Misc. Math for Data Science, Engineering, and/or Optimization

What is the Inverse of a Matrix?

https://www.mathsisfun.com/algebra/matrix-inverse.html

What is Norm?
“In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that satisfies certain properties pertaining to scalability and additivity, and assigns a strictly positive real number to each vector in a vector space over the field of real or complex numbers—except for the zero vector, which is assigned zero.[1]

A pseudonorm (seminorm), on the other hand, is allowed to assign zero to some non-zero vectors (in addition to the zero vector).[2]

The term “norm” is commonly used to refer to the vector norm in Euclidean space. It is known as the “Euclidean norm” (see below) which is technically called the L2-norm. The Euclidean norm maps a vector to its length in Euclidean space. Because of this, the Euclidean norm is often known as the magnitude.”

“A vector space on which a norm is defined is called a normed vector space. Similarly, a vector space with a seminorm is called a semi normed vector space. It is often possible to supply a norm for a given vector space in more than one way.”

https://en.wikipedia.org/wiki/Norm_(mathematics)

What is Linear programming?

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. ”

“More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where this function has the smallest (or largest) value if such a point exists.

Linear programs are problems that can be expressed in canonical form as

{\displaystyle {\begin{aligned}&{\text{Maximize}}&&\mathbf {c} ^{\mathrm {T} }\mathbf {x} \\&{\text{subject to}}&&A\mathbf {x} \leq \mathbf {b} \\&{\text{and}}&&\mathbf {x} \geq \mathbf {0} \end{aligned}}}

https://en.wikipedia.org/wiki/Linear_programming

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Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

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Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).

Investing in an ever-changing world

"Anything can happen in the short term but over a few decades the equity market has always produced very significant gains including periods of war, countless recessions and economic shocks. The best financial advice you can give to your children, grandchildren, nieces and nephews is to start as early as possible, stay invested and continue buying over time. Maximize tax advantaged accounts and stuff TFSAs with growth ETFs. Most importantly don’t lose money.

By Sinan Terzioglu, CFA, CIM, is a financial advisor with Turner Investments, Private Client Group, Raymond James Ltd."

https://www.greaterfool.ca/2020/01/26/investing-in-a-world-like-this/

Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada

*** . *** *** . *** . *** . ***

Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

Our free or paid training events: https://www.facebook.com/justetcsocial

Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).

Misc. Math. Might Relate to Optimization

find the equation for a line

http://www.webmath.com/_answer.php

Parametric forms for lines and vectors

https://www.futurelearn.com/courses/maths-linear-quadratic-relations/0/steps/12128

Solving Systems of Linear Equations Using Matrices

https://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html

Affine Space

Subspace
https://www.wolframalpha.com/input/?i=subspace

“What is an affine set?
A set is called “affine” iff for any two points in the set, the line through them is contained in the set. In other words, for any two points in the set, their affine combinations are in the set itself. Theorem 1. A set is affine iff any affine combination of points in the set is in the set itself.”
https://www.cse.iitk.ac.in/users/rmittal/prev_course/s14/notes/lec3.pdf [good one to check]

linear/conic/affine/convex combination

https://observablehq.com/@eliaskal/point-combinations-linear-conic-affine-convex

Related Course:
https://www.cse.iitk.ac.in/users/rmittal/prev_course/s14/course_s14.html

In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation.
en.wikipedia.org › wiki › Row_and_column_spaces

Row and column spaces – Wikipedia

Row and column spaces

https://en.wikipedia.org/wiki/Row_and_column_spaces

“Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:”

Infimum and supremum

From Wikipedia, the free encyclopedia

Jump to navigationJump to search
A set T of real numbers (hollow and filled circles), a subset S of T (filled circles), and the infimum of S. Note that for finite, totally ordered sets the infimum and the minimum are equal.


A set A of real numbers (blue circles), a set of upper bounds of A (red diamond and circles), and the smallest such upper bound, that is, the supremum of A (red diamond).

In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.[1] Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used.[1]

The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is the least element in T that is greater than or equal to all elements of S, if such an element exists.[1] Consequently, the supremum is also referred to as the least upper bound (or LUB).[1]


https://en.wikipedia.org/wiki/Infimum_and_supremum

Industry Job Prospect for Graph Mining

Industry Job Prospect for Graph Mining

Sample Jobs

https://www.careerbuilder.com/jobs-graph-mining

https://www.indeed.com/q-Graph-Mining-jobs.html

For example, Google works in the following areas of Graph Mining. Google has jobs for such. Also, Facebook and any other social networking site will have jobs in relation to Graph Mining. Computational Biology, Medicine Research, Drug Discovery, Disease Diagnosis, Transportation, Scheduling, Shipping Scheduling will have applications and jobs for Graph Mining.

Job Areas:

The general Mining (data based) jobs and Machine/Deep/Reinforcement Learning jobs will require Graph Mining expertise sometimes such as positions (real) : Research Intern – Deep Learning for Graphs, ML Engineer – Siri Knowledge Graph

Computer Networks, Network/Cyber Security application development (also R & D) positions might ask for Graph Mining expertise.

Graph Mining will have applications and jobs in Biological, Chemistry, Drug Design areas also in Transportation

Social Network Mining will always involve Graph Mining. Applications: Friend Recommendation

Trajectory Data Mining Jobs at Microsoft

https://www.microsoft.com/en-us/research/publication/trajectory-data-mining-an-overview/

Graph Mining Jobs (areas) at Google:
https://ai.google/research/teams/algorithms-optimization/graph-mining/

"Large-Scale Balanced Partitioning: Example Google Maps Driving Directions, Large-Scale Clustering:clustering graphs at Google scale, Large-Scale Connected Components, Large-Scale Link Modeling: similarity ranking and centrality metrics: link prediction and anomalous link discovery., Large-Scale Similarity Ranking: Personalized PageRank, Egonet similarity, Adamic Adar, and others, Public-private Graph Computation, Streaming and Dynamic Graph Algorithms, ASYMP: Async Message Passing Graph Mining, Large-Scale Centrality Ranking, Large-Scale Graph Building"

More Related Jobs:

Tools in Jobs/Jobs–https://www.researchgate.net/post/Can_you_suggest_a_graph_mining_tool

https://www.linkedin.com/jobs/gephi-jobs/

https://bit.ly/2Nwlnrp Data Scientist 2

Part X: Engineering Optimization: Mathematical Optimization

Good intro to: Quadratic Forms and Convexity
https://www.dr-eriksen.no/teaching/GRA6035/2010/lecture4.pdf

Concave Upward and Downward

https://www.mathsisfun.com/calculus/concave-up-down-convex.html

Convex functions and K-Convexityhttps://ljk.imag.fr/membres/Anatoli.Iouditski/cours/convex/chapitre_3.pdf



*** . *** . *** . ***
Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada

*** . *** *** . *** . *** . ***

Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

Our free or paid training events: https://www.facebook.com/justetcsocial

Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).

How Styline is Building the #FashionTech Company Where You Would Love to Work

"

How Styline is Building the #FashionTech Company Where You Would Love to Work

0
Since Marc Andreessen penned his famous “Why Software Is Eating the World” essay in The Wall Street Journal 8 years ago, the world of business has changed fundamentally. Today, the idea that every company needs to become a technology company is considered almost a cliché. No matter your industry, you’re expected to be reimagining your business. Fashion is no different. A new breed of companies that calls themselves fashion-tech is now slowly shaping the present and the future of fashion across the world. Some of these companies are mere marketplaces. Others are changing how and what people shop, wear and when. Others are launching new products using a combination of tech and common sense. We have seen the meteoric rise of companies like Rent the Runway to All Birds to a long list of other fashion-tech companies. "https://futurestartup.com/2019/12/25/how-styline-is-building-the-fashiontech-company-where-you-would-love-to-work/

Industry Job Prospect for Graph Mining

Industry Job Prospect for Graph Mining

Sample Jobs

https://www.careerbuilder.com/jobs-graph-mining

https://www.indeed.com/q-Graph-Mining-jobs.html

For example, Google works in the following areas of Graph Mining. Google has jobs for such. Also, Facebook and any other social networking site will have jobs in relation to Graph Mining. Computational Biology, Medicine Research, Drug Discovery, Disease Diagnosis, Transportation, Scheduling, Shipping Scheduling will have applications and jobs for Graph Mining.

Job Areas:

The general Mining (data based) jobs and Machine/Deep/Reinforcement Learning jobs will require Graph Mining expertise sometimes such as positions (real) : Research Intern – Deep Learning for Graphs, ML Engineer – Siri Knowledge Graph

Computer Networks, Network/Cyber Security application development (also R & D) positions might ask for Graph Mining expertise.

Graph Mining will have applications and jobs in Biological, Chemistry, Drug Design areas also in Transportation

Social Network Mining will always involve Graph Mining. Applications: Friend Recommendation

Trajectory Data Mining Jobs at Microsoft

https://www.microsoft.com/en-us/research/publication/trajectory-data-mining-an-overview/

Graph Mining Jobs (areas) at Google:
https://ai.google/research/teams/algorithms-optimization/graph-mining/

"Large-Scale Balanced Partitioning: Example Google Maps Driving Directions, Large-Scale Clustering:clustering graphs at Google scale, Large-Scale Connected Components, Large-Scale Link Modeling: similarity ranking and centrality metrics: link prediction and anomalous link discovery., Large-Scale Similarity Ranking: Personalized PageRank, Egonet similarity, Adamic Adar, and others, Public-private Graph Computation, Streaming and Dynamic Graph Algorithms, ASYMP: Async Message Passing Graph Mining, Large-Scale Centrality Ranking, Large-Scale Graph Building"

More Related Jobs:

Tools in Jobs/Jobs–https://www.researchgate.net/post/Can_you_suggest_a_graph_mining_tool

https://www.linkedin.com/jobs/gephi-jobs/

https://bit.ly/2Nwlnrp Data Scientist 2

https://bit.ly/2r04wFP Graph Jobs

https://indeedhi.re/2oHkOmo

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Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada

*** . *** *** . *** . *** . ***

Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

Our free or paid training events: https://www.facebook.com/justetcsocial

Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).

20 January, 2020 08:01

Background Required for taking a Graph Mining Course:

As long as you are interested, you can check a Graph Mining course.

However, a background in Computer Science/Engineering or related will be of great help. If you have taken courses such as Data Structure, Algorithms (and Computer Networks to some extent) – many course materials will be familiar to you.

No advance mathematics or statistics background is required. Will help for sure. However, there will be some equations here and there. In real applications, optimization approaches of such equations or creating (coming up with) such equations – will have research publication potentials.

In some areas, Big Data Technology Background such as Hadoop, Spark, or similar will help. Some Machine Learning Knowledge (clustering, Kmeans) will help you.

*** *** ***
Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada

*** . *** *** . *** . *** . ***

Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

Our free or paid training events: https://www.facebook.com/justetcsocial

Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).

Bayesian Statistics and Machine Learning

Bayesian Statistics and Machine Learning

“Bayesian inference is a method of statistical inference in which Bayes‘ theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics.”

en.wikipedia.org › wiki › Bayesian_inference

Bayesian inference – Wikipedia

“Firstly, (statistical) inference is the process of deducing properties about a population or probability distribution from data”

“Bayesian inference is therefore just the process of deducing properties about a population or probability distribution from data using Bayes’ theorem. That’s it.”
https://towardsdatascience.com/probability-concepts-explained-bayesian-inference-for-parameter-estimation-90e8930e5348

Introduction to Bayesian Inference

https://blogs.oracle.com/datascience/introduction-to-bayesian-inference

Bayesian Linear Regression

In the Bayesian viewpoint, we formulate linear regression using probability distributions rather than point estimates. The response, y, is not estimated as a single value, but is assumed to be drawn from a probability distribution. The model for Bayesian Linear Regression with the response sampled from a normal distribution is:”

https://towardsdatascience.com/introduction-to-bayesian-linear-regression-e66e60791ea7

“Bayesian model selection

Tom Minka

occam.gifBayesian model selection uses the rules of probability theory to select among different hypotheses. It is completely analogous to Bayesian classification.”

http://alumni.media.mit.edu/~tpminka/statlearn/demo/

Logistic Regression from Bayes’ Theorem

https://www.countbayesie.com/blog/2019/6/12/logistic-regression-from-bayes-theorem

Kernel Trick and Kernels
https://svivek.com/teaching/lectures/slides/svm/kernels.pdf

“When talking about kernels in machine learning, most likely the first thing that comes into your mind is the support vector machines (SVM)”

https://medium.com/@zxr.nju/what-is-the-kernel-trick-why-is-it-important-98a98db0961d

Gaussian Processes

“or why I don’t use SVMs”

https://mlss2011.comp.nus.edu.sg/uploads/Site/lect1gp.pdf

Gaussian Process Classification and Active Learning with Multiple Annotators

http://proceedings.mlr.press/v32/rodrigues14.pdf

“Assumed density filtering is an online inference algorithm. that incrementally updates the posterior over W after ob- serving new evidence.”

https://www.aaai.org/ocs/index.php/AAAI/AAAI16/paper/download/12391/11777

Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that leverages the factorization structure of the target distribution.

en.wikipedia.org › wiki › Expectation_propagation

Expectation propagation – Wikipedia

rejection sampling

In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or “accept-reject algorithm” and is a type of exact simulation method. The method works for any distribution in \mathbb {R} ^{m} with a density.

https://en.wikipedia.org/wiki/Rejection_sampling

Bayesian Deep learning

“However, graphical networks such as Bayesian networks are useful to model uncertainty along with causal inference and logic deduction. In this regard, Bayesian Deep learning combines perception (deep learning) with strong probabilistic inference which can estimate uncertainty.

www.quora.com › How-different-is-Bayesian-deep-learning-from-deep-…

How different is Bayesian deep learning from deep learning? – Quora

*** . . *** . ***
Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada

*** . *** *** . *** . *** . ***

Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

Our free or paid training events: https://www.facebook.com/justetcsocial

Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).

Salt

"DESCRIPTION

Pass the Salt is an investigation into the mysteries of one of our most fundamental elements. It’s a search for the real answers regarding the mounting debate about the benefits and dangers of salt.

https://gem.cbc.ca/media/the-nature-of-things/season-59/episode-9/38e815a-0122947a376"

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Note: Older short-notes from this site are posted on Medium: https://medium.com/@SayedAhmedCanada

*** . *** *** . *** . *** . ***

Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
Linkedin: https://ca.linkedin.com/in/sayedjustetc

Blog: http://Bangla.SaLearningSchool.com, http://SitesTree.com
Online and Offline Training: http://Training.SitesTree.com (Also, can be free and low cost sometimes)

Facebook Group/Form to discuss (Q & A): https://www.facebook.com/banglasalearningschool

Our free or paid training events: https://www.facebook.com/justetcsocial

Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. http://sitestree.com/training/

If you want to contribute to occasional free and/or low cost online/offline training or charitable/non-profit work in the education/health/social service sector, you can financially contribute to: safoundation at salearningschool.com using Paypal or Credit Card (on http://sitestree.com/training/enrol/index.php?id=114 ).