PPT-While dimensionality reduction

is an important tool in machine learningdata 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. 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 . local. image . descriptors. . into. . compact. . codes. Authors. :. Hervé. . Jegou. Florent. . Perroonnin. Matthijs. . Douze. Jorge. . Sánchez. Patrick . Pérez. Cordelia. Schmidt. Presented. Presented by: Johnathan Franck. Mentor: . Alex . Cloninger. Outline. Different Representations. 5 Techniques. Principal component . analysis (PCA)/. Multi-dimensional . scaling (MDS). Sammons non-linear mapping. Dimensionality Reduction. Author: . Christoph. . Eick. The material is mostly based on the . Shlens. PCA. Tutorial . http://www2.cs.uh.edu/~. ceick/ML/pca.pdf. . and . to a lesser extend based on material . http://www.cs.nyu.edu/yann (November2005.ToappearinCVPR2006)AbstractDimensionalityreductioninvolvesmappingasetofhighdimensionalinputpointsontoalowdimensionalmani-foldsothat 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. Kenneth D. Harris. April 29, 2015. Predictions in neurophysiology. Predict neuronal activity from sensory stimulus/behaviour. “encoding model”. Predict stimulus/behaviour from neuronal activity. “decoding model”. Devansh Arpit. Motivation. Abundance of data. Required storage space explodes!. Images. Documents. Videos. Motivation. Speedup Algorithms. Motivation. Dimensionality reduction for noise filtering. Vector Representation. Aayush Mudgal [12008]. Sheallika Singh [12665]. What is Dimensionality Reduction ?. Mapping . of data to lower dimension such . that:. . uninformative variance is . discarded,. . or a subspace where data lives is . k. Ramachandra . murthy. Why Dimensionality Reduction. ?. It . is so easy and convenient to collect . data. Data is not collected only for data mining. Data . accumulates in an unprecedented speed. Data pre-processing . 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.