import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
import matplotlib as mpl
import pandas as pd
mpl.rcParams["font.family"] = "Segoe UI Emoji"
text1 = """
🧁🧯 🤇🥌🦟 🤇🤫🥌😼🤫 🤇🤟 🦘🦊🥾
🤯🤯🧛😎😼 🥌🥦🤇🤇🦟😒 🧁🧛🧁🦊🧯 🦘😎🦘🦟🤯🦺 🥾🥾🥑🥑🥌
🤟🧁🥦 🥦😼🦊🥾🦺🤇 🧯🦟🦘🤶🦺🦟🥷🧯 😎🦟🦊🤟
🧁😎🦺🦊🤫🥌🧯 🦺😎 🦘😼🥦😎🥑 🤯🦘🦘🦺🦺 😼🤟🥾🤯🥾🤶🥦🦘
🦟😎🤟🦺😼🤶🤟 🧁🦟😎🤯🧛🤇🤟 🧯🤟 😎🦘🥌🧁🦘🤶🦺🦊 🤶🤶🤫🤟🦺
🤇🥌😎🥌🤟🤇 🥦🦺🦘🤇🥾🥷 🤯🦘🦺😒 🧯🦟🦊 🤇🧯🥌 🦟🤇🧛🧛🤟🤯🧛
🤫🦟 🥦🤶🥑🤇🥑 🥦🦊🥦 😼🤇🦟😎🥑 🧁🦊🤯🤫🦘🥾🦊
😎😼 🧛😎🧛🦊🤇🦊🦺🥷 🤯🦘🤶🧁🧁🧁🥌 🥷🤶🦊🦊😒🧛 😼😎🤫🧁"""
text2 = """
🦺🤶🦺🦟 🦘🧯 🧛🥑🤯 🤶🥌🤇🥷😒
🧁🦘🥾 😎🤯 🤫🧁🤟🦺🤟🧯 🦺🤟🦟🤫😼
🤶😒🦺🥾 🧁🤶🥷🧛🧛🤫🧛 🤇🥾🤫🤇😒🦟🦟 🤇🥦🥷🧁🥑
😎🧯🦘🦟 🧛🦟🤇🧛🤫 😼🤟🦘 😎🦟🤯
🥷🤯🤟🧯🧁 🧁🤶🧁🧛🦘 🧁🤶🧯🥑🤯😒 🥦🥾🤶🤫😎 😎😎🤯😼🤶🧁🥷🦟
🧛😼🤟 🥑🤇🥾 🥾😒🤫 🧁😎🧛🤟🦺🥑🤯🤇 🦟🧯🥷 🥾🤇🥾
🥦🧁🦊😎🧁😒 😎🤇😼🤯🦊🥾🥷 😎🥌🤯🦟🧛🧁🧛 🦘🧁 😎😒🦊🧛 🥾🥾🤶🤯
😎😒🧛🤯🧁 🤟🦺🤯🧛 🦊🤶🥾🥑🥷🦘🦺 🦟😼🦘 🦘🤶😼🤫 🦟🦘😼🤯🤯"""
text3 = """
🧯🧛🦟🤫🥦🤇🦟 😎🥑🤟🥷🧯🤫🤫 🥷🧯🦺🦺 🧛🥑🥾🦺🧁
🤇🦟🧁🥌🤇🥾🤶🥑 🥾🤫 😼🥑🦺 🤶🦺🦟 🤫🦺 🥦😼🧯🤫🦺🤶
🤟🥾🦺🤇 🤯🥦🤫🦟🤯🤟🤟🤶 🧛🥦🧁 🦘🧯🥾🧛🧯 🥑🤶😼
😎😎🥾🧛🧛 🦘🥑🧁😼🥌🤫🤟 🤟🤇🤶🦊🥾 🤫😼🤫🥾🦟🧁 🤇🦘🦺🧛😼 🥾🤇🥌🧁🤫🥷🦟🤫
🥑🧁🧁🤫🥑🦟🤟🥑 🧛🥌🥾 😼😼🤶🤟🦘 🤟🦺🤇🦘🧛🤯🥌 🧁🦟🤯🥾
🦘🥑 😼🥦🦟🧛🥑🧯🥌 🤇😼 😼🤫
🥾🦊🥷 🦘🤟 🦊🥑🤯🤫🥌🧛 🤇🤫😎🦺🥌 🥾🥦🥑🦊🧁 🥌😼😎🤫🤯
🥦🤶🧛🤟😒🦟🧁🧯 🤇🤫🧛🥦🦺🤟 🥦🤶🥑🦟 🦺🧛🦘🥦🧯🦺"""
text4 = """
😎🧁🥦🦊🦟🥦 🤶🧯🥌🧯🤟 🧯🦺🧯😒🧁🧛 🦊🧁🥑🤫🤶 🤶🧁🦺🦊😎🤫🧛🥷 😒🤇🥌🤯🤇🤶🤶🥾
🦊😼🦟🦘😎🧛🤟 😎🤇🤯🧛🤇🦘🦘😼 🥑🥷🥑🤇🤟🤇 🦊🥑🥌😼🦘🤇 😼🤟 🦺🦟🥷😒🥦🤯
🤇🦟 🧛🤟🥾🤯🥦 🥦😒😎🥑🥷🤟🥾 🥑🤶 🦺🤫🥷😒🦺🤟 🥦😒🧛🧯🤇🥑🤶🥾
😎🤟🦺😒🥾🤇🤯🤶 🥦🦟🥦🤟🤫🤯🥑🤇 🤟🦊🥾🤟🤶🧯 😼🤯😒 🥦🤇🧁
😒🤟🥌🥌🤫🧛😼 🤯🦟🥑🤇🥑 🥑🦟😎😼😎 🦘🦟🥦🤇🦘
🤯😎🥦🦊😼😎🤶🤇 😼🤯🤯😎🥾😼🥷 🤯🥑🦟😼 🥷😎🤇🥌 🦺🦺🦺🥌🦘🧛🤫🤇
🥷🧁🥦😎 🧁🤇😒🦊🤯🤯😎😼 🧯🧁🥦 😎🤯 🦟🤫🥑🤟🤫🦟 😼🧁🦺😒😒🦺🤫🥦
🧛🥦🦟😼😒😒🦘 🤇🥾 🥌🥦🧛🤯🤶 🦟🥷🤇🥌😒🤶 🦟🤯😼😼"""
text5 = """
🥌🦊🥾🦊🧁🧯🧛🤯 🧛😎🦟🥌🦘🥾🤯 😎🤶🧁🥌🦘🤇 🧛🦟🤯 🦊🦘🤶🦘🦊🥌 🥷🦊🧛
🧯😒🤫 😼🥌🧛🥾😼😎🤶 🧁🤫🧛🥾🤫 🦊🦟🦘🤶🥌😼
🧛🦊🤯🥾 🥑🦟🥑🤇😼 😒🦟 🦘🧛😎 🤟😼
😒🥾🤶😒🥾 🤇🦘 🥾😼 🥦🦊🥌🦘🦟
🤶🦘🦟 🧁🧯 🤫🤟😒😒🥦 🥦🧁🥌🦘😼🤟🤶
🤫🥑🦘🤇🥷🧁 🥑🧁 🤶🧛😒 🥷🥦
🧯🦊🧛 😼🤯🥑🤟 🧯😼🧯🦊😒🥦 🥾😒🦘🤫🦺🤟🧯 🧛😎🧛🧛😼🤯 🧁😒🦺🦺😒🦺
🧯😼🤯🧁🥌🤇🧛🦘 🧯🤯 😒🤟😼🥾🤟🤫 😎🤫"""
sequence = "😎😎🥦🦊🦺🥑🤇🧛🥦🦟🦘😼🥾🥦🤇🥌🦺🤶🦊😎🦟🥷🥷🥌😒🥑🦟🦺🤶🤶🥾🥾😼🥑😎🤫😎🦘🥷🦘🤯🤯🦟🤟🤯😎🥷🦊🥾🦟"
[Doku]def clean_text(text):
"""
**TODO**:
Clean the text by removing all white spaces and new line character (\\\\n)
:param text: The text to clean
:return: The same text witout white spaces and new line characters
"""
pass
[Doku]def character_propabilities(text, all_chars):
"""
**TODO**:
Given a text, calculate the empirical observation propability of
all characters from the "all_chars" list.
The observation propability for character c
is given as the number of occurrences of that character divided by the total
number of characters in the string.
:param text: The text for which character observation propabilities are to be calculated
:param all_chars: A set of unique characters. The propability for each such character is to be calcualted.
:return: A dictionary mapping all characters within the all_chars parameter to its respective observation propability.
"""
pass
[Doku]def get_emmision_propabilities(all_texts):
"""
**TODO**:
Return the emmision propabilities for each character in all the sets.
This is essentially a list of dictionaries provided by :py:meth:`forward.character_propabilities`
* Join all the texts together and clean the result (call :py:meth:`clean_text`).
* Convert the joined string into a set to retrieve the unique characters (call `set <https://www.w3schools.com/python/python_sets.asp>`_)
* Return a list of emmision propabilities dictionaries for all the texts (call :py:meth:`forward.character_propabilities`)
:param all_texts: A list of texts
:return: A list of dictionaries with emmision propabilities for each text
"""
# TODO: Join all texts and clean them
# TODO: Get a unique list of all characters across all five texts
# TODO: Now get the character emmision propabilities for each text
pass
[Doku]def get_initial_alpha():
"""
**TODO**:
Return the initial alpha vector for the forward algorithm.
Hint: In the beginning, all states are equally likely
:return: np.array of shape 5x1 with the initial (equally likely) alpha values.
"""
# In the begining, we don´t know which text our colleague choose
# to start with, so all texts are equally likely
pass
[Doku]def get_state_transition_matrix():
"""
**TODO**:
Return the state transition matrix for the forward algorithm.
Hint: With 90% chance the state stays the same while the remaining 10% shall be equally divided between the four other states.
:return: np.array of shape 5x5 with the correct state transition propabilities
"""
pass
[Doku]def forward(alpha, character, state_transition_matrix, emmision_propabilities):
"""
**TODO**: Implement one step of the forward algorithm.
* Given the past alpha-values and the newly read character, use the state_transition_matrix
to first predict the new state propabilities (new alpha values) according to the script.
* Then multiply the state propabilities with the emmision propabilities of the observed character
for each alphabet to retrieve the new alpha values.
* Normalize the alpha vector after each step by diving by its sum. This helps to achieve numerically more stable results
and allows for better interpretation of the results.
:param alpha: np.array of shape (5,1) holding the past alpha values
:param character: Observed character in this step
:param state_transition_matrix: np.array of shape (5,5) holding the state transition propabilities
:param emmision_propabilities: List of dictionaries holding the character emmision propabilities for each alphabet.
:return: New alpha-vector after state transition and observation update (np.array of shape 5,1)
"""
# TODO: Implement state transition and update the alpha vector accordingly
# TODO: Retrieve symbol emmision propabilties for the given character and update the alpha vector
# TODO: Normalize alpha for better visualization (divide by sum)
# TODO: Return alpha
pass
if __name__ == "__main__":
# Get initial alpha values
alpha = get_initial_alpha()
# Estimate the emmision propabilities for the five texts
emmision_propabilities = get_emmision_propabilities(
[text1, text2, text3, text4, text5]
)
# Build the state transition matrix
state_transition_matrix = get_state_transition_matrix()
alpha_matrix = np.zeros((50, 5)) # shape: (T, num_states)
# Clean the sequence
sequence = clean_text(sequence)
# Iterate over whole sequence
for t, character in enumerate(sequence):
# Run forward algorithm
alpha = forward(
alpha, character, state_transition_matrix, emmision_propabilities
)
# Store current alpha for later
alpha_matrix[t, :] = alpha
# Visualize alpha vectors as heat map
states = ["Text 1", "Text 2", "Text 3", "Text 4", "Text 5"]
df = pd.DataFrame(
alpha_matrix.T, index=states, columns=[f"t{t+1}" for t in range(len(sequence))]
)
plt.ioff()
plt.figure(figsize=(10, 4))
sns.heatmap(df, annot=False, cmap="YlGnBu", cbar=True)
plt.title("Alpha-Werte pro Zustand über die Zeit")
plt.xlabel("Zeit (Position in Sequenz)")
plt.ylabel("Zustand")
plt.tight_layout()
plt.show()