Advanced Mathematical Applications in Data Science

The field of data science relies heavily on mathematical analysis. A solid foundation in certain branches of mathematics is essential for every data scientist already working in the field or planning to enter it in the future. In whatever area we focus on, data science, machine learning engineering, business intelligence development, data architecture, or another area of expertise, it is important to examine the several kinds of mathematical prerequisites and insights and how they're applied in the field of data science. Machine learning algorithms, data analysis and analyzing require mathematics. Mathematics is not the only qualification for a data science education and profession but is often the most significant. Identifying and translating business difficulties into mathematical ones are a crucial phase in a data scientist's workflow. In this study, we describe the different areas of mathematics utilized in data science to understand mathematics and data science together. 

We provide here an analysis of Kalman filter, which has wide applications in the experimental and observational fields. Kalman filter is a data fusion algorithm or a mathematical tool which is based on the estimation theory. It basically is a set of mathematical equations which provide a computational mechanism for evaluating the state of discrete processes with noisy data. In fact, observations and data analysis is a very key aspect of all theories. In any set of data, to make it useful, one has to minimize the error/noise by taking into consideration various aspects like the estimated values (the theoretical values), the measurement values, experimental errors and the estimated errors. We have shown here how this can be done using Kalman Filtering technique. Kalman Filter is a tool which can take the observational data and improvise it to identify the best possible value of the parameters involved. Kalman filter and its variants such as the extended Kalman filter have wide applications mainly in the field of communication e.g., in GPS receivers (global positioning system receivers), radio equipment used for filtering and removing noise from the output of laptop trackpads, image processing, face recognition and many more. 

Mathematics is the rock-solid foundation of everything that happens when science is present, and it is also extremely important in the field of data science since mathematical ideas assist discover models and facilitate the development of algorithms. But, the concepts they present and the tools they enable are the only reasons statistics and arithmetic are so crucial to data science. There is a particular type of mathematical reasoning that is necessary to grasp data, beyond the fundamentals of calculus, discrete mathematics, and linear algebra. For the implementation of such algorithms in data science, a thorough understanding of the various principles of probability and statistics is essential. Machine learning is one of the many modern data science techniques that has a strong mathematical base. The evidence presented in this chapter backs up our earlier claim that math and statistics are the fields that offer the greatest tools and approaches for extracting structure from data. For newcomers coming from other professions to data science, math proficiency is crucial. 

Information extraction from images is now incredibly valuable for many new inventions. Even though there are several simple methods for extracting information from the images, feasibility and accuracy are critical. One of the simplest and most significant processes is feature extraction from the images. Many scientific approaches are derived by the experts based on the extracted features for a better conclusion of their work. Mathematical procedures, like Scientific methods, play an important role in image analysis. The Bag of Visual Words (BoVW) [1, 2, 3] is one of them, and it is helpful to figure out how similar a group of images is. A set of visual words characterises the images in the Bag of Visual Words model, which are subsequently aggregated in a histogram per image [4]. The histogram difference depicts the similarities among the images. The reweighting methodology known as Term Frequency – Inverse Document Frequency (TF-IDF) [5] refines this procedure. The overall weighting [6] for all words in each histogram is calculated before reweighting. As per the traditional way, the images are transformed into the matrix called as Cost matrix. It is constructed through two mathematical: Euclidean distances and Cosine distances. The main purpose of finding these distances is to detect similarity between the histograms. Further the histograms are normalized and both distances are calculated. The visual representation is also generated. The two mathematical methods are compared to see which one is appropriate for checking resemblance. The strategy identified as the optimum solution based on the findings aids in fraud detection in digital signature, Image Processing, and classification of images.

The word “data science” has become more popular in recent years, with a growing number of people embracing it. Only a small minority of people, on the other hand, are able to offer a clear explanation of what the term refers to when it is used in context. With no defined term to communicate and understand one another, it is difficult for organizations that are devoted to the collaboration, utilization, and application Data Science to communicate and understand one another. As a result of technological advancements, it has become increasingly difficult to define and execute Data Science in a way that is compatible with how it was previously considered and understood in the past. Specifically, we could now set out to develop definitions of Data Science that are representatives of current academic and industrial interpretations and perceptions, map these perspectives to newer domains of Data Science, and then determine whether or not this mapping translates into an effective practical curriculum for academics. Aspects of data science that differentiate it include how it is now used and how it is projected to be used in the future. Data science is also characterized by its ability to forecast the future.

The process of maintaining the right quantity of inventory to meet demand, minimising logistics costs, and avoiding frequent inventory problems, including reserve outs, overstocking, and backorders is known as inventory optimisation. One has a finite capacity and is referred to as an owned warehouse (OW), which is located near the market, while the other has an endless capacity and is referred to as a rented warehouse (RW), which is located away from the market. Here, lowering the overall cost is the goal. Neural networks are employed in these works to either maximise or minimise cost. The findings produced from the neural networks are compared with a mathematical model and neural networks. Findings indicate that neural networks outperformed both conventional mathematical models and neural networks in terms of optimising the outcomes. The best way to understand supervised machine learning algorithms like neural networks is in the context of function approximation. The benefits and drawbacks of the two-warehouse approach compared to the single warehouse plan will also be covered. We investigate cost optimisation using neural networks in this chapter, and the outcomes will also be compared using the same.

The implementation of data science in cyber security to help preserve against attacks and improve approach to better conflict cyber warning has many welfares. Honestly, data science has changed cyber security and the reaction has been profound and transformed. Cyber security uses data science to keep digital devices, services, systems, and software Safe from cyberattacks. Here, we talk about cyber security data science, present day uses for the cyber security field and data guide quickwitted managerial systems that can safeguard our system from cyber-attacks.

An Artificial Neural Network (ANN) is a data processing paradigm inspired by the way organic nervous systems, such as the brain, process data. The innovative structure of the information processing system is a crucial component of this paradigm. It is made up of a huge number of highly linked processing components (neurons) that work together to solve issues. Neural networks handle data in the same manner that the human brain does. The network is made up of several densely linked processing units (neurons) that operate in parallel to solve a given problem. They are unable to be programmed to execute a specific activity. ANN, like humans, learns by example. Through a learning process, an ANN is trained for a specific application, such as pattern recognition or data categorization. In biological systems, learning includes changes to the synaptic connections that occur between neurons. This is also true for ANNs. Artificial Neural Networks are used for classification, regression, and grouping. Stages of image processing are classified as preprocessing, feature extraction, and classification. It can be utilized later in the process. ANN should be provided with features and output should be classified. This paper provides an overview of Artificial Neural Networks (ANN), their operation, and training. It also explains the application and its benefits. Artificial Neural Network has been used to classify the MNIST dataset.

The greenhouse gas emissions mostly include carbon-dioxide as the major component. The CO2 level is increasing day-by-day which is a great cause of worry for the future world’s environment. The reason why greenhouse gases’ level increases in the environment is to be assessed and controlled. The greenhouse gases have heattrapping capacity. A rise in numerous activities, including transportation, power production, agriculture, business, and residential, which are the main drivers of the increase in GHG levels in the atmosphere, is to blame for the rise in GHG emissions. Nitrous oxide, Methane, and Carbon Dioxide are all part of the GHG portfolio. Deforestation, traffic, and soil degradation all contribute to an increase in CO2 . As a result of burning biomass and urban trash, methane levels are also rising. The chlorofloro carbons are also rising due to refrigeration and industrial operations; so keeping the above concern in mind, the researcher had decided to conduct the study title. Carbon Emission Assessment by Applying Clustering Technique to World Emission Datasets using Python Programming. The study considers a period of 169 years (1750-2019). The study is carried out in five steps data fetching in python programming, feature engineering, standardization, clustering. The study generates 6 clusters. Cluster one contains 220 countries, cluster two includes Russia, France, Germany, China, Europe (others). America (others), Asia Pacific. Cluster three includes the United Kingdom. Cluster four includes the United States. Cluster five includes EU-28. Cluster six includes Malawi. 

This study aims to develop a churn prediction model which can assist telecommunication companies in predicting customers who are most likely subject to churn. The model is developed by employing machine learning techniques on big data platforms. Customer churn is one of the most critical issues, especially in high investment telecommunication companies. Accordingly, the companies are looking for ways to predict potential customers to churn and take necessary actions to reduce the churn. To accomplish the objective of the study, it first compares eight machine learning techniques, i.e., ridge classifier, gradient booster, adaptive boosting, bagging classifier, k-nearest neighbour (kNN), decision tree, logistic regression, and random forest. By using five evaluation performance metrics (i.e., accuracy, AUC score, precision score, recall score, and the F score), kNN is selected since it outperforms other techniques. Second, the selected technique is used to predict the likelihood of customers churning.

 India is a vast country with variations in geography as well as in population density. The pollution in India is increasing day by day. The Greenhouse gas emission is on the rise due to various activities like agriculture, industry, power generation, transportation, etc. Carbon dioxide (CO2 ), Carbon Monoxide (CO), and Methane (CH4 ) are the major elements in greenhouse gases. The emission of greenhouse gases causes various threats to the environment and health. The states in India have been under development since independence. Various activities are on the rise. The states are not having balanced growth as far as the industrial and agriculture sectors are concerned. The powerhouse of industrial growth is the state of Maharashtra and Gujarat. The population density is also scattered in India. The states contribute differently to greenhouse gases emission and it is difficult for the government to make policy category-wise for the control of greenhouse gases emissions. The classification of states into different categories will help in the strategic formulation of policy and strategy for different states depending on their greenhouse gases emission and per capita analysis of these emissions. The per capita greenhouse gas emission is calculated by dividing the total emissions by the total population. After analyzing the above problem, the researchers have decided to conduct the study titled A state-wise Assessment of greenhouse gas emission in India by applying the K-mean Clustering Technique using Python Programming. Research is carried out in Five steps -Feature extraction and engineering, Data extraction, Standardizing and Scaling, Identification of Clusters, Cluster formation. The study period is 2020. The data selected for analysis is yearly data state-wise of different Indian states. Data taken for the study is from the Kaggle database. Findings - The k- mean algorithm (cluster analysis using Python Programming) classifies the states of India into three clusters. Cluster one includes 16 states of India viz. Arunachal, Assam, Bihar, Himachal Pradesh, Jammu & Kashmir, Jharkhand, Madhya Pradesh, Manipur, Meghalaya, Mizoram, Odisha, Rajasthan, Sikkim, Tripura, Uttar Pradesh, Uttarakhand. Cluster two includes 8 states of the India. Viz Andhra Pradesh, Goa, Gujarat, Karnataka, Kerala, Maharashtra, Tamilnadu, West Bengal. Cluster three includes 4 states of India Viz Haryana, Nagaland, Punjab, Chhattisgarh. The major contributors to greenhouse gase emission are in cluster three.The medium-range emission for greenhouse gases emission are grouped in cluster two and Minimum Range greenhouse gase emission states are included in cluster one.

The medical management sector assembles a large volume of unexposed data on the health status of patients. At times this hidden data could be useful in diagnosing diseases and making effective decisions. For providing an appropriate way out and planning a diagnostic system based on this information, now-a-days, the newest data mining strategies are in use. In this study, a thorough review has been done on the identification of an effective heart disease prediction system (EHDPS) designed by neural network for the prediction of the risk level of cardiovascular diseases. The study focused on the observation of various medical parameters, namely, age, height, weight, BMI, sex, blood pressure, cholesterol, and obesity. Based on this study, a concept map has been designed on the prediction ways for individuals with heart disease with the help of EHDPS. The study assembled considerable information about the multilayer perceptron neural network with rear proliferation as the algorithm for data analysis. The current review work may be significant in establishing knowledge of the association between health factors related to the risk level of heart disease. The study also suggests means of early intervention and prevention of medical emergencies posed by the late detection of cardiovascular diseases, especially in the context of post COVID 19 complications.

Data science is often used as an umbrella term to include various techniques for extracting insights and knowledge from complex structured and unstructured data. It often relies on a large amount of data (big data) and the application of different mathematical methods, including computer vision, NLP (or natural language processing), and data mining techniques. Advances in data science have resulted in a wider variety of algorithms, specialized for different applications and industries, such as healthcare, finance, marketing, supply chain, management, and general administration. Specifically, data science methods have shown promise in addressing key healthcare challenges and helping healthcare practitioners and leaders make data-driven decision-making. This chapter focuses on healthcare issues and how data science can help solve these issues. The chapter will survey different approaches to defining data science and why any organization should use data science. This chapter will also present different skills required for an effective healthcare data scientist and discusses healthcare leaders' behaviors that in impacting their organizational processes.