095580	-0.308015	0.280300	0.024267	1
0.128175	0.338845	-0.030990	0.019288	0
-0.116805	0.598020	0.154175	-0.272175	0
0.208325	-0.022245	0.011724	0.013922	0
0.049148	0.171130	-0.198460	-0.085580	1
0.196310	0.301495	-0.100780	-0.003277	0
0.046485	-0.189855	0.232145	-0.014785	0
0.075385	0.097980	-0.152920	-0.006122	1
0.192085	0.501075	-0.213495	-0.245795	0
-0.092920	0.394300	-0.083215	-0.091920	0
0.136065	0.352500	-0.029404	0.020905	0
-0.144785	-0.601025	0.595745	-0.137760	1
0.008179	-0.167920	0.068745	0.067845	1
0.026187	0.182200	-0.203730	-0.099545	1
0.018990	0.035490	0.037860	-0.022220	0
0.013666	0.243865	-0.245970	-0.290990	1
-0.043670	0.082665	-0.109820	-0.039031	1
0.094965	0.383125	0.007697	-0.155540	0
-0.169315	-0.649445	0.652725	-0.136010	1
-0.244305	0.352710	-0.008626	-0.347950	1
-0.012373	0.096840	-0.123485	-0.040259	1
0.208270	-0.172475	0.182150	0.054395	0
-0.095885	0.584470	0.127270	-0.163815	0
-0.020823	0.016244	-0.016809	-0.018018	1
0.041646	0.377020	0.032503	-0.046272	0
-0.102205	0.061355	0.009282	-0.054550	1
0.081745	0.164300	0.143765	0.004353	0
0.195830	0.512455	-0.204630	-0.223295	0
-0.098950	0.161505	-0.067875	-0.129095	1
0.053185	0.184785	-0.207970	-0.096895	1
0.043802	0.340705	0.042099	-0.008578	0
-0.038924	0.170095	-0.174295	-0.177845	1
-0.033004	-0.161300	0.190290	0.059180	1
0.120040	0.467965	-0.167825	-0.167630	0
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0.013259	0.120330	-0.142080	-0.029979	1
0.042273	0.174130	-0.181535	-0.069805	1
0.057160	-0.187065	0.278885	-0.031789	0
0.014981	0.356640	-0.015738	-0.059140	0
0.170200	0.436305	-0.149575	-0.028621	0
0.193220	0.185305	0.035202	0.017607	0
0.250925	0.429890	-0.146875	-0.064050	0
0.061395	0.201545	-0.232175	-0.195625	1
0.048354	0.192130	-0.246570	-0.206615	1
-0.180060	-0.326945	0.526170	-0.024484	1
0.057790	0.320015	0.077530	0.034805	0
0.134730	0.339880	-0.020151	0.022456	0
-0.103795	0.541115	0.132195	-0.241850	0
0.005843	0.186750	-0.221895	-0.218705	1
0.057360	0.179925	0.096935	-0.021703	0
-0.050250	0.004242	-0.012310	0.022844	1
-0.091715	-0.329535	0.282145	0.027499	1
0.148680	0.439720	-0.181795	-0.068770	0
0.195605	0.148675	0.046426	0.030279	0
0.207645	-0.196790	0.143165	-0.000884	0
0.202025	0.025762	0.051395	0.055300	0
-0.274040	0.409095	0.013909	-0.251615	1
0.269575	0.499730	-0.190405	-0.168210	0
0.053260	0.418410	-0.070020	-0.082545	0
0.197070	-0.164510	0.158370	0.054330	0
-0.237310	0.156025	0.053750	-0.064830	1
0.106595	-0.102015	0.127870	-0.003083	0
0.209810	0.037247	0.041628	0.037650	0
0.179910	0.356535	-0.065175	0.010624	0
-0.100745	0.184370	-0.096925	-0.194590	1
0.087480	-0.008795	0.259135	0.064610	0
-0.176795	0.015209	0.032845	-0.014785	1
-0.194470	-0.391610	0.491040	0.023749	1
0.037421	0.363780	0.057520	-0.026940	0
0.188835	0.488970	-0.195375	-0.176615	0
0.009434	0.035074	-0.025591	0.000279	1
0.011937	0.104395	-0.167610	-0.033277	1
0.023684	0.168025	-0.225320	-0.202155	1
0.201645	0.011588	0.044541	0.059115	0
-0.059295	-0.062595	0.113175	0.038620	1
-0.055965	0.536355	0.104690	-0.282520	0
-0.247235	0.165025	0.053150	-0.072200	1
-0.099610	0.582710	0.132710	-0.260535	0
-0.084940	-0.355815	0.289510	0.008362	1
0.046352	0.471590	-0.033132	-0.083640	0
0.051420	0.488350	-0.068435	-0.089265	0
-0.071085	0.582710	-0.002885	-0.355125	0
-0.102645	0.191925	-0.039772	-0.060690	1
-0.025408	0.143400	-0.090540	-0.113060	1
0.072395	-0.243970	0.417140	-0.105430	0
0.088735	-0.321670	0.407500	-0.044914	0
0.120980	0.323325	-0.037844	0.011400	0
-0.077860	-0.494040	0.405440	-0.054030	1
0.196810	0.508110	-0.191175	-0.200860	0
-0.149105	0.209930	-0.029490	-0.198210	1
0.194845	0.370815	-0.091225	0.007004	0
-0.179580	-0.311425	0.511945	-0.057715	1
0.007392	0.397300	0.053710	-0.167045	0
0.169240	0.163370	0.045484	0.012564	0
-0.032236	-0.230310	0.417350	-0.135495	0
-0.020476	-0.007761	0.003027	-0.004440	1
0.157785	0.144540	0.029847	0.039913	0
-0.114590	-0.362850	0.397985	0.046055	1
-0.083530	-0.104500	0.079200	0.035581	1
0.024399	0.178370	-0.219410	-0.190580	1
0.119625	0.489900	-0.151805	-0.141120	0
0.255645	-0.024936	0.031432	0.055945	0
0.058380	0.457830	-0.104335	-0.040324	0
0.025975	-0.163165	0.154475	-0.049245	0
0.205975	0.546290	-0.194645	-0.209010	0
-0.087795	0.597295	0.154730	-0.244890	0
0.148710	0.448000	-0.145120	-0.051895	0
0.075495	0.001965	0.311660	-0.015173	0
0.188175	0.139055	0.033060	0.017090	0
0.206865	0.024624	0.054650	0.091380	0
-0.043670	-0.001656	-0.010083	0.027887	1
-0.106170	0.059075	-0.027776	-0.040583	1
-0.139950	0.098395	-0.021179	-0.105625	1
0.204860	0.023486	0.083355	0.045797	0
-0.040740	-0.286905	0.219595	0.016055	1
-0.253380	-0.259385	0.521330	-0.043363	1
0.244530	-0.167920	0.171010	0.054525	0
-0.024541	0.142260	-0.182180	-0.155020	1
0.082040	0.212515	-0.245115	-0.133105	1
0.174025	0.485040	-0.187705	-0.171895	0
0.141485	0.317425	-0.036773	-0.029333	0
0.197395	-0.188615	0.144150	0.000991	0
0.052000	-0.346605	0.414440	-0.064955	0
0.191220	-0.155405	0.122685	0.026012	0
0.094835	-0.125815	0.140465	-0.039871	0
-0.054010	0.109980	-0.129310	-0.063795	1
-0.056530	0.092290	-0.067875	-0.069030	1
-0.113115	0.605885	0.014423	-0.387905	0
0.157260	0.291250	-0.025720	-0.074720	0
-0.129595	-0.052765	0.194745	0.038879	1
-0.116210	0.575880	0.091155	-0.268750	0
0.021415	-0.047491	-0.053655	0.016055	1
0.098235	0.346915	0.028861	0.033189	0
-0.057485	0.064770	0.385050	0.031314	0
0.196820	0.529425	-0.186250	-0.215665	0
0.012518	0.466310	-0.184365	-0.312715	0
-0.065000	0.513390	-0.147650	-0.293190	0
0.047813	0.123640	0.222890	0.010818	0
-0.132395	0.506870	-0.066550	-0.273535	0
0.044436	0.267245	0.102250	-0.009678	0
-0.153655	-0.026591	0.119385	0.038814	1
-0.049270	-0.333050	0.291225	0.027305	1
-0.047128	0.001965	-0.012096	0.015797	1
0.076780	0.458860	-0.113590	-0.036768	0
-0.123105	0.138225	-0.031289	-0.142865	1
-0.012406	-0.008899	0.245340	0.007715	0
0.013439	0.249350	-0.257540	-0.319565	1
0.028530	-0.001240	0.062105	-0.028105	0
0.037034	0.086495	-0.159815	-0.007285	1
-0.004610	0.019658	-0.016423	-0.006897	1
0.196470	0.070560	0.090380	0.044891	0
-0.110865	0.073355	-0.036345	-0.058620	1
-0.180425	0.166265	-0.025977	-0.178685	1
0.246810	0.380230	-0.117145	-0.042651	0
0.104610	-0.340500	0.423180	-0.030108	0
0.088100	0.218410	0.106920	0.037715	0
0.095785	0.304080	0.011853	-0.100580	0
0.002599	0.352605	-0.102705	-0.157540	0
0.043368	0.278215	0.083825	-0.008385	0
-0.071165	-0.049456	0.117930	0.019741	1
0.067015	0.206615	-0.235090	-0.129935	1
0.014760	0.244280	-0.257450	-0.311615	1
-0.026536	-0.004863	-0.010897	0.052130	1
-0.076260	-0.312670	0.267620	0.029956	1
0.178850	0.120020	0.094540	0.036616	0
-0.045392	-0.395130	0.339035	0.017090	1
-0.072860	0.456070	0.087125	-0.256205	0
0.131065	0.289595	0.003284	-0.078795	0
0.142615	0.450480	-0.188050	-0.166855	0
0.228395	0.159645	-0.105275	0.014827	0
-0.097115	0.018830	-0.064490	-0.041229	1
-0.138615	0.163885	-0.046755	-0.157285	1
-0.107025	-0.008381	0.066050	-0.010453	1
-0.178565	-0.624610	0.744405	-0.023514	1
-0.008648	-0.059080	0.069090	0.036680	1
0.008673	0.393475	0.013438	-0.189415	0
0.121175	0.476660	-0.153945	-0.138730	0
-0.045859	0.499420	0.059020	-0.261315	0
0.176700	0.468070	-0.181580	-0.062305	0
0.016462	-0.222760	0.228590	-0.049440	0
0.001251	0.169990	-0.221635	-0.213275	1
-0.194130	0.244900	-0.046156	-0.254005	1
-0.087450	-0.316600	0.304935	0.007133	1
0.002265	0.336670	0.053540	-0.046660	0
-0.120500	0.187165	-0.020108	-0.064765	1
-0.160255	-0.007140	0.048783	0.002284	1
0.016460	-0.222760	0.228590	-0.049440	0
0.190985	0.449755	-0.219150	-0.201635	0
-0.001179	0.358710	0.039229	-0.037867	0
0.044803	0.527355	-0.070875	-0.201635	0
0.042787	0.000413	0.330210	-0.026552	0
-0.065000	0.513390	-0.147650	-0.293190	0
-0.053720	-0.315565	0.267750	0.040236	1
0.254300	0.163990	-0.063505	0.055945	0
0.010108	0.095910	-0.164140	-0.030884	1
-0.141955	-0.331500	0.524245	-0.021057	1
-0.092415	0.015519	0.038672	0.070945	1
-0.110415	-0.455345	0.449955	-0.014203	1
0.113170	-0.224310	0.182790	-0.030626	0
0.089375	0.239000	-0.256810	-0.161810	1
-0.089300	-0.405785	0.354290	-0.060560	1
-0.094845	-0.339465	0.263805	-0.016272	1
0.104650	0.415305	0.001142	-0.163620	0
0.136030	0.454105	-0.165555	-0.048406	0
0.148475	0.281110	0.013781	-0.057780	0
-0.090230	-0.340705	0.335095	0.058405	1
0.029912	0.175060	-0.198975	-0.089205	1
0.016460	-0.222760	0.228590	-0.049440	0
0.000483	0.178060	-0.220350	-0.220515	1
-0.043917	0.162850	-0.183890	-0.164720	1
-0.118145	-0.005277	0.096680	0.056790	1
0.162015	-0.185410	0.264020	0.020646	0
0.019126	0.340605	0.090640	-0.030626	0
-0.044785	0.150125	-0.180335	-0.172285	1
-0.000064	0.006932	-0.009826	0.000409	1
-0.002400	-0.028039	0.386075	0.022650	0
-0.082570	-0.424925	0.455610	0.061895	1
-0.034873	-0.088360	-0.017237	-0.006186	1
0.188655	0.360365	-0.084070	-0.047371	0
-0.115710	-0.034247	0.099165	-0.022415	1
0.150045	0.290630	-0.111530	-0.033277	0
0.172955	0.555600	-0.210195	-0.254655	0
0.133995	0.156745	0.017037	0.029245	0
-0.133425	-0.522595	0.455695	-0.086615	1
0.064995	0.128810	0.100535	-0.009484	0
-0.242770	-0.295185	0.549090	-0.041100	1
-0.321235	0.476555	0.001142	-0.342585	1

Test data. You might lose the tabs if you copy-paste.

# banknote_test.txt
# 372 items
# variance, skewness, kurtosis, entropy (all div by 20.0)
# 0 = real, 1 = forgery
#
-0.145730	0.202685	-0.022850	-0.201635	1
-0.022531	-0.068390	0.354290	-0.020152	0
0.095525	0.443550	-0.116930	-0.037802	0
-0.093910	-0.329325	0.242430	-0.001078	1
0.231760	-0.150435	0.133865	0.060600	0
0.079510	0.114740	0.162015	0.009202	0
-0.111700	-0.351570	0.374680	0.030667	1
-0.174585	-0.608680	0.718445	-0.030820	1
0.055250	0.372160	0.020550	-0.151660	0
-0.000345	0.464655	-0.020622	-0.098190	0
-0.072270	-0.421925	0.442415	0.048447	1
0.146165	0.302320	-0.005584	-0.029333	0
-0.127630	-0.368125	0.346275	-0.033406	1
-0.017445	0.159645	-0.170270	-0.159160	1
0.000156	-0.200305	0.089780	0.045861	1
-0.336935	0.349395	0.033917	-0.379435	1
0.328165	0.490935	-0.220565	-0.161290	0
0.026428	0.048214	0.201215	-0.052415	0
-0.024974	0.088670	-0.112345	-0.034052	1
-0.069855	0.165955	-0.069635	-0.099740	1
-0.037162	-0.016451	-0.021393	0.011659	1
0.104555	0.047179	0.227560	0.061700	0
-0.087395	-0.291150	0.293495	0.060600	1
0.185110	0.349710	-0.092555	-0.006445	0
0.016663	0.165540	-0.225405	-0.200600	1
0.031060	0.183855	-0.203855	-0.103555	1
-0.106050	-0.002794	0.097450	0.067650	1
-0.090150	0.594090	0.102290	-0.263640	0
0.135805	-0.210030	0.209570	0.008491	0
-0.020402	0.027107	-0.026363	0.032930	1
0.005796	0.161095	-0.171510	-0.142285	1
0.239630	0.085355	-0.002585	0.074630	0
0.220360	-0.003518	0.102080	0.056595	0
0.173345	0.343500	-0.052840	-0.036574	0
-0.062840	-0.073665	0.143590	0.022327	1
0.012197	0.073665	-0.070960	-0.029268	1
0.139805	0.106050	0.091925	0.019159	0
-0.038397	0.172990	-0.172025	-0.171380	1
-0.121745	-0.462485	0.449610	-0.025001	1
-0.085320	0.165440	-0.114145	-0.109890	1
-0.308160	0.435480	-0.010811	-0.181725	1
0.233445	0.065490	0.002770	0.095450	0
-0.154330	-0.331810	0.527025	-0.044591	1
-0.031022	0.027935	-0.019294	-0.033212	1
0.212290	0.059905	0.033317	0.047348	0
0.213860	0.124775	0.024277	0.018060	0
0.208785	0.513075	-0.192760	-0.215280	0
0.033009	0.519390	-0.070145	-0.195755	0
-0.044771	0.101395	-0.118260	-0.063730	1
-0.129495	-0.019555	0.046726	0.021486	1
0.212030	-0.124260	0.080400	0.035775	0
0.056575	0.396060	0.054650	-0.142220	0
0.062860	0.243655	-0.264305	-0.293705	1
0.078155	0.044800	-0.098510	0.032736	1
0.112980	-0.001656	0.236775	-0.013880	0
-0.081220	-0.317220	0.232875	0.008491	1
-0.070470	-0.106260	-0.005199	-0.009613	1
0.100765	0.092395	0.156875	0.021422	0
-0.203930	0.146195	0.043513	-0.032695	1
0.197165	0.125085	0.076075	0.045150	0
0.161755	0.482350	-0.160370	-0.129740	0
-0.075390	-0.365955	0.394905	0.061445	1
0.066320	0.051630	0.282830	-0.020669	0
0.044222	0.329530	0.027919	-0.022091	0
-0.113125	-0.004967	0.140635	0.024331	1
-0.080880	0.054630	-0.017751	-0.029979	1
0.067810	0.160680	0.217325	0.039331	0
-0.258305	0.402165	0.002213	-0.224915	1
-0.029794	0.124055	-0.143365	-0.044914	1
-0.118375	-0.021832	0.084600	-0.021509	1
-0.019908	0.298905	0.069560	-0.058105	0
0.198860	0.016761	0.112830	0.108125	0
0.175760	0.341120	-0.033689	-0.023449	0
0.025407	0.023900	-0.099020	0.028857	1
-0.145490	-0.503560	0.420780	-0.099740	1
-0.099830	-0.475005	0.484100	-0.006445	1
0.122430	-0.315875	0.398160	0.010301	0
0.034044	0.116295	0.245425	0.027499	0
0.017170	0.006208	-0.014367	0.007327	1
0.050955	0.116500	0.246670	0.041465	0
0.045658	0.166885	-0.202785	-0.083705	1
0.130700	0.400405	-0.186290	-0.065345	0
0.092960	0.160370	-0.007983	-0.013104	0
0.134405	0.300975	-0.023321	-0.034634	0
0.177190	0.061975	0.099850	0.107735	0
0.087260	0.240140	0.104390	0.031314	0
0.041813	0.055355	-0.123530	-0.003147	1
0.200635	0.507385	-0.196830	-0.203640	0
0.196550	0.092705	-0.001171	0.061570	0
0.194995	0.086700	0.080055	0.048383	0
0.012131	0.028659	-0.097010	0.022004	1
-0.166015	-0.001346	0.148090	-0.022479	1
-0.069435	-0.243865	0.323870	0.017090	1
0.078505	0.395645	0.014509	-0.109765	0
0.050675	0.422755	-0.083600	-0.104075	0
0.018990	0.035490	0.037860	-0.022220	0
-0.091095	-0.344120	0.273405	0.002866	1
0.080100	0.306255	0.026462	0.023943	0
-0.180265	-0.298700	0.504580	-0.041423	1
-0.066945	0.077600	0.354030	0.051550	0
0.232195	-0.168645	0.129880	0.027629	0
0.197645	-0.117740	0.118960	0.024137	0
-0.011805	0.466105	0.106535	-0.218965	0
-0.024641	0.153025	-0.091780	-0.141700	1
-0.099915	-0.330360	0.241270	-0.020992	1
-0.148360	-0.664345	0.673635	-0.131355	1
0.097050	0.023176	0.232360	0.054395	0
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