### End-to-End Example with TF-IDF Similarity

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

Demonstrates the full workflow of TruthFinder, including TF-IDF-based similarity for handling variations in fact names. Requires setup with pandas, numpy, and scikit-learn.

```python
import pandas as pd
import numpy as np
from numpy.linalg import norm
from sklearn.feature_extraction.text import TfidfVectorizer
from truthdiscovery import TruthFinder

# Input data with variations in naming
dataframe = pd.DataFrame([
    ["a", "Einstein", "Special relativity"],
    ["a", "Newton", "Universal gravitation"],
    ["b", "Albert Einstein", "Special relativity"],  # Same as "Einstein"
    ["b", "Galileo Galilei", "Heliocentrism"],
    ["c", "Newton", "Special relativity"],
    ["c", "Galilei", "Universal gravitation"],       # Similar to "Galileo Galilei"
    ["c", "Einstein", "Heliocentrism"]
], columns=["website", "fact", "object"])

# Build TF-IDF vectorizer on all facts
vectorizer = TfidfVectorizer(min_df=1)
vectorizer.fit(dataframe["fact"])

def similarity(w1, w2):
    """Compute cosine similarity between two text strings"""
    V = vectorizer.transform([w1, w2])
    v1, v2 = np.asarray(V.todense())
    return np.dot(v1, v2) / (norm(v1) * norm(v2))

def implication(f1, f2):
    """Implication function: how much f1 supports f2"""
    return similarity(f1.lower(), f2.lower())

# Create and train finder
finder = TruthFinder(implication, dampening_factor=0.8, influence_related=0.6)

print("Initial state:")
print(dataframe)

# Train the model
result = finder.train(dataframe)

print("\nEstimation result:")
print(result)

# Analyze results: identify most trustworthy sources
trustworthiness = result.drop_duplicates("website")[["website", "trustworthiness"]]
print("\nSource trustworthiness ranking:")
print(trustworthiness.sort_values("trustworthiness", ascending=False))

# Identify highest confidence facts per object
for obj in result["object"].unique():
    obj_facts = result[result["object"] == obj]
    best_fact = obj_facts.loc[obj_facts["fact_confidence"].idxmax()]
    print(f"\n{obj}: {best_fact['fact']} (confidence: {best_fact['fact_confidence']:.4f})")
```

--------------------------------

### Setup Data and Run TruthFinder

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

This snippet demonstrates how to set up a pandas DataFrame with fact confidence values and then use the TruthFinder to update website trustworthiness. Ensure the TruthFinder class and pandas are imported.

```python
import pandas as pd
from truthdiscovery import TruthFinder

# Setup data with known fact confidence values
dataframe = pd.DataFrame([
    ["site_a", "Einstein", "Special relativity"],
    ["site_a", "Newton", "Universal gravitation"],
    ["site_b", "Einstein", "Special relativity"],
    ["site_b", "Galilei", "Heliocentrism"],
    ["site_c", "Newton", "Special relativity"],
    ["site_c", "Galilei", "Universal gravitation"],
    ["site_c", "Einstein", "Heliocentrism"]
], columns=["website", "fact", "object"])

# Pre-set fact confidence scores (simulating after confidence calculation)
dataframe["trustworthiness"] = 0.9
dataframe["fact_confidence"] = [0.9, 0.8, 0.9, 0.7, 0.3, 0.4, 0.2]

def implication(f1, f2):
    return 1

finder = TruthFinder(implication, dampening_factor=0.3, influence_related=0.5)

# Update trustworthiness based on fact confidence
# Trustworthiness = mean(fact_confidence) for all facts from that source
result = finder.update_website_trustworthiness(dataframe.copy())

# Check results
for site in ["site_a", "site_b", "site_c"]:
    trust = result[result["website"] == site]["trustworthiness"].iloc[0]
    facts = result[result["website"] == site]["fact_confidence"].values
    print(f"{site}: trustworthiness={trust:.2f} (mean of {facts})")
```

--------------------------------

### Updating Website Trustworthiness with update_website_trustworthiness()

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

Recalculates website trustworthiness based on the average confidence of facts provided by each source. Requires pandas, numpy, and TruthFinder.

```python
import pandas as pd
import numpy as np
from truthdiscovery import TruthFinder

```

--------------------------------

### Internal Methods: calculate_confidence() and adjust_confidence()

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

Illustrates the internal confidence calculation methods. `calculate_confidence` computes initial scores based on source trustworthiness, and `adjust_confidence` refines them by considering related facts. Requires pandas, numpy, and math.

```python
import pandas as pd
import numpy as np
import math
from truthdiscovery import TruthFinder

# Setup test data with pre-initialized trustworthiness
dataframe = pd.DataFrame([
    ["a", "Einstein", "Special relativity"],
    ["b", "Einstein", "Special relativity"],
    ["c", "Newton", "Special relativity"],
], columns=["website", "fact", "object"])

# Initialize with known trustworthiness values
dataframe["trustworthiness"] = [0.9, 0.9, 0.5]
dataframe["fact_confidence"] = [0.0, 0.0, 0.0]

def implication(f1, f2):
    return 1  # All facts equally support each other

finder = TruthFinder(implication, dampening_factor=0.3, influence_related=0.5)

# Step 1: Calculate initial confidence from trustworthiness
# Uses formula: confidence = sum(-log(1 - trustworthiness)) for all sources claiming fact
df = finder.calculate_confidence(dataframe.copy())
print("After calculate_confidence:")
print(df[["fact", "fact_confidence"]])
# "Einstein" claimed by a,b (trust=0.9): conf = -2*log(0.1) ≈ 4.605
# "Newton" claimed by c (trust=0.5): conf = -log(0.5) ≈ 0.693

# Step 2: Adjust confidence based on related facts
df = finder.adjust_confidence(df)
print("\nAfter adjust_confidence (related facts boost each other):")
print(df[["fact", "fact_confidence"]])

# Step 3: Apply sigmoid dampening to normalize scores
df = finder.compute_fact_confidence(df)
print("\nAfter compute_fact_confidence (sigmoid normalization):")
print(df[["fact", "fact_confidence"]])
```

--------------------------------

### Initialize and Use TruthFinder

Source: https://github.com/ishitatakeshi/truthfinder/blob/master/README.md

Initializes the TruthFinder model with a custom implication function and parameters for dampening factor and influence of related facts. This is the core step before running the truth discovery process.

```python
finder = TruthFinder(implication, dampening_factor=0.8, influence_related=0.6)
```

--------------------------------

### Train TruthFinder with Sample Data

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

Trains the TruthFinder model using a pandas DataFrame containing conflicting information. This method iteratively computes trustworthiness and confidence scores until convergence or maximum iterations are reached. The output DataFrame includes calculated 'trustworthiness' and 'fact_confidence' scores.

```python
import pandas as pd
from truthdiscovery import TruthFinder

# Prepare input data: conflicting information about scientific discoveries
# Columns: website (source), fact (claim), object (topic)
dataframe = pd.DataFrame([
    ["site_a", "Einstein", "Special relativity"],
    ["site_a", "Newton", "Universal gravitation"],
    ["site_b", "Albert Einstein", "Special relativity"],
    ["site_b", "Galileo Galilei", "Heliocentrism"],
    ["site_c", "Newton", "Special relativity"],      # Wrong claim
    ["site_c", "Galilei", "Universal gravitation"],  # Wrong claim
    ["site_c", "Einstein", "Heliocentrism"]          # Wrong claim
], columns=["website", "fact", "object"])

# Simple implication function (no similarity consideration)
def simple_implication(f1, f2):
    return 1 if f1.lower() == f2.lower() else 0

finder = TruthFinder(simple_implication, dampening_factor=0.3, influence_related=0.5)

# Run training
# max_iterations: maximum iterations before stopping (default: 200)
# threshold: convergence threshold for trustworthiness change (default: 1e-6)
# initial_trustworthiness: starting trust score for all sources (default: 0.9)
result = finder.train(
    dataframe,
    max_iterations=200,
    threshold=1e-6,
    initial_trustworthiness=0.9
)

# Output includes two new columns:
# - trustworthiness: reliability score of each website
# - fact_confidence: confidence score of each fact
print(result[["website", "trustworthiness", "fact", "object", "fact_confidence"]])

# Expected output shows site_c with lower trustworthiness due to incorrect claims:
#   website  trustworthiness             fact                 object  fact_confidence
# 0  site_a         0.862090         Einstein     Special relativity         0.894279
# 1  site_a         0.862090           Newton  Universal gravitation         0.829901
# 2  site_b         0.862090  Albert Einstein     Special relativity         0.894279
# 3  site_b         0.862090  Galileo Galilei          Heliocentrism         0.829901
# 4  site_c         0.754878           Newton     Special relativity         0.754878

```

--------------------------------

### Unit Test for Trustworthiness Update

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

This unit test verifies that the trustworthiness of a website is correctly calculated as the average of its fact confidences. It uses numpy testing utilities for assertions. Ensure pandas, numpy, unittest, and TruthFinder are imported.

```python
import math
import unittest
import numpy as np
from numpy.testing import assert_array_equal, assert_array_almost_equal
import pandas as pd
from truthdiscovery import TruthFinder

class TestTruthFinder(unittest.TestCase):
    def setUp(self):
        # Use constant implication for predictable testing
        def implication(f1, f2):
            return 1

        self.dampening_factor = 0.1
        self.influence_related = 0.5
        self.finder = TruthFinder(
            implication,
            dampening_factor=self.dampening_factor,
            influence_related=self.influence_related
        )

        self.dataframe = pd.DataFrame([
            ["a", "Einstein", "Special relativity"],
            ["a", "Newton", "Universal gravitation"],
            ["b", "Einstein", "Special relativity"],
            ["b", "Galilei", "Heliocentrism"],
            ["c", "Newton", "Special relativity"],
            ["c", "Galilei", "Universal gravitation"],
            ["c", "Einstein", "Heliocentrism"]
        ], columns=["website", "fact", "object"])

        self.dataframe["trustworthiness"] = 0.9
        self.dataframe["fact_confidence"] = [0.5, 0.3, 0.6, 0.8, 0.1, 0.0, 0.8]

    def test_trustworthiness_update(self):
        """Verify trustworthiness is average of fact confidences"""
        df = self.finder.update_website_trustworthiness(self.dataframe.copy())

        # site_a: mean([0.5, 0.3]) = 0.4
        assert_array_equal(
            df.loc[df["website"] == "a", "trustworthiness"], 0.4
        )
        # site_b: mean([0.6, 0.8]) = 0.7
        assert_array_equal(
            df.loc[df["website"] == "b", "trustworthiness"], 0.7
        )
        # site_c: mean([0.1, 0.0, 0.8]) = 0.3
        assert_array_equal(
            df.loc[df["website"] == "c", "trustworthiness"], 0.3
        )

if __name__ == "__main__":
    unittest.main()
```

--------------------------------

### Initialize TruthFinder with Custom Implication

Source: https://context7.com/ishitatakeshi/truthfinder/llms.txt

Initializes the TruthFinder class with a custom implication function based on TF-IDF similarity and sets hyperparameters for convergence. The implication function defines how related facts influence each other's confidence scores.

```python
import pandas as pd
import numpy as np
from numpy.linalg import norm
from sklearn.feature_extraction.text import TfidfVectorizer
from truthdiscovery import TruthFinder

# Define implication function using TF-IDF similarity
vectorizer = TfidfVectorizer(min_df=1)
facts = ["Einstein", "Albert Einstein", "Newton", "Galilei", "Galileo Galilei"]
vectorizer.fit(facts)

def similarity(w1, w2):
    V = vectorizer.transform([w1, w2])
    v1, v2 = np.asarray(V.todense())
    return np.dot(v1, v2) / (norm(v1) * norm(v2))

def implication(f1, f2):
    """Returns implication score from f1 to f2, range [-1, 1]"""
    return similarity(f1.lower(), f2.lower())

# Initialize TruthFinder
# dampening_factor (gamma): controls convergence speed, must be in (0, 1)
# influence_related (rho): weight for related facts' influence, must be in [0, 1]
finder = TruthFinder(
    implication=implication,
    dampening_factor=0.8,  # Higher value = faster convergence
    influence_related=0.6   # Higher value = more influence from related facts
)
```

--------------------------------

### Create Pandas DataFrame for TRUTHFINDER

Source: https://github.com/ishitatakeshi/truthfinder/blob/master/README.md

Represents the input data for TRUTHFINDER, where each row contains information about a website, a fact, and the object it pertains to. Ensure the DataFrame columns match 'website', 'fact', and 'object'.

```python
dataframe = pd.DataFrame([
        ["a", "Einstein", "Special relativity"],
        ["a", "Newton", "Universal gravitation"],
        ["b", "Einstein", "Special relativity"],
        ["b", "Galilei", "Heliocentrism"],
        ["c", "Newton", "Special relativity"],
        ["c", "Galilei", "Universal gravitation"],
        ["c", "Einstein", "Heliocentrism"]
    ],
    columns=["website", "fact", "object"]
)
```

--------------------------------

### Define Implication Function using TF-IDF

Source: https://github.com/ishitatakeshi/truthfinder/blob/master/README.md

Defines the implication between facts based on their similarity, calculated using TF-IDF vectorization. This function is crucial for TRUTHFINDER to understand how facts support or conflict with each other. Requires 'TfidfVectorizer' and 'numpy'.

```python
vectorizer = TfidfVectorizer(min_df=1)
vectorizer.fit(dataframe["fact"])


def similarity(f1, f2):
    V = vectorizer.transform([f1.lower(), f2.lower()])
    v1, v2 = np.asarray(V.todense())
    return np.dot(v1, v2) / (norm(v1) * norm(v2)))

def implication(f1, f2):
    return similarity(f1, f2)
```

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