import pandas as pd
import numpy as np
from sklearn.svm import OneClassSVM
from sklearn.svm import SVC
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt
import warnings
import seaborn as sns
warnings.filterwarnings('ignore')
from google.colab import files
import io
uploaded = files.upload()
df_bank = pd.read_csv('bank-additional-full_normalised.csv')
df_bank.head()
| age | job=housemaid | job=services | job=admin. | job=blue-collar | job=technician | job=retired | job=management | job=unemployed | job=self-employed | ... | previous | poutcome=nonexistent | poutcome=failure | poutcome=success | emp.var.rate | cons.price.idx | cons.conf.idx | euribor3m | nr.employed | class | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.209877 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0.000000 | 1 | 0 | 0 | 1.000000 | 0.882307 | 0.376569 | 0.980730 | 1.000000 | 0 |
| 1 | 0.296296 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0.000000 | 1 | 0 | 0 | 1.000000 | 0.484412 | 0.615063 | 0.981183 | 1.000000 | 0 |
| 2 | 0.246914 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0.000000 | 1 | 0 | 0 | 0.937500 | 0.698753 | 0.602510 | 0.957379 | 0.859735 | 0 |
| 3 | 0.160494 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0.142857 | 0 | 1 | 0 | 0.333333 | 0.269680 | 0.192469 | 0.150759 | 0.512287 | 0 |
| 4 | 0.530864 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ... | 0.000000 | 1 | 0 | 0 | 0.333333 | 0.340608 | 0.154812 | 0.174790 | 0.512287 | 1 |
5 rows × 63 columns
SVM Model
data = df_bank
data.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 41188 entries, 0 to 41187
Data columns (total 63 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 age 41188 non-null float64
1 job=housemaid 41188 non-null int64
2 job=services 41188 non-null int64
3 job=admin. 41188 non-null int64
4 job=blue-collar 41188 non-null int64
5 job=technician 41188 non-null int64
6 job=retired 41188 non-null int64
7 job=management 41188 non-null int64
8 job=unemployed 41188 non-null int64
9 job=self-employed 41188 non-null int64
10 job=unknown 41188 non-null int64
11 job=entrepreneur 41188 non-null int64
12 job=student 41188 non-null int64
13 marital=married 41188 non-null int64
14 marital=single 41188 non-null int64
15 marital=divorced 41188 non-null int64
16 marital=unknown 41188 non-null int64
17 education=basic.4y 41188 non-null int64
18 education=high.school 41188 non-null int64
19 education=basic.6y 41188 non-null int64
20 education=basic.9y 41188 non-null int64
21 education=professional.course 41188 non-null int64
22 education=unknown 41188 non-null int64
23 education=university.degree 41188 non-null int64
24 education=illiterate 41188 non-null int64
25 default=0 41188 non-null int64
26 default=unknown 41188 non-null int64
27 default=1 41188 non-null int64
28 housing=0 41188 non-null int64
29 housing=1 41188 non-null int64
30 housing=unknown 41188 non-null int64
31 loan=0 41188 non-null int64
32 loan=1 41188 non-null int64
33 loan=unknown 41188 non-null int64
34 contact=cellular 41188 non-null int64
35 month=may 41188 non-null int64
36 month=jun 41188 non-null int64
37 month=jul 41188 non-null int64
38 month=aug 41188 non-null int64
39 month=oct 41188 non-null int64
40 month=nov 41188 non-null int64
41 month=dec 41188 non-null int64
42 month=mar 41188 non-null int64
43 month=apr 41188 non-null int64
44 month=sep 41188 non-null int64
45 day_of_week=mon 41188 non-null int64
46 day_of_week=tue 41188 non-null int64
47 day_of_week=wed 41188 non-null int64
48 day_of_week=thu 41188 non-null int64
49 day_of_week=fri 41188 non-null int64
50 duration 41188 non-null float64
51 campaign 41188 non-null float64
52 pdays 41188 non-null float64
53 previous 41188 non-null float64
54 poutcome=nonexistent 41188 non-null int64
55 poutcome=failure 41188 non-null int64
56 poutcome=success 41188 non-null int64
57 emp.var.rate 41188 non-null float64
58 cons.price.idx 41188 non-null float64
59 cons.conf.idx 41188 non-null float64
60 euribor3m 41188 non-null float64
61 nr.employed 41188 non-null float64
62 category 41188 non-null int64
dtypes: float64(10), int64(53)
memory usage: 19.8 MB
from sklearn.svm import OneClassSVM
from sklearn.metrics import accuracy_score, classification_report
outlier_fraction = len(data[data['category']==1])/float(len(data[data['category']==0]))
clfsvm = OneClassSVM(kernel="rbf", nu=outlier_fraction)
X = data.loc[:,data.columns!='category']
Y = data['category']
y_pred = clfsvm.fit_predict(X)
y_pred[y_pred == 1] = 0
y_pred[y_pred == -1] = 1
n_errors = (y_pred != Y).sum()
print("{}: {}".format("No. of Anomalous Points with One-Class SVM ",n_errors))
print("Accuracy Score :")
print(accuracy_score(Y,y_pred))
print("Classification Report :")
print(classification_report(Y,y_pred))
No. of Anomalous Points with One-Class SVM : 7252
Accuracy Score :
0.8239292997960571
Classification Report :
precision recall f1-score support
0 0.91 0.89 0.90 36548
1 0.25 0.28 0.27 4640
accuracy 0.82 41188
macro avg 0.58 0.59 0.58 41188
weighted avg 0.83 0.82 0.83 41188
import seaborn as sns
import matplotlib.pyplot as plt
plt.style.use("ggplot")
sns.FacetGrid(data, hue="category").map(plt.scatter, "nr.employed", "age", edgecolor="k").add_legend()
plt.show()
data.shape
(41188, 63)
from scipy import spatial
sample_data = data.head(41180)
samples = data.loc[41181:41188]
%%javascript
IPython.OutputArea.prototype._should_scroll = function(lines) {
return False;
}
<IPython.core.display.Javascript object>
frame = []
for i in range(41181, 41188):
t1 = samples.loc[i]
cls = samples.loc[i]["category"]
for j in range(41180):
t2 = sample_data.loc[j]
class_label = data.loc[j]["category"]
similarity = 1 - spatial.distance.cosine(t1, t2)
if (class_label == 1):
frame.append([class_label, similarity, j])
df = pd.DataFrame(frame, columns=['category', 'Similarity', 'Transaction ID'])
df_sorted = df.sort_values("Similarity", ascending=False)
print("Top 5 suspected-fraud transactions having highest similarity with transaction ID = "+str(i)+ ":")
print(df_sorted.iloc[:5])
print("\n")
frame = []
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41181:
category Similarity Transaction ID
4417 1.0 0.933260 39073
218 1.0 0.933256 1837
3959 1.0 0.865343 35210
626 1.0 0.865231 5502
514 1.0 0.865045 4597
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41182:
category Similarity Transaction ID
1531 1.0 0.901827 13014
3355 1.0 0.898451 29863
3898 1.0 0.836246 34601
2518 1.0 0.835903 22287
4289 1.0 0.835808 37988
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41183:
category Similarity Transaction ID
163 1.0 0.876614 1366
3052 1.0 0.794651 27036
162 1.0 0.794483 1353
349 1.0 0.793905 3079
176 1.0 0.793708 1473
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41184:
category Similarity Transaction ID
4572 1.0 0.859526 40607
3707 1.0 0.859427 32960
3564 1.0 0.858049 31552
4536 1.0 0.858018 40266
2369 1.0 0.854684 20918
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41185:
category Similarity Transaction ID
3333 1.0 0.892698 29636
4084 1.0 0.892566 36207
985 1.0 0.892001 8525
3469 1.0 0.891721 30819
21 1.0 0.891262 153
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41186:
category Similarity Transaction ID
1893 1.0 0.896340 16376
3690 1.0 0.896141 32785
4619 1.0 0.895991 40949
3078 1.0 0.895785 27266
45 1.0 0.895512 332
Top 5 suspected-fraud transactions having highest similarity with transaction ID = 41187:
category Similarity Transaction ID
3800 1.0 0.964525 33717
3119 1.0 0.893301 27606
1254 1.0 0.892938 10897
4181 1.0 0.892748 37092
1063 1.0 0.892707 9180
data.shape
(41188, 63)
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from mpl_toolkits.mplot3d import Axes3D
pca = PCA(n_components=3) #Considered only 3 components to put into 3 dimensions
to_model_cols = data.columns[0:63]
outliers = data.loc[data['category']==1]
outlier_index=list(outliers.index)
scaler = StandardScaler()
X = scaler.fit_transform(data[to_model_cols])
X_reduce = pca.fit_transform(X)
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot(111, projection='3d')
ax.set_zlabel("x_composite_3_using_PCA")
# Plotting compressed data points
ax.scatter(X_reduce[:, 0], X_reduce[:, 1], zs=X_reduce[:, 2], s=3, lw=1, label="inliers",c="green")
# Plot x for the ground truth outliers
ax.scatter(X_reduce[outlier_index,0],X_reduce[outlier_index,1], X_reduce[outlier_index,2],
s=60, lw=2, marker="x", c="red", label="outliers")
ax.legend()
plt.show()
from sklearn.manifold import TSNE
standardized_data = StandardScaler().fit_transform(data)
data = standardized_data
tsne = TSNE(n_components=3, verbose=1, perplexity=40, n_iter=250)
data = tsne.fit_transform(data)
[t-SNE] Computing 121 nearest neighbors...
[t-SNE] Indexed 41188 samples in 0.007s...
[t-SNE] Computed neighbors for 41188 samples in 6.399s...
[t-SNE] Computed conditional probabilities for sample 1000 / 41188
[t-SNE] Computed conditional probabilities for sample 2000 / 41188
[t-SNE] Computed conditional probabilities for sample 3000 / 41188
[t-SNE] Computed conditional probabilities for sample 4000 / 41188
[t-SNE] Computed conditional probabilities for sample 5000 / 41188
[t-SNE] Computed conditional probabilities for sample 6000 / 41188
[t-SNE] Computed conditional probabilities for sample 7000 / 41188
[t-SNE] Computed conditional probabilities for sample 8000 / 41188
[t-SNE] Computed conditional probabilities for sample 9000 / 41188
[t-SNE] Computed conditional probabilities for sample 10000 / 41188
[t-SNE] Computed conditional probabilities for sample 11000 / 41188
[t-SNE] Computed conditional probabilities for sample 12000 / 41188
[t-SNE] Computed conditional probabilities for sample 13000 / 41188
[t-SNE] Computed conditional probabilities for sample 14000 / 41188
[t-SNE] Computed conditional probabilities for sample 15000 / 41188
[t-SNE] Computed conditional probabilities for sample 16000 / 41188
[t-SNE] Computed conditional probabilities for sample 17000 / 41188
[t-SNE] Computed conditional probabilities for sample 18000 / 41188
[t-SNE] Computed conditional probabilities for sample 19000 / 41188
[t-SNE] Computed conditional probabilities for sample 20000 / 41188
[t-SNE] Computed conditional probabilities for sample 21000 / 41188
[t-SNE] Computed conditional probabilities for sample 22000 / 41188
[t-SNE] Computed conditional probabilities for sample 23000 / 41188
[t-SNE] Computed conditional probabilities for sample 24000 / 41188
[t-SNE] Computed conditional probabilities for sample 25000 / 41188
[t-SNE] Computed conditional probabilities for sample 26000 / 41188
[t-SNE] Computed conditional probabilities for sample 27000 / 41188
[t-SNE] Computed conditional probabilities for sample 28000 / 41188
[t-SNE] Computed conditional probabilities for sample 29000 / 41188
[t-SNE] Computed conditional probabilities for sample 30000 / 41188
[t-SNE] Computed conditional probabilities for sample 31000 / 41188
[t-SNE] Computed conditional probabilities for sample 32000 / 41188
[t-SNE] Computed conditional probabilities for sample 33000 / 41188
[t-SNE] Computed conditional probabilities for sample 34000 / 41188
[t-SNE] Computed conditional probabilities for sample 35000 / 41188
[t-SNE] Computed conditional probabilities for sample 36000 / 41188
[t-SNE] Computed conditional probabilities for sample 37000 / 41188
[t-SNE] Computed conditional probabilities for sample 38000 / 41188
[t-SNE] Computed conditional probabilities for sample 39000 / 41188
[t-SNE] Computed conditional probabilities for sample 40000 / 41188
[t-SNE] Computed conditional probabilities for sample 41000 / 41188
[t-SNE] Computed conditional probabilities for sample 41188 / 41188
[t-SNE] Mean sigma: 2.229839
[t-SNE] KL divergence after 250 iterations with early exaggeration: 84.140144
[t-SNE] KL divergence after 251 iterations: 179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.000000
fig = plt.figure(figsize=(10,6))
ax = fig.add_subplot(111, projection='3d')
ax.set_zlabel("x_composite_3_using_tSNE")
# Plotting the compressed data points
ax.scatter(data[:, 0], data[:, 1], zs=data[:, 2], s=3, lw=1, label="inliers",c="green")
# Plot x(s) for the ground truth outliers
out_index = [i for i in outlier_index if i <= 41188]
ax.scatter(data[out_index,0],data[out_index,1], data[out_index,2], lw=2, s=60,
marker="x", c="red", label="outliers")
ax.legend()
plt.show()
df_bank.columns
Index(['age', 'job=housemaid', 'job=services', 'job=admin.', 'job=blue-collar',
'job=technician', 'job=retired', 'job=management', 'job=unemployed',
'job=self-employed', 'job=unknown', 'job=entrepreneur', 'job=student',
'marital=married', 'marital=single', 'marital=divorced',
'marital=unknown', 'education=basic.4y', 'education=high.school',
'education=basic.6y', 'education=basic.9y',
'education=professional.course', 'education=unknown',
'education=university.degree', 'education=illiterate', 'default=0',
'default=unknown', 'default=1', 'housing=0', 'housing=1',
'housing=unknown', 'loan=0', 'loan=1', 'loan=unknown',
'contact=cellular', 'month=may', 'month=jun', 'month=jul', 'month=aug',
'month=oct', 'month=nov', 'month=dec', 'month=mar', 'month=apr',
'month=sep', 'day_of_week=mon', 'day_of_week=tue', 'day_of_week=wed',
'day_of_week=thu', 'day_of_week=fri', 'duration', 'campaign', 'pdays',
'previous', 'poutcome=nonexistent', 'poutcome=failure',
'poutcome=success', 'emp.var.rate', 'cons.price.idx', 'cons.conf.idx',
'euribor3m', 'nr.employed', 'category'],
dtype='object')
df_bank_part1 = df_bank[[ 'default=1', 'housing=0', 'housing=1',
'housing=unknown', 'loan=0', 'loan=1', 'loan=unknown',
'contact=cellular', 'duration', 'campaign', 'pdays',
'previous', 'poutcome=nonexistent', 'poutcome=failure',
'poutcome=success', 'emp.var.rate', 'cons.price.idx', 'cons.conf.idx',
'euribor3m', 'nr.employed', 'category']]
plt.figure(figsize=(15,15))
sns.heatmap(df_bank_part1.corr().round(2), annot=True, cmap='YlGnBu')
#plt.show()
<Axes: >
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import tensorflow as tf
from sklearn.metrics import accuracy_score, precision_score, recall_score
from sklearn.model_selection import train_test_split
from tensorflow.keras import layers, losses
from tensorflow.keras.datasets import fashion_mnist
from tensorflow.keras.models import Model
df_values = df_bank.values
# The last element contains the labels
labels = df_values[:, -1]
# The other data points are the features
data = df_values[:, 0:-1]
train_data, test_data, train_labels, test_labels = train_test_split(data, labels, test_size=0.2, random_state=21)
print(sum(labels==1))
print(sum(labels==0))
4640
36548
Rescale the data into the range 0 to 1
Convert it to tensorflow data, 32 bit float
Tensor flow has it’s own data types- storage control
Note the scaling uisng only the range of the train data, not test data
min_val = tf.reduce_min(train_data)
max_val = tf.reduce_max(train_data)
train_data = (train_data - min_val) / (max_val - min_val)
test_data = (test_data - min_val) / (max_val - min_val)
train_data = tf.cast(train_data, tf.float32)
test_data = tf.cast(test_data, tf.float32)
Split into normal and anomalous data sets
train_labels = train_labels.astype(bool)
test_labels = test_labels.astype(bool)
normal_train_data = train_data[train_labels]
normal_test_data = test_data[test_labels]
anomalous_train_data = train_data[~train_labels]
anomalous_test_data = test_data[~test_labels]
Plot a couple of normal and anomalous ECG patterns
#change hard encoded number to reference the amount of columns
plt.grid()
plt.plot(np.arange(62), normal_train_data[0])
plt.title("Normal Data")
plt.show()
plt.grid()
plt.plot(np.arange(62), anomalous_train_data[0])
plt.title("Anomalous Data")
plt.show()
#decoders last layer needs to be numbver of columns
class AnomalyDetector(Model):
def __init__(self):
super(AnomalyDetector, self).__init__()
self.encoder = tf.keras.Sequential([
layers.Dense(32, activation="relu"),
layers.Dense(16, activation="relu"),
layers.Dense(8, activation="relu")])
self.decoder = tf.keras.Sequential([
layers.Dense(16, activation="relu"),
layers.Dense(32, activation="relu"),
layers.Dense(62, activation="sigmoid")])
def call(self, x):
encoded = self.encoder(x)
decoded = self.decoder(encoded)
return decoded
autoencoder = AnomalyDetector()
autoencoder.compile(optimizer='adam', loss='mae')
history = autoencoder.fit(normal_train_data, normal_train_data,
epochs=20,
batch_size=512,
validation_data=(test_data, test_data),
shuffle=True)
Epoch 1/20
8/8 [==============================] - 7s 32ms/step - loss: 0.4746 - val_loss: 0.4734
Epoch 2/20
8/8 [==============================] - 0s 11ms/step - loss: 0.4692 - val_loss: 0.4651
Epoch 3/20
8/8 [==============================] - 0s 10ms/step - loss: 0.4590 - val_loss: 0.4479
Epoch 4/20
8/8 [==============================] - 0s 10ms/step - loss: 0.4375 - val_loss: 0.4138
Epoch 5/20
8/8 [==============================] - 0s 10ms/step - loss: 0.3949 - val_loss: 0.3528
Epoch 6/20
8/8 [==============================] - 0s 11ms/step - loss: 0.3245 - val_loss: 0.2732
Epoch 7/20
8/8 [==============================] - 0s 11ms/step - loss: 0.2456 - val_loss: 0.2091
Epoch 8/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1917 - val_loss: 0.1733
Epoch 9/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1639 - val_loss: 0.1551
Epoch 10/20
8/8 [==============================] - 0s 11ms/step - loss: 0.1503 - val_loss: 0.1500
Epoch 11/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1466 - val_loss: 0.1483
Epoch 12/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1456 - val_loss: 0.1478
Epoch 13/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1452 - val_loss: 0.1474
Epoch 14/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1447 - val_loss: 0.1454
Epoch 15/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1444 - val_loss: 0.1453
Epoch 16/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1442 - val_loss: 0.1454
Epoch 17/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1438 - val_loss: 0.1443
Epoch 18/20
8/8 [==============================] - 0s 11ms/step - loss: 0.1433 - val_loss: 0.1442
Epoch 19/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1427 - val_loss: 0.1443
Epoch 20/20
8/8 [==============================] - 0s 10ms/step - loss: 0.1422 - val_loss: 0.1426
plt.plot(history.history["loss"], label="Training Loss")
plt.plot(history.history["val_loss"], label="Validation Loss")
plt.legend()
<matplotlib.legend.Legend at 0x7f1594f9f2b0>
encoded_data = autoencoder.encoder(normal_test_data).numpy()
decoded_data = autoencoder.decoder(encoded_data).numpy()
plt.plot(normal_test_data[0], 'b')
plt.plot(decoded_data[0], 'r')
plt.fill_between(np.arange(62), decoded_data[0], normal_test_data[0], color='lightcoral')
plt.legend(labels=["Input", "Reconstruction", "Error"])
plt.show()
encoded_data = autoencoder.encoder(anomalous_test_data).numpy()
decoded_data = autoencoder.decoder(encoded_data).numpy()
plt.plot(anomalous_test_data[0], 'b')
plt.plot(decoded_data[0], 'r')
plt.fill_between(np.arange(62), decoded_data[0], anomalous_test_data[0], color='lightcoral')
plt.legend(labels=["Input", "Reconstruction", "Error"])
plt.show()
reconstructions = autoencoder.predict(normal_train_data)
train_loss = tf.keras.losses.mae(reconstructions, normal_train_data)
plt.hist(train_loss[None,:], bins=50)
plt.xlabel("Train loss")
plt.ylabel("No of examples")
plt.show()
118/118 [==============================] - 0s 1ms/step
threshold = np.mean(train_loss) + np.std(train_loss)
print("Threshold: ", threshold)
Threshold: 0.17724909
reconstructions = autoencoder.predict(anomalous_test_data)
test_loss = tf.keras.losses.mae(reconstructions, anomalous_test_data)
plt.hist(test_loss[None, :], bins=50)
plt.xlabel("Test loss")
plt.ylabel("No of examples")
plt.show()
230/230 [==============================] - 0s 1ms/step
plt.hist(train_loss[None,:], bins=50,color="blue")
plt.hist(test_loss[None, :], bins=50,color='red')
plt.plot([threshold,threshold],[0,350],linestyle=":")
[<matplotlib.lines.Line2D at 0x7f1120282ef0>]
def predict(model, data, threshold):
reconstructions = model(data)
loss = tf.keras.losses.mae(reconstructions, data)
return tf.math.less(loss, threshold)
def print_stats(predictions, labels):
print("Accuracy = {}".format(accuracy_score(labels, predictions)))
print("Precision = {}".format(precision_score(labels, predictions)))
print("Recall = {}".format(recall_score(labels, predictions)))
preds = predict(autoencoder, test_data, threshold)
print_stats(preds, test_labels)
Accuracy = 0.2391357125515902
Precision = 0.10843900306077832
Recall = 0.8312849162011173
from sklearn.metrics import confusion_matrix
sns.set_context("poster", font_scale = .75)
cm = confusion_matrix(test_labels, preds)
fig, ax = plt.subplots(figsize=(6, 5))
ax.imshow(cm)
ax.grid(False)
ax.xaxis.set(ticks=(0, 1), ticklabels=('Predicted 0s', 'Predicted 1s'))
ax.yaxis.set(ticks=(0, 1), ticklabels=('Actual 0s', 'Actual 1s'))
ax.set_ylim(1.5, -0.5)
for i in range(2):
for j in range(2):
ax.text(j, i, cm[i, j], ha='center', va='center', color='red')
plt.show()
