Math and Statistics for Data Science, and Engineering
Misc. Math. Data Science. Machine Learning. Optimization. Vector, PCA, Basis, Covariance Orthonormality: Orthonormal Vectors “In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. …
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“In mathematics, a set B of elements (vectors) in a vector space V is called a basis, if every element of V may be written in a unique way as a (finite) linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates on B of the …
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Optimization Problem: Advances in Missile Guidance, Control, and Estimation Preview: https://play.google.com/books/reader?id=A2PMBQAAQBAJ&hl=en_GB&pg=GBS.PR14 https://books.google.ca/books?id=A2PMBQAAQBAJ&pg=PA595&lpg=PA595&dq=force+moment+interaction+with+thrusters&source=bl&ots=BruxnXwLzp&sig=ACfU3U39G-l3xDzbotOBJHcMV5uR7DkciQ&hl=en&sa=X&ved=2ahUKEwjZpsT44afnAhXRJt8KHfPYCroQ6AEwCnoECAoQAQ#v=onepage&q=force%20moment%20interaction%20with%20thrusters&f=false "What is the difference between affine and linear? 4 Answers. A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so while the linear part fixes …
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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 …
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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. …
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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 …
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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) …
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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 …
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Optimization and Linear Algebra/Math from the Internet First order taylor approximation formula? https://www.thestudentroom.co.uk/showthread.php?t=1247928 Hessian Matrix https://en.wikipedia.org/wiki/Hessian_matrix "In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables." Use in optimization "Hessian matrices are …
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SeDuMi MATLAB add-on: solve optimization problems with linear, quadratic and semidefiniteness constraints "Abstract SeDuMi is an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This …
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https://www.coursera.org/lecture/state-estimation-localization-self-driving-cars/lesson-1-the-linear-kalman-filter-7DFmY https://d3c33hcgiwev3.cloudfront.net/gWbwrisXEem4egrIUlgmqg.processed/full/360p/index.webm?Expires=1579392000&Signature=gLd7RN8aqZhrNLNLl-huuNsIrkWnUp8gPUAMNqk6Xnkx0lmkMKE8XdXs5v7GGSMvq9ieVeR7MAi2bDz6pxUhgWspfMtnZZ2k2ZpKKzKdNoiFHW-zBVcnFTq~yPyC0ssd1gHzenk2SHqPBu1BhkHTqz7nhdXU08UQS-Z1w7qhwcw_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A *** *** 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: …
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“What is machine learning optimization? Optimization is the most essential ingredient in the recipe of machine learning algorithms. It starts with defining some kind of loss function/cost function and ends with minimizing the it using one or the other optimization routine.Sep 5, 2018” https://towardsdatascience.com/demystifying-optimizations-for-machine-learning-c6c6405d3eea Ordered vector space “Given a vector space V over the real …
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Design optimization https://medium.com/generative-design/design-optimization-2ec2ba3b40f7 Learning from nature https://medium.com/generative-design/learning-from-nature-fe5b7290e3de *** . **** . *** 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 FB Group on Learning/Teaching: https://www.facebook.com/banglasalearningschool Our …
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" The World is for Polymaths: An Interview with Sajid Amit, Academic, Researcher, and Development Strategist (Part One) Future Startup Face to Face | The Interview November 4, 2019 0 “When you have multiple lenses with which to consider a problem, it is an incredible advantage. The world is for polymaths,” says Sajid Amit as …
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"The core topics are cross-validation, shrinkage methods (ridge regression, the LASSO, etc.), neural networks, gradient boosting, separating hyperplanes, support vector machines, basis expansion and regularization (e.g., smoothing splines, wavelet smoothing, kernel smoothing), generalized additive models, bump hunting, multivariate adaptive regression splines (MARS), self-organizing maps, mixture model-based clustering, ensemble learning, and p>>n problems. For computing, the …
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Part 4: Some Basic Math/Stat Concepts for the wanna be Data Scientists Also for the Engineers in General Quadratic form “In multivariate statistics, if is a vector of random variables, and is an -dimensional symmetric matrix, then the scalar quantity is known as a quadratic form in . ” Ref: https://en.wikipedia.org/wiki/Quadratic_form_(statistics) Please also check matrix …
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Conditional Probability and PDF “The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A. ” “In the case where events A and B are independent (where event …
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Part 2: Some basic Math/Statistics concepts that Data Scientists (the true ones) will usually know/use (came across, studied, learned, used) Covariance and Correlation “Covariance is a measure of how two variables change together, but its magnitude is unbounded, so it is difficult to interpret. By dividing covariance by the product of the two standard deviations, …
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Chebyshev’s inequality “In probability theory, Chebyshev’s inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution’s values can be more than k standard deviations …
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Optimization Concepts: Convex sets: "A convex set is a set of points such that, given any two points A, B in that set, the line AB joining them lies entirely within that set. Intuitively, this means that the set is connected (so that you can pass between any two points without leaving the set) and …
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Learn more about Nonparametric Test https://www.sciencedirect.com/topics/medicine-and-dentistry/nonparametric-test Sensor Management for Large-Scale Multisensor-Multitarget Tracking," in Integrated Tracking, Classification, and Sensor Management: Theory and Applications http://download.e-bookshelf.de/download/0000/7142/31/L-G-0000714231-0002366034.pdf Approaches to Multisensor Data Fusion in Target Tracking: A Survey https://www.computer.org/csdl/journal/tk/2006/12/k1696/13rRUxBa56w Sensor fusion https://en.wikipedia.org/wiki/Sensor_fusion Sensor Fusion: Sensor fusion is the process of merging data from multiple sensors such that to reduce the …
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Kaiser-Meyer-Olkin (KMO) Test for Sampling Adequacy https://www.statisticshowto.datasciencecentral.com/kaiser-meyer-olkin/ KMO and Bartlett’s Test https://www.ibm.com/support/knowledgecenter/SSLVMB_23.0.0/spss/tutorials/fac_telco_kmo_01.html What should be ideal KMO value for factor analysis? https://www.researchgate.net/post/What_should_be_ideal_KMO_value_for_factor_analysis
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" Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function usinggradient descent, one takes steps proportional to the negative of the gradient (or approximategradient) of the function at the current point. Gradient descent – Wikipedia https://en.wikipedia.org/wiki/Gradient_descent " Gradient Descend # From …
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