Natural Language Processing - Relations Among Lexemes and Their Senses

 

Relations Among Lexemes and Their Senses

In the world of linguistics and natural language processing (NLP), the relationships among lexemes (the base forms of words) and their meanings (senses) play a critical role in understanding how words interact in language. Below, we explore four fundamental types of semantic relationships between lexemes and their senses: homonymy, polysemy, synonymy, and hyponymy.

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Homonymy: Same Form, Different Meanings

Definition: Homonymy occurs when two or more lexemes share the same spelling or pronunciation but have completely different, unrelated meanings. These lexemes are considered homonyms.

Types of Homonyms:

1. Homophones: Words that sound the same but have different spellings and meanings.
   Example: "flower" (a plant) vs. "flour" (a cooking ingredient).

2. Homographs: Words that are spelled the same but have different meanings and sometimes different pronunciations.
   Example: "lead" (to guide) vs. "lead" (a type of metal).

Impact on NLP and Search Engines: Homonymy can negatively affect precision in search queries. For instance, if a user searches for the word "bank" intending to find information about financial institutions, they may also receive documents about riverbanks due to the homonymy of the word.

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Polysemy: One Word, Multiple Related Meanings

Definition: Polysemy refers to the phenomenon where a single lexeme has multiple related senses or meanings. Unlike homonymy, polysemous meanings are semantically connected.

Example: The word "bank" can refer to:

• A financial institution: "I need to withdraw money from the bank."
• The side of a river: "We had a picnic on the riverbank."

Impact on NLP and Search Engines: Polysemy can reduce precision in search results. A query for "bank" might retrieve documents about both financial institutions and riverbanks, even if the user is only interested in one sense of the word.

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Synonymy: Different Words, Similar Meanings

Definition: Synonymy occurs when two or more lexemes have different forms but share the same or nearly identical meanings. Synonyms often have subtle differences in connotation or usage but can generally be used interchangeably in many contexts.

Example:

• "big" and "large"
• "movie" and "film"

Impact on NLP and Search Engines: Synonymy can affect recall. A search query for "car" may not retrieve documents containing the word "automobile," even though the two terms are synonymous. Modern search engines use synonym expansion to mitigate this issue, but it remains a challenge in many retrieval systems.

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Hyponymy: Specific Terms and Their General Categories

Definition: Hyponymy describes a hierarchical relationship between words, where one word (the hyponym) represents a more specific concept, and another word (the hypernym) represents a more general category. Hyponyms are specific instances of hypernyms.

Example:

• Hyponym: "Rose" is a hyponym of "flower."
• Hypernym: "Flower" is the hypernym for specific flowers like "rose," "tulip," and "daisy."

Impact on NLP and Search Engines: Hyponymy can influence both recall and precision. A user searching for "flower" (hypernym) may retrieve documents that mention specific types of flowers (hyponyms) like roses or tulips. Conversely, a search for "rose" might not retrieve documents about "flowers" in general, reducing recall in some cases.

Natural Language Processing - Information Retrieval

 Information Retrieval (IR) refers to the process of finding and retrieving information from a collection of resources, typically text-based documents, based on user queries. It is a crucial aspect of how we access and utilize data in various contexts, from search engines to databases.

Key Concepts

1. Word-Based Indexing:

   • Many modern IR systems rely on word-based indexing methods, which categorize documents based solely on the words they contain. This approach focuses on the lexical content of documents without considering the structure or syntax of the sentences.

2. Compositional Semantics:

   • Compositional semantics involves understanding how meanings are constructed from smaller units (like words). In extreme interpretations used in IR, the meaning is derived strictly from the individual words, treating the order of words as inconsequential.

3. Bag of Words (BoW):

   • In IR, systems often adopt a Bag of Words (BoW) model, which simplifies the representation of documents by ignoring syntax and word order. Instead, documents are treated as collections of words, where the frequency of each word matters more than its position in the text.
   • For example, the phrases "the cat sat on the mat" and "the mat sat on the cat" would be considered identical in meaning under the BoW approach since they contain the same words, regardless of their arrangement.

Terminology in Information Retrieval

1. Document:

   • A document is the fundamental unit of text in an IR system. It can vary in size and type, ranging from newspaper articles and encyclopedia entries to shorter texts like paragraphs or even individual sentences. In web applications, a document may refer to a webpage, a segment of a page, or an entire website.

2. Collection:

   • A collection is a set of documents that the IR system utilizes to respond to user queries. For instance, a collection may consist of articles in a news database or research papers in an academic repository.

3. Term:

   • A term represents any lexical item found within the collection. This can include single words or phrases. Terms are crucial for indexing and searching documents.

4. Query:

   • A query is the user’s expression of information needs, typically formulated as a set of terms. For example, a user might enter "climate change impacts" as a query to find relevant documents about the effects of climate change.

Ad Hoc Retrieval

• Ad Hoc Retrieval is a specific type of information retrieval task where a user submits a query to an IR system without prior assistance. The system processes the query and returns a potentially ordered list of relevant documents that may satisfy the user's information need.

Example of Ad Hoc Retrieval:

1. User Query: A user types "best practices for renewable energy" into a search engine.

2. Processing: The IR system breaks down the query into individual terms and uses its indexing method to search through the document collection for matches.

3. Results: The system retrieves a list of documents (like research papers, articles, or guides) containing relevant information about renewable energy practices. The results may be ordered based on relevance or quality as determined by the system's algorithms.

Natural Language Processing - Selection Restriction Based Disambiguation

The Context is discussing two primary approaches to dealing with ambiguity in word sense disambiguation (WSD), which is the process of determining the correct meaning of a word in context. This is analogous to part-of-speech (POS) tagging, where each word in a sentence is assigned its correct syntactic category (like noun, verb, adjective, etc.) depending on the context.

Here’s a breakdown of the two approaches mentioned:

1. Sense Selection during Semantic Analysis (as a Side-Effect):

In this approach, the correct meaning of a word (its sense) is chosen during the process of semantic analysis, which is the phase where the meaning of sentences is computed. Ambiguities are resolved as a natural consequence of trying to build meaningful representations of the sentence. If a combination of word senses results in a semantically ill-formed or incoherent sentence, that combination is ruled out. This is guided by selection restrictions, which are constraints based on the meanings of words that dictate how they can combine in a sentence. For example, the verb drink requires its object to be a liquid; hence if the object is something like rock, it would be ruled out during semantic analysis.

Selection restrictions thus play a key role in this method because they help filter out nonsensical interpretations of a sentence by ensuring that only semantically valid combinations of senses are allowed.

2. Sense Disambiguation as a Stand-alone Task:

In the second approach, disambiguating word senses is treated as an independent task, performed before the main process of semantic analysis. The idea here is to resolve all lexical ambiguities first—so that when semantic analysis occurs, the correct senses have already been assigned to the words, making the process smoother. This approach treats WSD as a pre-processing step that is separated from the compositional analysis of sentence meaning.

BCA PART B 8.R program to calculate simple linear regression.

 Linear Regression is a statistical method used to model and analyze the relationship between two (or more) variables by fitting a linear equation to observed data. The main goal of linear regression is to predict the value of a dependent variable (often referred to as the response variable) based on the value of one or more independent variables (often referred to as predictors or features).

Key Concepts of Linear Regression

1. Dependent and Independent Variables:

   • Dependent Variable (Y): The variable that we want to predict or explain. It is also known as the response variable.
   • Independent Variable (X): The variable(s) used to make predictions about the dependent variable. These are also known as predictor variables.

2. Linear Relationship:

   • Linear regression assumes a linear relationship between the independent and dependent variables. This means that changes in the independent variable(s) are associated with proportional changes in the dependent variable.
   • The relationship can be expressed with a linear equation of the form: $$Y = b_0 + b_1X_1 + b_2X_2 + ... + b_nX_n + \epsilon$$ Where:
     • $Y$: Dependent variable.
     • $b_0$: Intercept (the value of $Y$ when all $X$ values are zero).
     • $b_1, b_2, ..., b_n$: Coefficients (slopes) representing the change in $Y$ for a one-unit change in $X$.
     • $X_1, X_2, ..., X_n$: Independent variables.
     • $\epsilon$: Error term (the difference between the observed and predicted values).

3. Types of Linear Regression:

   • Simple Linear Regression: Involves one independent variable. The model fits a straight line to the data points.
   • Multiple Linear Regression: Involves two or more independent variables. It fits a hyperplane (a generalization of a line) to the data.

4. Assumptions of Linear Regression: To validly apply linear regression, several assumptions should be met:

   • Linearity: The relationship between the independent and dependent variables should be linear.
   • Independence: The residuals (errors) should be independent. This means that the value of one observation does not influence another.
   • Homoscedasticity: The residuals should have constant variance at all levels of the independent variable(s). In simpler terms, the spread of the residuals should be the same regardless of the value of the independent variable.
   • Normality: The residuals should be approximately normally distributed, especially for smaller sample sizes.

5. Evaluating the Model: After fitting a linear regression model, various metrics are used to evaluate its performance:

   • R-squared ($R^2$): Measures the proportion of variance in the dependent variable that can be explained by the independent variable(s). An $R^2$ value of 1 indicates a perfect fit, while 0 indicates no explanatory power.
   • Adjusted R-squared: Similar to $R^2$, but adjusts for the number of predictors in the model, making it a more reliable measure when multiple predictors are used.
   • p-values: Tests the null hypothesis that a coefficient is equal to zero (no effect). A low p-value (typically < 0.05) indicates that we can reject the null hypothesis.
   • Residual Analysis: Analyzing the residuals can help diagnose problems with the model, such as non-linearity or heteroscedasticity.

6. Applications of Linear Regression:

   • Predictive Analysis: Used in various fields such as economics, finance, biology, and engineering to predict outcomes based on observed data.
   • Trend Analysis: Helps in identifying trends in data, such as how sales figures might respond to advertising spend.
   • Risk Management: In finance, linear regression can assess the risk associated with investment portfolios.

Program :

# Function to perform simple linear regression

simple_linear_regression <- function(x, y) {

  # Check if the inputs are numeric

  if (!is.numeric(x) || !is.numeric(y)) {

    stop("Both x and y must be numeric.")

  }

  # Check if both vectors have the same length

  if (length(x) != length(y)) {

    stop("Vectors x and y must have the same length.")

  }

  # Fit the simple linear regression model

  regression_model <- lm(y ~ x)

  # Print the model summary

  cat("Simple Linear Regression Model Summary:\n")

  print(summary(regression_model))

  # Extract and print coefficients (Intercept and Slope)

  cat("\nCoefficients:\n")

  coefficients <- coef(regression_model)

  cat("Intercept:", coefficients[1], "\n")

  cat("Slope:", coefficients[2], "\n")

  # Plotting the data points and the regression line

  plot(x, y, main = "Simple Linear Regression", xlab = "Predictor (x)", ylab = "Response (y)", pch = 19, col = "blue")

  abline(regression_model, col = "red", lwd = 2)

  legend("topleft", legend = c("Data Points", "Regression Line"), col = c("blue", "red"), pch = c(19, NA), lty = c(NA, 1), lwd = 2)

}

# Example data for testing the function

x <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

y <- c(2.3, 2.9, 3.1, 4.0, 4.5, 5.0, 6.1, 6.8, 7.3, 8.0)

# Call the function to perform simple linear regression

simple_linear_regression(x, y)

Output :

Simple Linear Regression Model Summary:

Call:
lm(formula = y ~ x)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.32545 -0.13682  0.04636  0.16045  0.22909 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1.4200     0.1421   9.993 8.54e-06 ***
x             0.6509     0.0229  28.421 2.54e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.208 on 8 degrees of freedom
Multiple R-squared:  0.9902,	Adjusted R-squared:  0.989 
F-statistic: 807.8 on 1 and 8 DF,  p-value: 2.539e-09


Coefficients:
Intercept: 1.42 
Slope: 0.6509091 

BCA PART B 7.R program to calculate frequency distribution for discrete & continuous series.

 Frequency distribution is a way of summarizing data to show how often each value (or range of values) occurs in a dataset. It helps in understanding the distribution of data, making it easier to interpret and analyze. The concept of frequency distribution differs depending on whether the data is discrete or continuous.

Frequency Distribution for Discrete Series

Discrete Series represents data that takes on distinct, separate values. These values are typically countable and finite. For example, the number of students in different classes, the number of times a specific number appears in a dice roll, or the number of books read by individuals in a group.

Characteristics of a Discrete Frequency Distribution:

1. Distinct Values: Each value in a discrete dataset can be distinctly identified.
2. Counting Occurrences: We determine the frequency by counting how often each unique value appears.
3. Simple Tabulation: The frequency distribution is represented as a table where each row lists a unique value and the number of times it occurs in the dataset.

Example:

Consider the dataset: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5. This is a discrete series because the values are distinct and countable.

To calculate the frequency distribution:

• Value 1 appears 1 time.
• Value 2 appears 2 times.
• Value 3 appears 3 times.
• Value 4 appears 4 times.
• Value 5 appears 1 time.

Value	Frequency
1	1
2	2
3	3
4	4
5	1

This type of table makes it easy to see the frequency with which each value occurs, allowing us to interpret trends, such as which value appears most frequently.

Frequency Distribution for Continuous Series

Continuous Series represents data that can take any value within a given range. These values are typically measurable and not countable in discrete steps. Examples include measurements like height, weight, temperature, or the time taken to complete a task. Continuous data can take on an infinite number of possible values within a given interval.

Characteristics of a Continuous Frequency Distribution:

1. Class Intervals: Continuous data is grouped into ranges known as class intervals or bins (e.g., 0-10, 10-20, etc.). The width of these intervals depends on the spread of the data and how many intervals are chosen.
2. Grouping: To create a frequency distribution for continuous data, we count how many data points fall within each interval.
3. Frequency Count: The frequency count shows how many data points are present in each interval.

Example:

Consider the dataset: 2.5, 3.7, 5.1, 6.4, 7.8, 3.3, 4.9, 6.1, 7.2, 8.5, 9.0, 5.5. This is a continuous series because the values represent measurements and can take on a continuous range.

To create a frequency distribution, we group the data into intervals (e.g., 4 intervals).

1. Find the range:

   • Minimum value: 2.5
   • Maximum value: 9.0
   • Range = 9.0 - 2.5 = 6.5

2. Divide the range into class intervals:

   • Let's choose 4 intervals, so the width of each interval = 6.5 / 4 ≈ 1.625.
   • Rounding slightly, we might create intervals like:
     • 2.5 - 4.0
     • 4.0 - 5.5
     • 5.5 - 7.0
     • 7.0 - 9.0

3. Count the frequency in each interval:

   • 2.5 - 4.0: 3 values fall within this range (2.5, 3.3, 3.7).
   • 4.0 - 5.5: 3 values fall within this range (4.9, 5.1, 5.5).
   • 5.5 - 7.0: 3 values fall within this range (6.1, 6.4, 7.0).
   • 7.0 - 9.0: 3 values fall within this range (7.2, 8.5, 9.0).

Class Interval	Frequency
2.5 - 4.0	3
4.0 - 5.5	3
5.5 - 7.0	3
7.0 - 9.0	3

In this continuous frequency distribution:

• The frequency distribution table shows how many data points fall into each interval.
• We can see the spread of the data and identify ranges with the most or least data points.

Key Differences Between Discrete and Continuous Frequency Distribution:

1. Nature of Data:

   • Discrete Series: Contains specific, separate values that are countable (e.g., the number of students).
   • Continuous Series: Contains data that can take any value within a range (e.g., height or weight).

2. Representation:

   • Discrete Series: Frequency is calculated for each unique value.
   • Continuous Series: Frequency is calculated for ranges of values (class intervals).

3. Visualization:

   • Discrete data is often visualized with bar charts since the data points are distinct.
   • Continuous data is often visualized with histograms or frequency polygons, where data is grouped into intervals and represented by bars or lines, respectively.

Practical Applications:

• Discrete Frequency Distribution is used in situations where data points are well-defined and countable, such as the number of cars sold per day.
• Continuous Frequency Distribution is used for data involving measurements, such as the distribution of people’s weights in a population.

Program :

# Function to calculate frequency distribution for a discrete series

calculate_discrete_frequency <- function(series) {

  # Use table to calculate the frequency of each unique value

  freq_table <- table(series)

  return(freq_table)

}

# Function to calculate frequency distribution for a continuous series

calculate_continuous_frequency <- function(series, num_classes) {

  # Determine the range and calculate breaks for creating classes

  min_value <- min(series)

  max_value <- max(series)

 

  # Create class intervals using pretty() or seq() for equal interval breaks

  breaks <- pretty(seq(min_value, max_value, length.out = num_classes + 1))

 

  # Use cut() to segment data into the class intervals

  class_intervals <- cut(series, breaks = breaks, include.lowest = TRUE)

 

  # Use table() to calculate the frequency of each interval

  freq_table <- table(class_intervals)

 

  return(freq_table)

}

# Main function to calculate frequency distribution

calculate_frequency <- function(series, type = "discrete", num_classes = 5) {

  if (!is.numeric(series)) {

    stop("Input series must be numeric.")

  }

 

  cat("Input Series: ", series, "\n\n")

 

  if (type == "discrete") {

    freq <- calculate_discrete_frequency(series)

    cat("Frequency Distribution (Discrete Series):\n")

    print(freq)

  } else if (type == "continuous") {

    freq <- calculate_continuous_frequency(series, num_classes)

    cat("Frequency Distribution (Continuous Series):\n")

    print(freq)

  } else {

    stop("Type must be either 'discrete' or 'continuous'.")

  }

}

# Test the program with a discrete series

discrete_series <- c(1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5)

calculate_frequency(discrete_series, type = "discrete")

cat("\n")

# Test the program with a continuous series

continuous_series <- c(2.5, 3.7, 5.1, 6.4, 7.8, 3.3, 4.9, 6.1, 7.2, 8.5, 9.0, 5.5)

calculate_frequency(continuous_series, type = "continuous", num_classes = 4)

Output :

Input Series: 1 2 2 3 3 3 4 4 4 4 5 Frequency Distribution (Discrete Series): series 1 2 3 4 5 1 2 3 4 1 Input Series: 2.5 3.7 5.1 6.4 7.8 3.3 4.9 6.1 7.2 8.5 9 5.5 Frequency Distribution (Continuous Series): class_intervals [2,3] (3,4] (4,5] (5,6] (6,7] (7,8] (8,9] 1 2 1 2 2 2 2

BCA PART B 6.R program to calculate cumulative sums, and products, minima, maxima

 The purpose of this R program is to calculate several cumulative properties for a given numeric vector:

• Cumulative Sum: The running total of elements.
• Cumulative Product: The running product of elements.
• Cumulative Minimum: The smallest element encountered at each step.
• Cumulative Maximum: The largest element encountered at each step.

Program :

# Define a function to calculate cumulative sums

cumulative_sum <- function(vec) {

  return(cumsum(vec))

}

# Define a function to calculate cumulative products

cumulative_product <- function(vec) {

  return(cumprod(vec))

}

# Define a function to calculate cumulative minima

cumulative_minimum <- function(vec) {

  return(cummin(vec))

}

# Define a function to calculate cumulative maxima

cumulative_maximum <- function(vec) {

  return(cummax(vec))

}

# Main function to calculate all cumulative values

calculate_cumulative <- function(vec) {

  if (!is.numeric(vec)) {

    stop("Input vector must be numeric.")

  }

  cat("Input Vector: ", vec, "\n\n")

 

  cat("Cumulative Sum: ", cumulative_sum(vec), "\n")

  cat("Cumulative Product: ", cumulative_product(vec), "\n")

  cat("Cumulative Minimum: ", cumulative_minimum(vec), "\n")

  cat("Cumulative Maximum: ", cumulative_maximum(vec), "\n")

}

# Test the program with a sample vector

sample_vector <- c(5, 2, -3, 10, 4)

calculate_cumulative(sample_vector)

Output :

Input Vector: 5 2 -3 10 4 Cumulative Sum: 5 7 4 14 18 Cumulative Product: 5 10 -30 -300 -1200 Cumulative Minimum: 5 2 -3 -3 -3 Cumulative Maximum: 5 5 5 10 10

BCA PART B 5.R program to calculate arithmetic mean for grouped and ungrouped data

1. Ungrouped Data (mean_ungrouped):

   • The mean_ungrouped function computes the mean of a vector of data using the mean() function, which calculates the sum of all values divided by the number of values.

2. Grouped Data (mean_grouped):

   • For grouped data, we first calculate the midpoints of each class interval using the formula: $$\text{midpoint} = \frac{\text{lower bound} + \text{upper bound}}{2}$$
   • Then, we compute the arithmetic mean using the frequency-weighted mean formula: $$\text{Mean} = \frac{\sum (\text{midpoint} \times \text{frequency})}{\sum \text{frequency}}$$

Program:

# Function to calculate arithmetic mean for ungrouped data

mean_ungrouped <- function(data) {

  mean_val <- mean(data)

  return(mean_val)

}

# Function to calculate arithmetic mean for grouped data

mean_grouped <- function(lower_bound, upper_bound, frequency) {

  # Calculate midpoints of the class intervals

  midpoints <- (lower_bound + upper_bound) / 2

 

  # Calculate the weighted mean for the grouped data

  mean_val <- sum(midpoints * frequency) / sum(frequency)

 

  return(mean_val)

}

# Example Usage for Ungrouped Data

ungrouped_data <- c(10, 20, 30, 40, 50)  # Example ungrouped data

cat("Arithmetic Mean for Ungrouped Data:\n")

print(mean_ungrouped(ungrouped_data))

# Example Usage for Grouped Data

lower_bound <- c(0, 10, 20, 30)  # Lower bounds of class intervals

upper_bound <- c(10, 20, 30, 40) # Upper bounds of class intervals

frequency <- c(5, 10, 8, 7)      # Frequency of each class interval

cat("\nArithmetic Mean for Grouped Data:\n")

print(mean_grouped(lower_bound, upper_bound, frequency))

Output:

Arithmetic Mean for Ungrouped Data:

[1] 30

Arithmetic Mean for Grouped Data:

[1] 20