Use QuanticSVM with real data from Kaggle’s Titanic Dataset

Practical application of quantum-enhanced SVM to the titanic dataset: https://www.kaggle.com/c/titanic/data

# Author: Adrien Veres
# License: BSD (3-clause)

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
from sklearn.decomposition import PCA
from sklearn.impute import KNNImputer
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import balanced_accuracy_score
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import LabelEncoder, StandardScaler
from sklearn.svm import SVC

from pyriemann_qiskit.classification import QuanticSVM

print(__doc__)

Useful functions

def correlation_ratio(categories, measurements):
    fcat, _ = pd.factorize(categories)
    cat_num = np.max(fcat) + 1
    y_avg_array = np.zeros(cat_num)
    n_array = np.zeros(cat_num)
    for i in range(0, cat_num):
        cat_measures = measurements[np.argwhere(fcat == i).flatten()]
        n_array[i] = len(cat_measures)
        y_avg_array[i] = np.average(cat_measures)
    y_total_avg = np.sum(np.multiply(y_avg_array, n_array)) / np.sum(n_array)
    numerator = np.sum(
        np.multiply(n_array, np.power(np.subtract(y_avg_array, y_total_avg), 2))
    )
    denominator = np.sum(np.power(np.subtract(measurements, y_total_avg), 2))
    if numerator == 0:
        eta = 0.0
    else:
        eta = numerator / denominator
    return eta


def clean(data):
    # "Embarked" missing values replaced by U(unknown)
    data["embarked"].fillna("U", inplace=True)

    # "sibsp", "parch" missing values replaced by 0
    data["sibsp"].fillna(0, inplace=True)
    data["parch"].fillna(0, inplace=True)

    return data

Download data

# Skip Kaggle, download data publicly from Zenodo.
dataset = pd.read_csv("https://zenodo.org/record/5987761/files/titanic.csv")


# # *Data Dictionary*
# * Variable        Definition      Key
# * survival        Survival        0 = No, 1 = Yes
# * pclass  Ticket class    1 = 1st, 2 = 2nd, 3 = 3rd
# * sex     Sex
# * sibsp   # of siblings / spouses aboard the Titanic
# * parch   # of parents / children aboard the Titanic
# * embarked        Port of Embarkation     C = Cherbourg, Q = Queenstown, S = Southampton
#
# # Variable Notes
# **pclass:** A proxy for socio-economic status (SES)
# 1. * 1st = Upper
# 1. * 2nd = Middle
# 1. * 3rd = Lower
#
# **sibsp:** The dataset defines family relations in this way...
# 1. * Sibling = brother, sister, stepbrother, stepsister
# 1. * Spouse = husband, wife (mistresses and fiancés were ignored)
# **parch:** The dataset defines family relations in this way...
# 1. * Parent = mother, father
# 1. * Child = daughter, son, stepdaughter, stepson
# 1. * Some children travelled only with a nanny, therefore parch=0 for them.

Exploration

dataset.head()

# Compute dataset statistics
dataset.describe()

# Display missing values
print(dataset.isna().sum())
sns.heatmap(dataset.isna())

# Compute fill-ness
fill_rate = dataset.notnull().mean()
print(fill_rate)

print(dataset["pclass"].describe())
sns.displot(x="pclass", data=dataset)

print(dataset["sex"].describe())
sns.displot(x="sex", data=dataset)

print(dataset["embarked"].describe())
sns.displot(x="embarked", data=dataset)

sns.catplot(
    data=dataset,
    y="pclass",
    hue="survived",
    kind="count",
    palette="pastel",
    edgecolor=".6",
)

sns.boxplot(data=dataset, x="embarked", y="pclass", hue="survived")

sns.catplot(
    data=dataset,
    y="sibsp",
    hue="survived",
    kind="count",
    palette="pastel",
    edgecolor=".6",
)

sns.catplot(
    data=dataset,
    y="parch",
    hue="survived",
    kind="count",
    palette="pastel",
    edgecolor=".6",
)

sns.catplot(
    data=dataset,
    y="embarked",
    hue="survived",
    kind="count",
    palette="pastel",
    edgecolor=".6",
)

sns.catplot(
    data=dataset,
    y="sex",
    hue="survived",
    kind="count",
    palette="pastel",
    edgecolor=".6",
)

sns.catplot(
    data=dataset,
    y="pclass",
    hue="survived",
    kind="count",
    palette="pastel",
    edgecolor=".6",
)

Imputation with KNNs (Feature Engineering)

# Select appropriate features
features = dataset[["sex", "embarked", "pclass", "survived"]]

features.head()

# Compute the number of survivors/deceased persons
survived_counts = dataset["survived"].value_counts()
print(survived_counts)

# Survival rate is about **38.38%**

sns.countplot(x="survived", data=dataset)

# Histogram before imputation
dataset.hist(sharex=True, sharey=True)

# Select features to impute
cols_to_fill = ["pclass", "sibsp", "parch"]

# Imput
imputer = KNNImputer(n_neighbors=5)
dataset[cols_to_fill] = imputer.fit_transform(dataset[cols_to_fill])

print(dataset.head())

# Check missing values are now fulfilled
print(dataset.isna().sum())

# Histogram after imputation
dataset.hist(sharex=True, sharey=True)


# # Compute survival rate

sex_group = dataset.groupby(["sex"])["survived"].mean()

embarked_group = dataset.groupby(["embarked"])["survived"].mean()

class_group = dataset.groupby(["pclass"])["survived"].mean()

print("Survival rate by sex :\n", sex_group)
print("\nSurvival rate by embarkation point :\n", embarked_group)
print("\nSurvival rate by class :\n", class_group)

# Compute correlation matrix between Embarked & Class

# Label-encoding of "Embarked"
le = LabelEncoder()
embarked_encoded = le.fit_transform(dataset["embarked"])

R2 = np.corrcoef(embarked_encoded, dataset["pclass"])
print(R2)

Multivariate analysis

# # ANOVA Rule of thumb
correlation_ratio(features["sex"], features["survived"])

# Correlation should be weak
correlation_ratio(features["embarked"], features["survived"])

# Correlation should be average
correlation_ratio(features["pclass"], features["survived"])


# # PCA and correlation circle

# Select features
variables = ["pclass", "sibsp", "parch"]

X = dataset[variables].values

# Standard scaler
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Dimension reduction
pca = PCA(n_components=2)
principal_components = pca.fit_transform(X_scaled)
components_df = pd.DataFrame(data=principal_components, columns=["PC1", "PC2"])

# Add target
components_df["survived"] = dataset["survived"]

# Display correlation circle
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(1, 1, 1)
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.axhline(0, color="gray", lw=1)
ax.axvline(0, color="gray", lw=1)
ax.set_xlabel("PC1")
ax.set_ylabel("PC2")
for i, variable in enumerate(variables):
    ax.annotate(variable, (pca.components_[0, i], pca.components_[1, i]))
    ax.arrow(
        0,
        0,
        pca.components_[0, i],
        pca.components_[1, i],
        color="r",
        width=0.01,
        head_width=0.05,
    )
plt.show()

Classification

# Cleaning
dataset = clean(dataset)

# One-hot encoding
dataset = pd.get_dummies(dataset, columns=["sex", "embarked", "pclass"])

# train/test validation
# (the same for all classifiers - avoid biases in comparison)
X_train, X_test, y_train, y_test = train_test_split(
    dataset.drop("survived", axis=1),
    dataset["survived"],
    test_size=0.2,
    random_state=42,
)

# Logistic Regression
model = LogisticRegression()
model.fit(X_train, y_train)

y_pred = model.predict(X_test)

score = balanced_accuracy_score(y_test, y_pred)
print("Balanced accuracy LR:", score)

# linear SVC

# Use same train/test set as for logistic regression
model = SVC()
model.fit(X_train, y_train)

y_pred = model.predict(X_test)

score = balanced_accuracy_score(y_test, y_pred)
print("Balanced accuracy linear SVC:", score)

# SVC + RBF

model = SVC(kernel="rbf")
model.fit(X_train, y_train)

y_pred = model.predict(X_test)

score = balanced_accuracy_score(y_test, y_pred)
print("Balanced accuracy SVC+RBF:", score)


# SVM + quantum kernel

# Tackles type conversion issue with QuanticSVM
X_train2 = X_train.astype("float64")

# Use quantum=False for Ci/Cd optimization
# In general, accuracy is > 0.7 with quantum True
# (this is better then linear and rbf kernel)
model = QuanticSVM(quantum=False, pegasos=False)
model.fit(X_train2, y_train)

y_pred = model.predict(X_test)

score = balanced_accuracy_score(y_test, y_pred)
print("Balanced accuracy quantum SVC:", score)