1 - 7 of 7 Chapters
[A brief introduction to dimensionality reduction and manifold learning is provided and supported by a visual example. The goals of the book and its place in the literature is given, while the chapter is concluded by an outline of the remainder of the book.]
[In this chapter a common mathematical framework is provided which forms the basis for subsequent chapters. Generic aspects are covered, after which specific dimensionality reduction approaches are briefly described.]
[In this chapter, an overview of some of the key issues associated with modelling manifolds are provided. This covers the construction of neighbourhood graphs, and automatic estimation of relevant parameters; how manifold modelling techniques deal with various topologies of the data; and the...
[In this chapter, various approaches are considered to estimate the intrinsic dimensionality of datasets. These approaches look at the spectrum of eigenvalues and also local and global aspects of the data. In addition, limitations of existing dimensionality reduction approaches are discussed,...
[This chapter seeks to outline and assess the various methods for the out-of-sample extension problem (incorporating new points from the high-dimensional space to the low-dimensional space) and the pre-image problem (incorporating new points from the low-dimensional space to the high-dimensional...
[In this chapter the problems of using spectral dimensionality reduction with large scale datasets are outlined along with various solutions to these problems. The computational complexity of various spectral dimensionality reduction algorithms are looked at in detail. There is also often much...
[In this “postscript” a number of aspects are discussed which include how to measure success, non-spectral dimensionality techniques, and also available implementations. The chapter concludes with future research considerations.]
Read and print from thousands of top scholarly journals.
Continue with Facebook
Log in with Microsoft
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Sign Up Log In
To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.