This document provides an introduction to principal component analysis (PCA) for feature extraction. It describes PCA as a method to project high-dimensional data into a lower-dimensional subspace while retaining the most important information. The key steps are outlined as calculating the mean of each column, centering the data, computing the covariance matrix, performing eigendecomposition of the covariance matrix to obtain eigenvalues and eigenvectors, and projecting the data onto the new subspace defined by the principal components with the highest eigenvalues. Implementing PCA using scikit-learn's PCA class is also briefly discussed.
Introductory session for basic matlab commands and a brief overview of K-mean clustering algorithm with image processing example.
NOTE: you can find code of k-mean clustering algorithm for image processing in notes.
Introductory session for basic matlab commands and a brief overview of K-mean clustering algorithm with image processing example.
NOTE: you can find code of k-mean clustering algorithm for image processing in notes.
Cost Efficient PageRank Computation using GPU : NOTESSubhajit Sahu
Highlighted notes on:
Cost Efficient PageRank Computation using GPU
This paper discusses the use of Aitken extrapolated Power method for PageRank computation. However, the results are unclear whether the performance improvement is due to GPU implementation, or due to use of Aitken extrapolation. The paper mentions a good performance improvement for damping factor values close to 1, and very low tolerance values which are usually not used for PageRank computation. It needs to be cross-checked to see if Aitken extrapolation provides and reduction of iterations on CPU only (as the same effect would be observed on the GPU, only timings change).
k-Means is a rather simple but well known algorithms for grouping objects, clustering. Again all objects need to be represented as a set of numerical features. In addition the user has to specify the number of groups (referred to as k) he wishes to identify. Each object can be thought of as being represented by some feature vector in an n dimensional space, n being the number of all features used to describe the objects to cluster. The algorithm then randomly chooses k points in that vector space, these point serve as the initial centers of the clusters. Afterwards all objects are each assigned to center they are closest to. Usually the distance measure is chosen by the user and determined by the learning task. After that, for each cluster a new center is computed by averaging the feature vectors of all objects assigned to it. The process of assigning objects and recomputing centers is repeated until the process converges. The algorithm can be proven to converge after a finite number of iterations. Several tweaks concerning distance measure, initial center choice and computation of new average centers have been explored, as well as the estimation of the number of clusters k. Yet the main principle always remains the same. In this project we will discuss about K-means clustering algorithm, implementation and its application to the problem of unsupervised learning
Dimensionality Reduction and feature extraction.pptxSivam Chinna
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.
Cost Efficient PageRank Computation using GPU : NOTESSubhajit Sahu
Highlighted notes on:
Cost Efficient PageRank Computation using GPU
This paper discusses the use of Aitken extrapolated Power method for PageRank computation. However, the results are unclear whether the performance improvement is due to GPU implementation, or due to use of Aitken extrapolation. The paper mentions a good performance improvement for damping factor values close to 1, and very low tolerance values which are usually not used for PageRank computation. It needs to be cross-checked to see if Aitken extrapolation provides and reduction of iterations on CPU only (as the same effect would be observed on the GPU, only timings change).
k-Means is a rather simple but well known algorithms for grouping objects, clustering. Again all objects need to be represented as a set of numerical features. In addition the user has to specify the number of groups (referred to as k) he wishes to identify. Each object can be thought of as being represented by some feature vector in an n dimensional space, n being the number of all features used to describe the objects to cluster. The algorithm then randomly chooses k points in that vector space, these point serve as the initial centers of the clusters. Afterwards all objects are each assigned to center they are closest to. Usually the distance measure is chosen by the user and determined by the learning task. After that, for each cluster a new center is computed by averaging the feature vectors of all objects assigned to it. The process of assigning objects and recomputing centers is repeated until the process converges. The algorithm can be proven to converge after a finite number of iterations. Several tweaks concerning distance measure, initial center choice and computation of new average centers have been explored, as well as the estimation of the number of clusters k. Yet the main principle always remains the same. In this project we will discuss about K-means clustering algorithm, implementation and its application to the problem of unsupervised learning
Dimensionality Reduction and feature extraction.pptxSivam Chinna
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
1. Ashoka bairwa
Page 1
CENTRAL UNIVERSITY OF HARYANA
Department of Computer Science & Engineering under SOET
MACHINE LEARNING LAB
Submitted by
Ashoka
Roll No:- 191890
Submitted to
Dr. Sangeeta
Assistant Professor
Central University of Haryana (SOET)
2. Ashoka bairwa
Page 2
PRACTICAL-1
Aim: Introduction about Principal Component Analysis (PCA) feature extraction.
Theory:
Principal Component Analysis, or PCA for short, is a method for reducing the dimensionality of
data.
It can be thought of as a projection method where data with m-columns (features) is projected into a
subspace with m or fewer columns, whilst retaining the essence of the original data.
The PCA method can be described and implemented using the tools of linear algebra.
Implementation:
PCA is an operation applied to a dataset, represented by an n x m matrix A that results in a projection
of A which we will call B. Let’s walk through the steps of this operation.
The first step is to calculate the mean values of each column.
Or
Next, we need to center the values in each column by subtracting the mean column value.
The next step is to calculate the covariance matrix of the centered matrix C.
Correlation is a normalized measure of the amount and direction (positive or negative) that two columns
change together. Covariance is a generalized and unnormalized version of correlation across multiple
columns. A covariance matrix is a calculation of covariance of a given matrix with covariance scores for
every column with every other column, including itself.
3. Ashoka bairwa
Page 3
Finally, we calculate the eigen decomposition of the covariance matrix V. This results in a list of eigenvalues
and a list of eigenvectors.
The eigenvectors represent the directions or components for the reduced subspace of B, whereas the
eigenvalues represent the magnitudes for the directions. For more on this topic, see the post:
Gentle Introduction to Eigen decomposition, Eigenvalues, and Eigenvectors for Machine Learning
The eigenvectors can be sorted by the eigenvalues in descending order to provide a ranking of the
components or axes of the new subspace for A.
If all eigenvalues have a similar value, then we know that the existing representation may already be
reasonably compressed or dense and that the projection may offer little. If there are eigenvalues close to
zero, they represent components or axes of B that may be discarded.
A total of m or less components must be selected to comprise the chosen subspace. Ideally, we would select
k eigenvectors, called principal components, that have the k largest eigenvalues.
Other matrix decomposition methods can be used such as Singular-Value Decomposition, or SVD. As such,
generally the values are referred to as singular values and the vectors of the subspace are referred to as
principal components.
Once chosen, data can be projected into the subspace via matrix multiplication.
Where A is the original data that we wish to project, B^T is the transpose of the chosen principal
components and P is the projection of A.
This is called the covariance method for calculating the PCA, although there are alternative ways to to
calculate it.
5. Ashoka bairwa
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Reusable Principal Component Analysis
➢ We can calculate a Principal Component Analysis on a dataset using the PCA() class in the
scikit-learn library. The benefit of this approach is that once the projection is calculated, it can
be applied to new data again and again quite easily.
➢ When creating the class, the number of components can be specified as a parameter.
➢ The class is first fit on a dataset by calling the fit() function, and then the original dataset or
other data can be projected into a subspace with the chosen number of dimensions by calling the
transform() function.
➢ Once fit, the eigenvalues and principal components can be accessed on the PCA class via the
explained_variance_ and components_ attributes.