Elements of Dimensionality Reduction and Manifold Learning
暫譯: 降維與流形學習的元素

降維（Dimensionality reduction），也稱為流形學習（manifold learning），是機器學習的一個領域，用於從數據中提取有用的特徵，以便更好地表示數據或區分類別。本書對線性和非線性降維及流形學習進行了全面的回顧。降維的三個主要方面包括：光譜降維（spectral dimensionality reduction）、概率降維（probabilistic dimensionality reduction）和基於神經網絡的降維（neural network-based dimensionality reduction），這三者分別從幾何學、概率學和信息論的角度探討降維的問題。本書還解釋了線性代數、優化和核函數的必要背景和前提知識，以確保讀者對算法有全面的理解。

本書中介紹的工具可應用於各種涉及特徵提取、圖像處理、計算機視覺和信號處理的應用。這本書適合希望深入了解各種提取、轉換和理解數據結構方法的廣泛讀者群。目標讀者包括學術界、學生和行業專業人士。學術研究人員和學生可以將本書作為機器學習和降維的教科書。數據科學家、機器學習科學家、計算機視覺科學家和計算機科學家可以將本書作為參考資料。對於統計學家在統計學習領域和應用數學家在流形及子空間分析領域也會有所幫助。行業專業人士，包括應用工程師、數據工程師以及從事機器學習的各科學領域的工程師，可以將本書作為從數據中提取特徵的指南，因為行業中的原始數據通常需要預處理。

本書以理論為基礎，但提供了詳細的解釋和多樣的例子，以提高讀者對高級主題的理解。高級方法以逐步的方式進行解釋，使各個水平的讀者都能跟隨推理，深入理解概念。本書不假設讀者具備機器學習的高級理論背景，並提供必要的背景知識，雖然建議具備本科級別的線性代數和微積分背景。

Benyamin Ghojogh received the B.Sc. degree in electrical engineering from the Amirkabir University of Technology, Tehran, Iran, in 2015, the M.Sc. degree in electrical engineering from the Sharif University of Technology, Tehran, Iran, in 2017, and the Ph.D. in electrical and computer engineering (in the area of pattern analysis and machine intelligence) from the University of Waterloo, Waterloo, ON, Canada, in 2021. He was a postdoctoral fellow, focusing on machine learning, at the University of Waterloo, in 2021. His research interests include machine learning, dimensionality reduction, manifold learning, computer vision, data science, and deep learning.

Mark Crowley:

Mark Crowley has a PhD in Computer Science from the University of British Columbia and was a postdoctoral fellow at the Oregon State University. He is now an Associate Professor in the Department of Electrical and Computer Engineering at the University of Waterloo and regularly teaches undergraduate and graduate courses on software programming, artificial intelligence, and data analysis. He is a member of the Waterloo Artificial Intelligence Institute. He carries out research to find dependable and transparent ways to augment human decision making in complex domains, especially in the presence of spatial structure, streaming data, and uncertainty. His research group focuses on developing new algorithms within the fields of reinforcement learning, deep learning, and manifold learning. This often involves collaboration with industry and policy makers in diverse fields such as sustainable forest management, ecology, autonomous driving, physical chemistry, and medical imaging.

Fakhri Karray:

Fakhreddine (Fakhri) Karray is the Loblaws Research Chair in Artificial Intelligence in the department of electrical and computer engineering at the University of Waterloo, Canada. He is the founding co-director of the University of Waterloo AI Institute. He is currently serving as the Provost and Professor of Machine Learning at the Mohamed bin Zayed University of Artificial Intelligence, a first of its kind graduate level, research based artificial intelligence university. Fakhri's research interests are in the areas of advances in machine learning, operational AI, cognitive machines, natural human-machine interaction, autonomous and intelligent systems. Applications of his research include virtual care systems, cognitive and self-aware machines/robots/vehicles, predictive analytics in supply chain management and intelligent transportation systems. Recent work of Fakhri and his research team on deep learning-based driver behavior recognition and prediction has been featured on The Washington Post, Wired Magazine, Globe and Mail, CBC radio and Canada's Discovery Channel. He was honored in 2021 by the IEEE Vehicular Technology Society (VTS) for his novel work on improving traffic flow prediction using weather Information in connected cars through deep learning and tools of AI and received the Society's 2021 Best Land Transportation Paper Award.

Fakhri is the co-author of a textbook on applied artificial intelligence: Soft Computing and Intelligent Systems Design (Pearson Education Publishing, 2004). He has published extensively in the general field of pattern analysis and machine intelligence and is the author of 20 US registered patents. He is the Associate Editor (AE) of flagship journals in the field of AI and intelligent systems, including the IEEE Transactions on Cybernetics, the IEEE Transactions on Neural Networks and Learning Systems and the IEEE Computational Intelligence Magazine. He served as the AE and Guest Editor for the IEEE Transactions on Mechatronics, the IEEE Computational Intelligence Magazine and IEEE Access (special issue on IoMT). He also serves on several editorial boards of AI-related journals and has served as the General Chair/Program Chair for several international conferences in the field of intelligent systems. Fakhri is the co-founder and Chief Scientist of Yourika.ai, a provider of AI based online learning systems. He is a Fellow of the IEEE, a Fellow of the Canadian Academy of Engineering, a Fellow of the Engineering Institute of Canada and a Fellow of the Kavli Frontiers of. He received his PhD from the University of Illinois Urbana-Champaign, USA, and completed his undergraduate engineering degree at the National Engineering School of Tunis, Tunisia.

Ali Ghodsi:

Ali Ghodsi is a Professor of Statistics and Computer Science at the University of Waterloo in Ontario, Canada, and a member of the Waterloo Artificial Intelligence Institute. His current research sweeps across a broad swath of AI encompassing machine learning, deep learning, and dimensionality reduction. He regularly teaches courses on these topics. He studies theoretical frameworks and develops new machine-learning algorithms for analyzing large-scale data sets, with applications in natural language processing, bioinformatics, pattern recognition, computer vision, and sequential decision making. Dr. Ghodsi's work has been published extensively in high-quality proceedings and journals, and he is the co-author of several US patents. His popular lectures on YouTube have more than one million views.

**Benyamin Ghojogh:**
Benyamin Ghojogh於2015年在伊朗德黑蘭的阿米爾卡比爾科技大學獲得電機工程學士學位，2017年在伊朗德黑蘭的沙里夫科技大學獲得電機工程碩士學位，並於2021年在加拿大安大略省滑鐵盧大學獲得電機與計算機工程博士學位（專攻於模式分析與機器智慧）。他於2021年在滑鐵盧大學擔任專任研究員，專注於機器學習。他的研究興趣包括機器學習、降維、流形學習、計算機視覺、數據科學和深度學習。

**Mark Crowley:**
Mark Crowley擁有不列顛哥倫比亞大學的計算機科學博士學位，並曾在俄勒岡州立大學擔任專任研究員。他目前是滑鐵盧大學電機與計算機工程系的副教授，定期教授有關軟體編程、人工智慧和數據分析的本科及研究生課程。他是滑鐵盧人工智慧研究所的成員。他的研究旨在尋找可靠且透明的方法，以增強人類在複雜領域中的決策能力，特別是在存在空間結構、串流數據和不確定性的情況下。他的研究小組專注於在強化學習、深度學習和流形學習領域內開發新算法，這通常涉及與可持續森林管理、生態學、自動駕駛、物理化學和醫學影像等多個領域的產業和政策制定者的合作。

**Fakhri Karray:**
Fakhreddine (Fakhri) Karray是加拿大滑鐵盧大學電機與計算機工程系的人工智慧Loblaws研究主席。他是滑鐵盧大學人工智慧研究所的創始共同主任。目前，他擔任阿布扎比穆罕默德·本·扎耶德人工智慧大學的教務長及機器學習教授，這是一所首創的研究型人工智慧研究生大學。Fakhri的研究興趣包括機器學習的進展、操作性人工智慧、認知機器、自然人機互動、自主和智能系統。他的研究應用包括虛擬護理系統、認知和自我意識的機器/機器人/車輛、供應鏈管理中的預測分析和智能交通系統。Fakhri及其研究團隊近期在基於深度學習的駕駛行為識別和預測方面的工作曾被《華盛頓郵報》、《連線雜誌》、《環球郵報》、《CBC廣播電台》和加拿大探索頻道報導。他於2021年因其在連接汽車中利用天氣資訊改善交通流量預測的創新工作而獲得IEEE車輛技術學會(VTS)的榮譽，並獲得該學會的2021年最佳陸上交通論文獎。
Fakhri是應用人工智慧教科書《軟計算與智能系統設計》（Pearson Education Publishing, 2004）的共同作者。他在模式分析和機器智慧的廣泛領域發表了大量論文，並擁有20項美國註冊專利。他是人工智慧和智能系統領域的旗艦期刊的副編輯，包括IEEE《網絡控制學報》、《神經網絡與學習系統學報》和IEEE《計算智能雜誌》。他曾擔任IEEE《機電一體化學報》、《計算智能雜誌》和IEEE Access（物聯網醫療特刊）的副編輯和客座編輯。他還在多個與人工智慧相關的期刊編輯委員會中任職，並曾擔任多個智能系統領域國際會議的總主席/程序主席。Fakhri是Yourika.ai的共同創辦人和首席科學家，該公司提供基於人工智慧的在線學習系統。他是IEEE會士、加拿大工程學院會士、加拿大工程學會會士及Kavli Frontiers的會士。他在美國伊利諾伊大學香檳分校獲得博士學位，並在突尼西亞國立工程學院完成本科学位。

**Ali Ghodsi:**
Ali Ghodsi是加拿大安大略省滑鐵盧大學的統計學和計算機科學教授，也是滑鐵盧人工智慧研究所的成員。他目前的研究涵蓋機器學習、深度學習和降維等廣泛的人工智慧領域。他定期教授這些主題的課程。他研究理論框架並開發新的機器學習算法，以分析大規模數據集，應用於自然語言處理、生物信息學、模式識別、計算機視覺和序列決策。Ghodsi博士的研究成果在高品質的會議和期刊上廣泛發表，並且是幾項美國專利的共同作者。他在YouTube上的熱門講座已獲得超過一百萬次觀看。