I specialize in the dynamic and ever-evolving field of Artificial Intelligence, Data Science. My expertise lies in harnessing the power of AI, Natural Language Processing (NLP), Data Engineering, and cutting-edge AI-ML technologies to unravel complex problems and unlock new possibilities.
I specialize in the dynamic and ever-evolving field of Artificial Intelligence, Data Science. My expertise lies in harnessing the power of AI, Natural Language Processing (NLP), Data Engineering, and cutting-edge AI-ML technologies to unravel complex problems and unlock new possibilities.
With a passion for creating intelligent systems, I thrive on developing innovative solutions that bridge the gap between raw data and actionable insights. Whether it’s crafting robust algorithms, engineering data pipelines, or delving into the realms of machine learning, I am dedicated to pushing the boundaries of what AI can achieve.
I’ve actively engaged in developing AI-driven applications, collaborating on research initiatives, and contributing to the advancement of the field. My current endeavors include spearheading two significant projects – one focused on exploring the intersection of AI and healthcare, and another involving the development of a platform that seamlessly integrates AI into everyday life.
Pune, Maharashtra ‧ Government
Karad 415110, Satara, Maharashtra
Wing, Karad, Maharashtra
The basic and most important part of the Machine learning and Data analysis is to understand the Data, Analyze the pattern in technical way we will say distribution of the data, we will discuss as follow:
To understand the machine learning and data science perfectly you must know the statistics. we are going to discuss most important techniques in the Statistics.
Measures of central tendency are statistical metrics that summarize a dataset by identifying its central point. They provide insights into the “typical” or “average” value in a dataset, making them essential for analyzing and comparing data distributions.
There are three main measures of central tendency: Mean, Median, and Mode.
The mean is the sum of all values in a dataset divided by the number of values. It is the most commonly used measure of central tendency.
For a dataset with nnn values: Mean(xˉ)=∑xin\text{Mean} (\bar{x}) = \frac{\sum x_i}{n}Mean(xˉ)=n∑xi
where:
Consider the dataset: {4, 8, 10, 12, 14} xˉ=4+8+10+12+145=485=9.6\bar{x} = \frac{4 + 8 + 10 + 12 + 14}{5} = \frac{48}{5} = 9.6xˉ=54+8+10+12+14=548=9.6
Thus, the mean is 9.6.
✅ Easy to calculate and widely used.
✅ Considers all values in the dataset.
❌ Sensitive to outliers (e.g., extreme values can skew the mean).
The median is the middle value when the dataset is arranged in ascending or descending order. If there are an odd number of values, the median is the middle one. If there are an even number of values, the median is the average of the two middle values.
Dataset: {3, 7, 9, 11, 15}
Dataset: {2, 5, 8, 12, 14, 18}
✅ Not affected by outliers, making it a good measure for skewed distributions.
✅ Works well for ordinal data.
❌ Ignores extreme values in the dataset.
The mode is the value that appears most frequently in a dataset. A dataset can have:
Dataset: {2, 4, 4, 6, 8, 10}
Dataset: {1, 3, 3, 5, 7, 7, 9}
Dataset: {2, 5, 8, 11, 14}
✅ Useful for categorical data (e.g., finding the most common brand, product, or category).
✅ Works well for non-numeric data.
❌ May not exist or may be multiple, making interpretation difficult.
| Scenario | Best Measure |
|---|---|
| Symmetric data with no outliers | Mean |
| Skewed data with outliers | Median |
| Categorical or qualitative data | Mode |
| Bimodal/multimodal distribution | Mode |
Consider the house prices (in $1000s):
{120, 130, 135, 140, 500}
In this case, the median is the best measure because it is unaffected by the extreme value (500).
While measures of central tendency (mean, median, mode) tell us about the center of the data, measures of dispersion describe how spread out the data points are. The most common measures of dispersion include Variance and Standard Deviation.
Variance measures how much each data point deviates from the mean, squared.
🔹 Why use (n-1) in the sample variance formula?
The denominator (n−1)(n-1)(n−1) is known as Bessel’s correction, which corrects for bias in estimating the population variance from a sample.
Standard deviation is simply the square root of variance. It provides a measure of spread in the same units as the data.
Example Calculation: Consider the dataset {10, 12, 14, 18, 20}
Thus, the sample standard deviation is 4.15.
A population includes all members of a defined group. When we calculate statistics for an entire population, we use N in the denominator.
Example: The average height of all people in a country.
A sample is a subset of a population. Since we usually cannot collect data from the entire population, we estimate statistics using a sample and use n-1 in the denominator.
Example: Measuring the height of 1,000 randomly selected people to estimate the national average.
Variables are classified into categorical and numerical types.
Categorical variables represent distinct groups or categories.
Numerical variables represent measurable quantities.
A histogram is a graphical representation of the frequency distribution of numerical data. It consists of bins, where each bin represents a range of values, and the height of the bar represents the frequency.
🔹 Example of a Histogram:
🔹 Advantages of Histograms: ✅ Shows the distribution of data
✅ Helps detect skewness and outliers
A Kernel Density Estimate (KDE) is a smoothed version of a histogram. Instead of using bars, KDE uses a smooth curve to estimate the probability density function of a dataset.
🔹 Why Use KDE?
🔹 Example: If we have a dataset of student heights, a KDE plot would give a smooth curve that helps visualize the probability density of different height ranges.
🔹 Difference Between Histogram & KDE
| Feature | Histogram | KDE |
|---|---|---|
| Representation | Binned Bars | Smooth Curve |
| Sensitivity | Depends on bin width | Depends on kernel bandwidth |
| Use Case | Discrete counts | Probability density estimation |
When you’re trying to understand a dataset or detect outliers, few tools are more powerful and intuitive than percentiles, quartiles, and the 5-number summary. These help you explore how your data is distributed and identify extreme values with precision.
Percentiles divide the dataset into 100 equal parts. Each percentile tells you the value below which a certain percentage of data falls.
Percentiles help describe the relative standing of a value in the dataset.
Quartiles are specific percentiles that divide your data into four equal parts.
| Quartile | Percentile Equivalent | Meaning |
|---|---|---|
| Q1 (1st Quartile) | 25th Percentile | 25% of data below |
| Q2 (Median) | 50th Percentile | Middle value |
| Q3 (3rd Quartile) | 75th Percentile | 75% of data below |
The 5-number summary is one of the most important techniques in descriptive statistics. It gives a quick overview of the distribution of your data and is crucial for visualizations like box plots.
The Interquartile Range (IQR) measures the spread of the middle 50% of the data. IQR=Q3−Q1
This is a robust measure of variability that is not affected by outliers.
The IQR can be used to create fences beyond which data points are considered outliers.
Lower Fence=Q1−1.5×IQR
Upper Fence=Q3+1.5×IQR
Any value below the lower fence or above the upper fence is typically classified as an outlier.
data = [7, 8, 8, 10, 12, 13, 14, 15, 16, 22, 40]
So the 5-number summary is:
[Minimum = 7, Q1 = 9, Median = 13, Q3 = 16, Maximum = 40]
IQR=Q3−Q1=16−9=7
Any value > 26.5 or < -1.5 is an outlier.
✅ So, in this dataset, 40 is an outlier.
The 5-number summary is used in box plots to visually summarize data.
| Feature | Reason |
|---|---|
| Exploratory Data Analysis (EDA) | Quickly understand the spread and central tendency |
| Outlier Detection | IQR-based fences help detect anomalies |
| Feature Scaling & Normalization | Useful for feature engineering |
| Robust Statistics | Median and IQR are unaffected by extreme values, unlike mean & standard deviation |
| Term | Description | Formula |
|---|---|---|
| Q1 | 25th percentile | – |
| Q2 (Median) | 50th percentile | – |
| Q3 | 75th percentile | – |
| IQR | Interquartile range | Q3−Q1Q3 – Q1Q3−Q1 |
| Lower Fence | Threshold for low outliers | Q1−1.5×IQR |
| Upper Fence | Threshold for high outliers | Q3+1.5×IQR |
| Outliers | Values outside fences | x<LF or x> UF x < LF |
Covariance and correlation are fundamental statistical concepts used to measure the relationship between variables. While they serve similar purposes, they differ in important ways. Let’s explore both concepts in depth.
Covariance measures how two variables change together. It indicates the direction of the linear relationship between variables.
The sample covariance formula is:
Cov(X,Y) = Σ[(x_i – x̄)(y_i – ȳ)] / (n-1)
Where:
Let’s consider stock prices for two companies, A and B, over 5 days:
Day | Company A | Company B —-|———–|———- 1 | $10 | $5 2 | $12 | $6 3 | $11 | $4 4 | $13 | $7 5 | $14 | $8Step 1: Calculate means
Step 2: Calculate deviations and their products
Day | A-Mean(A) | B-Mean(B) | Product —-|———–|———–|——– 1 | -2 | -1 | 2 2 | 0 | 0 | 0 3 | -1 | -2 | 2 4 | 1 | 1 | 1 5 | 2 | 2 | 4Step 3: Sum products and divide by (n-1) Cov(A,B) = (2+0+2+1+4)/(5-1) = 9/4 = 2.25
The positive covariance indicates that when stock A increases, stock B tends to increase as well.
Indicates that variables tend to move in the same direction.
Example: Height and weight in humans typically have positive covariance because taller people generally weigh more than shorter people.
Indicates that variables tend to move in opposite directions.
Example: Hours spent studying and number of errors on a test typically have negative covariance because more study time usually results in fewer errors.
Indicates no linear relationship between variables.
Example: Shoe size and intelligence would likely have zero covariance because there’s no reason one would affect the other.
Measures the covariance of a variable with itself at different time points.
Example: In time series analysis, the price of gold today might have a high autocovariance with its price yesterday.
Measures the similarity between two different time series at different time lags.
Example: Rainfall amounts and reservoir levels might show cross-covariance with a lag, as it takes time for rainfall to affect reservoir levels.
Correlation is a standardized version of covariance that measures both the strength and direction of a linear relationship between variables. It always falls between -1 and 1.
The Pearson correlation coefficient is:
ρ(X,Y) = Cov(X,Y) / (σ_X × σ_Y)
Where:
Continuing with our stock price example:
Step 1: Calculate standard deviations
Step 2: Calculate correlation
(Note: In practice, correlation should always be between -1 and 1. The slight discrepancy here is due to rounding. The actual correlation would be 1, indicating perfect positive correlation.)
Measures linear relationships between variables with continuous, normally distributed data.
Example: The relationship between height and weight typically follows a linear pattern suitable for Pearson correlation.
Measures monotonic relationships, where variables tend to change together but not necessarily at a constant rate.
Example: The relationship between age and reading ability in children might be monotonic (generally increasing) but not strictly linear.
Let me explain both correlation methods in detail, including their formulas, interpretations, and when to use each one.
The Pearson correlation coefficient (r) measures the linear relationship between two continuous variables. It’s the most commonly used correlation measure in statistics.
For two variables X and Y with n observations, the Pearson correlation coefficient is calculated as:
r = Σ[(xᵢ – x̄)(yᵢ – ȳ)] / √[Σ(xᵢ – x̄)² × Σ(yᵢ – ȳ)²]
Alternatively, it can be expressed as:
r = Cov(X,Y) / (σₓ × σᵧ)
Where:
Consider these data points:
CopyX: 1, 2, 3, 4, 5
Y: 2, 3, 5, 7, 11Step 1: Calculate means
Step 2: Calculate deviations, squares, and products
X | Y | X-x̄ | Y-ȳ | (X-x̄)² | (Y-ȳ)² | (X-x̄)(Y-ȳ) —–|—–|—–|—–|———|———|———— 1 | 2 | -2 | -3.6| 4 | 12.96 | 7.2 2 | 3 | -1 | -2.6| 1 | 6.76 | 2.6 3 | 5 | 0 | -0.6| 0 | 0.36 | 0 4 | 7 | 1 | 1.4| 1 | 1.96 | 1.4 5 | 11 | 2 | 5.4| 4 | 29.16 | 10.8 —–|—–|—–|—–|———|———|———— Sum: | | | | 10 | 51.2 | 22.0Step 3: Calculate r r = 22.0 / √(10 × 51.2) = 22.0 / √512 = 22.0 / 22.63 ≈ 0.972
This indicates a very strong positive linear relationship between X and Y.
The Spearman rank correlation coefficient (ρ or rₛ) measures the monotonic relationship between two variables by using their ranks rather than actual values.
For two variables X and Y with n observations, the Spearman correlation is calculated as:
ρ = 1 – (6 × Σd²) / (n(n² – 1))
Where:
If there are no tied ranks, this simplifies to:
ρ = Pearson correlation coefficient between the ranks of X and Y
Consider these data points:
X: 5, 10, 15, 20, 25
Y: 2, 4, 5, 9, 12Step 1: Rank the values in each variable (1 = lowest, n = highest)
X | Y | Rank X | Rank Y | d (difference) | d² —–|—–|——–|——–|—————-|—– 5 | 2 | 1 | 1 | 0 | 0 10 | 4 | 2 | 2 | 0 | 0 15 | 5 | 3 | 3 | 0 | 0 20 | 9 | 4 | 4 | 0 | 0 25 | 12 | 5 | 5 | 0 | 0 —–|—–|——–|——–|—————-|—– Σd² = 0Step 2: Calculate ρ ρ = 1 – (6 × 0) / (5(5² – 1)) = 1 – 0/120 = 1
This indicates a perfect monotonic relationship between X and Y.
When ties occur, each tied value is assigned the average of the ranks they would have received if they were distinct. For example, if the 2nd and 3rd positions are tied, both receive rank 2.5.
For tied ranks, the formula can be adjusted to:
ρ = (Σ(xᵢ – x̄)(yᵢ – ȳ)) / √(Σ(xᵢ – x̄)² × Σ(yᵢ – ȳ)²)
Where xᵢ and yᵢ are now the ranks.
The PMF applies to discrete random variables and gives the probability that a random variable X equals a specific value x.
Mathematical Definition: P(X = x) = PMF(x)
Properties:
Example: For a fair six-sided die, the PMF is:
The PDF applies to continuous random variables and represents the relative likelihood of the random variable taking on a specific value.
Mathematical Definition: f(x) = dF(x)/dx, where F(x) is the CDF
Properties:
Example: The PDF of a standard normal distribution is: f(x) = (1/√(2π)) * e^(-x²/2)
The CDF applies to both discrete and continuous random variables and gives the probability that X is less than or equal to x.
Mathematical Definition: F(x) = P(X ≤ x)
For discrete variables: F(x) = Σ PMF(t) for all t ≤ x For continuous variables: F(x) = ∫(from -∞ to x) f(t)dt
Properties:
Example: For a standard normal distribution, the CDF doesn’t have a simple closed form but is often denoted as Φ(x).
Probability distributions come in two main categories:
The Bernoulli distribution is the simplest discrete probability distribution, modeling a single binary outcome.
Flipping a coin once with p = 0.5 probability of heads:
Bernoulli Distribution
Image
The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials.
Flipping a fair coin 10 times and counting heads:
Binomial Distribution
Image
The Poisson distribution models the number of events occurring in a fixed interval of time or space, when these events happen at a constant average rate.
If emails arrive at an average rate of 5 per hour:
Poisson Distribution
Image
The normal distribution is the most important continuous probability distribution, characterized by its bell-shaped curve.
Human heights often follow a normal distribution. If adult male heights have μ = 175 cm and σ = 7 cm:
Text Mining (also called Text Analytics) is the process of deriving useful insights, patterns, and structure from unstructured textual data.
Since over 80% of real-world data is unstructured (emails, chats, reviews, social media, documents), text mining plays a critical role in data science, NLP, and business intelligence.
Feature Engineering is the art of converting raw data into meaningful features that enhance machine learning models.
In text mining, this typically involves:
This is where Regex (Regular Expressions) becomes incredibly powerful.
Regex stands for Regular Expressions – a sequence of characters used to search, match, or extract patterns in text data.
Think of regex as a search engine for patterns, capable of performing:
You can use regex to:
import re
text = "Email me at [email protected] or visit https://site.com"
clean_text = re.sub(r"(https?://\S+|www\.\S+)", "", text)
Regex can extract domain-specific features such as:
#\w+)@\w+)[A-Z]{2,})\d{2}/\d{2}/\d{4})These extracted features can be used in model training!
Regex helps normalize inconsistent formats like:
text = "Price: $25.00 Date: 04/04/2025"
normalized = re.sub(r"\s+", " ", text) # removes extra spaces
Rather than writing complex logic or loops, regex allows compact one-liners that scale across datasets with thousands/millions of records.
In advanced NLP preprocessing, regex is used to:
Proper feature engineering using regex improves accuracy, precision, and recall by:
In a spam detection model, regex can be used to extract:
https?://\S+[A-Z]{2,}These become input features that help the model learn to distinguish spam from non-spam.
| Task | Regex Pattern | Use |
|---|---|---|
| Remove URLs | https?://\S+ | Clean text |
| Extract hashtags | #\w+ | Feature creation |
| Emails | \S+@\S+ | PII removal or extraction |
| Dates | \d{2}/\d{2}/\d{4} | Standardization |
| Uppercase words | [A-Z]{2,} | Spam detection |
| Emojis | [^\w\s,] | Clean noisy text |
Text mining, also known as text data mining, is the process of transforming unstructured text into a structured format to identify meaningful patterns and new insights. Large textual datasets can be analyzed using text mining to uncover hidden links, patterns, and important topics.
r'd{1,2}[/-]d{1,2}[/-]d{2,4}|(?:Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)+[.]?[s-]?d{1,2}[-,s][s]?d{2,4}|'
r'd{1,2}[s](?:Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)+[.,s]?[s]?d{2,4}|'
r'(?:Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)[A-Za-z]*[s]?[,]?[s]?d{2,4}|'
r'd{1,2}[/]d{2,4}|'
r'[^-][s]?d{4}[s,][^-]'04/20/2009; 04/20/09; 4/20/09; 4/3/09Mar-20-2009; Mar 20, 2009; March 20, 2009; Mar. 20, 2009; Mar 20 2009;20 Mar 2009; 20 March 2009; 20 Mar. 2009; 20 March, 2009Mar 20th, 2009; Mar 21st, 2009; Mar 22nd, 2009Feb 2009; Sep 2009; Oct 20106/2008; 12/20092009; 2010# handling the Duration using regex pattern
fp[['duration_in_hr', 'duration_in_min']] = fp['Duration'].str.extract(r'(?:(d+)h)?s?(?:(d+)m)?').fillna(0).astype(int)fp.head()
A Decentralized Autonomous Organization to Improve Coordination Between Nations Using Blockchain Technology, Artificial Intelligence and Natural Language Processing for Sentiment analysis on News Data.
This paper is about Establishing a Decentralized organization with the Different Countries as members where all the countries will be considered as the node of the blockchain. All the countries in the organization will be treated equally there will not be any superpower amongst them. Therefore, The Organization will gather huge amount of the data from the different countries from all the sectors like health, education, economy, technology, culture, and agriculture which represents the overall development of the countries. All this gathered data will be further analyzed for their positive and negative impacts on all the mentioned sectors. This will give brief idea about situation of an individual country in different areas on that basis, members of the Organizations or we can say all the member countries will decide the reward or penalty case for the respective country. Blockchains have the potential to enhance systems by getting rid of middlemen. Artificial Intelligence will play a major role in this organization as dealing with massive amount of data will be in the frame and to deal with this data, we need AI to improve data integrity of the result which will be used by Smart-Contract for decision making purpose, automating, and optimizing the smart contract. AI promises to remove oversight and increase the objectivity of our systems. This organization offers a framework for participants to work together to create a dataset and host a model that is continuously updated using smart contracts. As data is growing rapidly. AI will manage that data efficiently with less energy consumption
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1 Page with Elementor
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MAintaine Design
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All the Lorem Ipsum generators on the Internet tend to repeat predefined chunks as necessary
1 Page with Elementor
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Design Figma
MAintaine Design
Content Upload
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