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Rehabilitating Isomap: Euclidean Representation of Geodesic Structure

arXiv.org Machine Learning

Manifold learning techniques for nonlinear dimension reduction assume that high-dimensional feature vectors lie on a low-dimensional manifold, then attempt to exploit manifold structure to obtain useful low-dimensional Euclidean representations of the data. Isomap, a seminal manifold learning technique, is an elegant synthesis of two simple ideas: the approximation of Riemannian distances with shortest path distances on a graph that localizes manifold structure, and the approximation of shortest path distances with Euclidean distances by multidimensional scaling. We revisit the rationale for Isomap, clarifying what Isomap does and what it does not. In particular, we explore the widespread perception that Isomap should only be used when the manifold is parametrized by a convex region of Euclidean space. We argue that this perception is based on an extremely narrow interpretation of manifold learning as parametrization recovery, and we submit that Isomap is better understood as constructing Euclidean representations of geodesic structure. We reconsider a well-known example that was previously interpreted as evidence of Isomap's limitations, and we re-examine the original analysis of Isomap's convergence properties, concluding that convexity is not required for shortest path distances to converge to Riemannian distances.


Two New Ways to Program Your AI

#artificialintelligence

"Some people have a way with words, and other people, uh, not have way." The scariest part of moving to a new country is learning a new language. You step off the plane and into a new land with illegible signs, strange customs, and unfamiliar culture. Whom do I ask for help? Where do I even start?


How To Create An AI (Artificial Intelligence) Startup

#artificialintelligence

Group of young business people are working together in modern office. According to research from IDC, the global spending on AI (Artificial Intelligence) is expected to hit $97.9 billion by 2023, up from $37.5 billion in 2019. This represents a compound annual growth rate of 28.4%. No doubt, this is an enormous opportunity for startups. "These days, almost every company needs to leverage AI in order to thrive and build a meaningful future," said Saar Yoskovitz, who is the CEO of Augury.


Artificial Intelligence Expert Certification

#artificialintelligence

Free Coupon Discount Preview this course Online Courses Udemy - ย Artificial Intelligence Expert Certification, A groundbreaking course that uncovers Artificial Intelligence (AI) powered secretive technologies, tools and websites Created by Srinidhi Ranganathan, Saranya Srinidhi


England ditches its shitty exam result algorithm after it penalized poorer students

#artificialintelligence

English school-leaving exam results will now be based on teacher assessments after the government scrapped a controversial algorithm that downgraded nearly 40% of predicted grades. The U-turn came after evidence emerged that students from fee-paying schools had disproportionately benefited from the algorithm, which used a formula based on a school's historical results and each pupil's attainment. In response, the government said students could appeal the results or resit exams in the fall. But a wave of student protests and a backlash from Conservative MPs have convinced the government to revert to center-assessed grades for both A-levels and GCSEs, the exams taken by 18 and 16โ€“year-old students respectively. However, students who had their results marked up by the algorithm can keep the higher grade.


Perform Cloud Data Science with Azure Machine Learning 2021

#artificialintelligence

Perform Cloud Data Science with Azure Machine Learning 2021 Udemy Coupon ED Final Prep For The Exam Test Your Knowledge Pass The First Time Job Interview Questions New Get Coupon Included in This Course 33 questions Description FULLY UPDATED to the last exam version! There are a lot of courses out there that are claiming that their courses are fully updated, but they're actually not! Our practice tests contain the new exam version. These questions and answers are the final step in your test preparation. Each Practice Test has: the right answer for each question Based on recent certification exams.


Full Stack Data Science: The Next Gen of Data Scientists Cohort

#artificialintelligence

Data science has been an eye-catching field for many years now to young individuals having formal education with a bachelors, masters or Ph.D. in computer science, statistics, business analytics, engineering management, physics, maths, or obviously data science. However, there are a lot of myths that people presume about data science. Over the years, I have spoken to a lot of data science aspirants about breaking into this field. Why is there all the hype about data science? Is it still statistics and machine learning that can help you break into this field?


Inbuilt biases and the problem of algorithms

#artificialintelligence

As the founders of the Institute for Ethical Artificial Intelligence in Education, we are appalled by the manner in which an algorithm has been used to decide students' A-level and GCSE grades (A-level results: No 10 hints algorithm set to be ditched in England, 17 August). The exam grading algorithm may not be sophisticated AI, but to be ethical it should still adhere to certain principles, including that it should impact positively on teaching and learning; be fair and explainable to the people on whom it impacts; and that it should use data that is not biased towards or against any particular group of people. The algorithm used this year to decide the grades for students who have worked hard in extremely difficult circumstances adheres to none of these principles. It is, without question, unethical and harmful to education in general and a significant number of pupils in particular. It is a gross abuse of the algorithmic approach.


The algorithms that make decisions about your life

#artificialintelligence

Thousands of students in England are angry about the controversial use of an algorithm to determine this year's GCSE and A-level results. They were unable to sit exams because of lockdown, so the algorithm used data about schools' results in previous years to determine grades. It meant about 40% of this year's A-level results came out lower than predicted, which has a huge impact on what students are able to do next. GCSE results are due out on Thursday. There are many examples of algorithms making big decisions about our lives, without us necessarily knowing how or when they do it.


The problem with AI developer tools for enterprises (and what IKEA has to do with it)

#artificialintelligence

The emergence of new technologies is usually accompanied with subsequent phases of expansion and contraction in the number of possible solution designs. It is no longer contentious that AI will transform many industries, often becoming a strategic advantage and even creating new "AI first" business models and companies. As a result, all major Cloud vendors (and countless startups) are piling on resources to bring AI developer tools to a broader audience, most importantly big enterprises. All of these vendors broadly attempt to solve the same user needs, but with distinctly different approaches and outcomes, leading to a proliferation in different designs. This phenomenon exists at every level of the stack and usually progresses from the bottom up.