Big Data Analytics. Special Topics for Computer Science CSE CSE Jan 21

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1 Big Data Analytics Special Topics for Computer Science CSE CSE Jan 1 Fei Wang Associate Professor Department of Computer Science and Engineering fei_wang@uconn.edu

2 Project Rules

3 Literature Survey Define a topic yourself. I will also provide a set of topics. The papers you surveyed should be prestigious (i.e., either on major conference/journal venues or with good GoogleScholar citations) Proposal should include topic and a set of references (at least 0) The report should include the following components: 1) introduction of the topic; ) the state-of-the-art; ) empirical comparative study; ) discussion; ) future directions

4 Final Project You need to find topic, define problem, find data yourself. Do not expect I will find project/provide data for you. However, if at proposal I see problems and you really have difficulties, I will help. Proposal should include the following aspects: 1) problem; ) data; ) what tools/algorithms you want to apply; ) what results/ insights you expect to see. Proposal should be at least pages. Final project report should include the following components: 1) introduction and background of the problem; ) data description; ) tool/algorithm description; ) comprehensive experimental results and analysis; ) open problems/future research.

5 Other Requirements Each group with maximum of students, minimum of 1 student, i.e., you can do project by yourself. I expect the same group do both literature survey and final project. For students also taking my Independent Study: You must do the literature survey and project by yourself! You are strongly encouraged to hook up your project with your own research While I use Python or MATLAB in the course instruction, but definitely you can use other languages for your survey and project You are required to write your proposals and reports using Latex. Please follow this page to find the templates.

6 Survey Topics Predictive Modeling Logistic Regression Support Vector Machine Decision Tree Regression (least square, generalized linear model ) Ensemble methods (Bagging, Boosting, Random Forest, Generalized Additive Model, TreeNet )

7 Survey Topics Clustering Kmeans and Hierarchical Clustering Spectral Clustering Ensemble Methods

8 Survey Topics Feature Engineering Feature selection methods Linear feature extraction methods Nonlinear feature extraction methods Temporal feature extraction

9 Survey Topics Scalability Online methods Distributed methods

10 Survey Topics Matrix Factorization Multitask Learning Transfer learning Kernel Learning Sparse Learning Differential Privacy Survival Analysis Deep Learning

11 Reference Book

12 Where to Find Papers Data Mining Conference: KDD, ICDM, SDM Journal: ACM TKDD, IEEE TKDE, DMKD Machine Learning Conference: ICML, NIPS Journal: JMLR, Machine Learning, IEEE PAMI Statistics: JASA, AoS, JRSSB, Biometrika Optimization: SIAM Journal on Optimization

13 Mathematical & Programming Basics

14 MATLAB

15 Python

16 Definitions

17 Scalar A number length, area, density, pressure, temperature, Magnitude only! a, b, c...

18 Vector x a = A collection of scalars a 1 a... a> =[a 1,a,,a d ] o magnitude direction y a d a a.t Transpose d is called the dimensionality of vector a Scalar is one-dimensional vector

19 Matrix A A collection of vectors A 11 A 1 A 1n A 1 A A n A =[a 1, a,, a n ]= A d1 A d A dn > A 11 A 1 A n1 A 1 A A n A > = A 1d A d A nd A.T

20 Tensor mode 1 mode A collection of matrices mode mode (i,j,k)... mode k mode

21 Operations

22 Vector Addition > a 1 a a + b =. a d + b 1 b. b d = a 1 + b 1 a + b. a d + b d 1. Can vectors with different x a a+b dimensionalities be added b together?. The resultant thing is a o y vector or scalar? a+b a+b

23 Vector Inner Product ha, bi = a > b = P d k > i=1 a ib i = kak kbk cos( ) 1. Can inner product be operated x a s b on vectors with different o y dimensionalities?. The resultant thing is a vector or scalar? a *b numpy.dot(a.t,b)

24 Vector Outer Product Vector outer product: a 1 a a b = ab > = P. a d = P [b 1,b,,b d ] a 1 b 1 a 1 b a 1 b d a b 1 a b a b d a d b 1 a d b a d b d a*b numpy.outer(a,b) 1. Can outer product be operated on vectors with different dimensionalities?. The resultant thing is a vector or scalar?

25 Vector Norm ( ) :R d! R s (ca) =c (a)! (a + b) (a)+ (b) If (a) =0then a is a zero vector h i > P 1. The resultant thing is a 1-norm: kak 1 = P d i=1 a i > -norm: kak h = i p a > a P norm(a,k) vector or scalar?. Can vector norms be negative? numpy.linalg.norm(a,k)

26 Angle cos = a> b kak kbk x A A p The area under the parallelogram is > o a s b y kak kbk sin( )

27 Matrix Addition A 11 A 1 A 1n B 11 B 1 B 1n A 1 A A n A + B = B 1 B B n A d1 A d A dn B d1 B d B dn A 11 + B 11 A 1 + B 1 A 1n + B 1n A 1 + B 1 A + B A n + B n A d1 + B d1 A d + B d A dn + B dn A+B A+B 1. Can matrices with different dimensionalities be added together?. The resultant thing is a vector or scalar?

28 Hadamard Product A B oduct A 11 A 1 A 1n A 1 A A n A d1 A d A dn A 11 B 11 A 1 B 1 A 1n B 1n A 1 B 1 A B A n B n A d1 B d1 A d B d A dn B dn P A.*B A*B d1 d B 11 B 1 B 1n B 1 B B n B d1 B d B dn 1. What is the dimensionality requirement for matrix Hadamard product?. What is the dimensionality of the resultant matrix?

29 Matrix Multiplication A B AB i ij (AB) ij = P k A ikb ik j 1. What is the dimensionality requirement for matrix multiplication? A*B numpy.dot(a,b). What is the dimensionality of the resultant matrix?

30 Kronecker Product kron(a,b) P A B = numpy.kron(a,b) A 11 B A 1 B A 1n B A 1 B A B A n B A d1 B A d B A dn B 1. What is the dimensionality requirement for matrix Kronecker product?. What is the dimensionality of the resultant matrix?

31 More Definitions

32 Diagonal Matrix I = > D = D D D nn eye(n) numpy.identity(n) diag(d) numpy.diag(n)

33 Orthogonal Matrix A > A = AA > = I Semi- Orthogonal Matrix > A > A = I AA > = I

34 Eigenvalue Decomposition Av = v eig(a) numpy.linalg.eig(a) V is an orthogonal matrix AV = V. A = V V >

35 A = U V > Singular Value Decomposition svd(a) numpy.linalg.svd(a)

36 r vector decomposition Matrix Inverse AA 1 = A 1 A = I inv(a) numpy.linalg.inv(a) Matrix Moore-Penrose Pseudoinverse AA A = I A AA = I (AA ) > = AA pinv(a) numpy.linalg.pinv(a) (A A) > = A A