PPT-Dimensionality Reduction:

SVD amp CUR Mining of Massive Datasets Jure Leskovec Anand Rajaraman Jeff Ullman Stanford University httpwwwmmdsorg Note to other teachers and users of these slides We would be delighted if you found this our material useful in giving your own lectures Feel free to use these slides verbatim or to modify them to fit your own needs. PCA facilitates dimensionality reduction for of64258ine clus tering of users and rapid computation of recommendations For a database of users standard nearestneighbor tech niques require processing time to compute recom mendations whereas Eigentaste We extend this concept to robotic hands and show how a similar dimensionality reduction can be de64257ned for a number of different hand models This framework can be used to derive planning algorithms that produce stable grasps even for highly compl JP van der Maaten EO Postma HJ van den Herik MICC Maastricht University PO Box 616 6200 MD Maastricht The Netherlands Abstract In recent years a variety of nonlinear dimensionality reduction techniques have been proposed many of which rely on the Introduction Mapping of multivariate data low-dimensional manifolds for visual in- spection is a commonly used technique in data analysis. The discovery of mappings that reveal the salient features of Presented by: Johnathan Franck. Mentor: . Alex . Cloninger. Outline. Different Representations. 5 Techniques. Principal component . analysis (PCA)/. Multi-dimensional . scaling (MDS). Sammons non-linear mapping. Computer Graphics Course. June 2013. What is high dimensional data?. Images. Videos. Documents. Most data, actually!. What is high dimensional data?. Images – dimension 3·X·Y. Videos – dimension of image * number of frames. Brendan and Yifang . April . 21 . 2015. Pre-knowledge. We define a set A, and we find the element that minimizes the error. We can think of as a sample of . Where is the point in C closest to X. . CISC 5800. Professor Daniel Leeds. The benefits of extra dimensions. Finds existing complex separations between classes. 2. The risks of too-many dimensions. 3. High dimensions with kernels over-fit the outlier data. Principle Component Analysis. Why Dimensionality Reduction?. It becomes more difficult to extract meaningful conclusions from a data set as data dimensionality increases--------D. L. . Donoho. Curse of dimensionality. Presented by: Johnathan Franck. Mentor: . Alex . Cloninger. Outline. Different Representations. 5 Techniques. Principal component . analysis (PCA)/. Multi-dimensional . scaling (MDS). Sammons non-linear mapping. is an important tool in machine learning/data mining, we must always be aware that it can distort the data in misleading ways.. Above is a two dimensional projection of an intrinsically three dimensional world….. Devansh Arpit. Motivation. Abundance of data. Required storage space explodes!. Images. Documents. Videos. Motivation. Speedup Algorithms. Motivation. Dimensionality reduction for noise filtering. Vector Representation. John A. Lee, Michel Verleysen, . Chapter4 . 1. Distance Preservation. دانشگاه صنعتي اميرکبير. (. پلي تکنيک تهران). 2. The motivation behind distance preservation is that any . Chapter 3. . Data Preprocessing. Jiawei Han, Computer Science, Univ. Illinois at Urbana-Champaign. , 2017. 1. 9/11/17. 2. Chapter 3: Data Preprocessing. Data Preprocessing: An Overview. Data . Cleaning.