CS 168 : The Modern Algorithmic Toolbox
نویسندگان
چکیده
Principal components analysis (PCA) is a basic and widely used technique for exploring data. If you go on to take specialized courses in machine learning or data mining, you’ll certainly hear more about it. The goal of this lecture is develop your internal mapping between the linear algebra used to describe the method and the simple geometry that explains what’s really going on. Ideally, after understanding this lecture, PCA should seem almost obvious in hindsight.
منابع مشابه
CS 168 : The Modern Algorithmic Toolbox Lectures # 17 and # 18 : Spectral Graph Theory
Most of our lectures thus far have been motivated by concrete problems, and the problems themselves led us to the algorithms and more widely applicable techniques and insights that we then went on to discuss. This section has the opposite structure: we will begin with the very basic observation that graphs can be represented as matrices, and then ask “what happens if we apply the linear algebra...
متن کاملCS 168 : The Modern Algorithmic Toolbox Lectures # 11 and # 12 : Spectral Graph Theory
Most of our lectures thus far have been motivated by concrete problems, and the problems themselves led us to the algorithms and more widely applicable techniques and insights that we then went on to discuss. This section has the opposite structure: we will begin with the very basic observation that graphs can be represented as matrices, and then ask “what happens if we apply the linear algebra...
متن کاملCS 168 : The Modern Algorithmic Toolbox Lecture # 5 : Generalization ( Or , How Much Data Is Enough ?
When analyzing a data set, you can be in one of two different modes. In the first mode, you really care about understanding the data set at hand. For example, in sociology, often the main point of a research project is to understand deeply the peculiarities of a single data set (e.g., the friendship structure among the 34 members of a karate club [3]). In the second mode, you care about the dat...
متن کاملCS 168 : The Modern Algorithmic Toolbox Lecture # 8 : How PCA Works
Last lecture introduced the idea of principal components analysis (PCA). The definition of the method is, for a given data set and parameter k, to compute the k-dimensional subspace (through the origin) that minimizes the average squared distance between the points and the subspace, or equivalently that maximizes the variance of the projections of the data points onto the subspace. We talked ab...
متن کاملCS168: The Modern Algorithmic Toolbox Lecture #14: Linear and Convex Programming, with Applications to Sparse Recovery
Recall the setup in compressive sensing. There is an unknown signal z ∈ R, and we can only glean information about z through linear measurements. We choose m linear measurements a1, . . . , am ∈ R. “Nature” then chooses a signal z, and we receive the results b1 = 〈a1, z〉, . . . , bm = 〈am, z〉 of our measurements, when applied to z. The goal is then to recover z from b. Last lecture culminated i...
متن کامل