data science course

Views:
 
Category: Education
     
 

Presentation Description

If you are looking for data science certification in Muscat. You are at the right place - ExcelR … ExcelR is global training provider pertaining to Data Science delivering training in Middle east, USA, UK, Malaysia and India. ExcelR offers data science certification the most comprehensive Data Science course in the market. The program will cover the complete Data Science lifecycle concepts starting from Data Extraction, Data Cleansing, Data Exploration, Data Transformation, Feature Engineering, Data Integration, Data Mining, building Prediction models, Data Visualization and deploying the solution to the customer.

Comments

Presentation Transcript

slide 1:

Singular Value Decomposition SVD

slide 2:

Matrix Transpose

slide 3:

Matrix Multiplication

slide 4:

Matrix Inverse                 × 1 0 ... 0 0 0 ...1 0 0 . ... . . . . . . 0 0 ... 1 0 0 0 ... 0 1 : matrix Identity A 1 - B Then matrix identity If I B A

slide 5:

X UΣV T rxr diagonal matrix with r non-zero diagonal elements U and V are Orthonormal matrices

slide 6:

OPTIONAL OPTIONAL OPTIONAL OPTIONAL R Code Mmatrixc10000004030000002000nrow4ncol5 XsvdM Xu Xd Xv XudiagXdtXv 1 0 0 0 2 0 0 1 0 4 0 0 0 0 1 0 0 0 0 0 3 0 0 0 1 0 0 0 3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 2.24 0 0.45 0 0 0 0.89 0 4 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 V T x x X U ∑

slide 7:

Applications of SVD in image processing – closest rank-k approximation for a matrix X – Each term in the summation expression above is called principal image v u X T i i k i i k Σ ∑ 1

slide 8:

Original matrix X Original size 1 0 0 0 2 4520 bytes 0 0 3 0 0 0 0 0 0 0 0 4 0 0 0 1 0 0 0 2 0 0 1 0 4 0 0 0 0 1 0 0 0 0 0 3 0 0 0 1 0 0 0 3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 2.24 0 0.45 0 0 0 0.89 0 4 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 V T x x X U ∑ k1 0 x 4 x 0 1 0 0 0 0 0 0 0 0 Compressed size 0 0 0 0 0 0 41+1+1510 bytes 0 0 0 0 0 0 1 0 4 0 0 0

slide 9:

k2 0 0 x 4 0 x 0 1 0 0 0 0 0 0 0 0 Compressed size 0 1 0 3 0 0 1 0 0 0 0 3 0 0 42+2+2520 bytes 0 0 0 0 0 0 0 1 0 0 4 0 0 0 k3 0 0 1 x 4 0 0 x 0 1 0 0 0 1 0 0 0 2 Com pressed size 0 1 0 0 3 0 0 0 1 0 0 0 0 3 0 0 4 3 +3+3 5 3 0 bytes 0 0 0 0 0 2.2 4 0 .4 5 0 0 0 0 .89 0 0 0 0 0 1 0 0 0 4 0 0 0 k4 0 0 1 0 4 0 0 0 0 1 0 0 0 1 0 0 0 2 Com pressed size 0 1 0 0 0 3 0 0 0 0 1 0 0 0 0 3 0 0 4 4 +4 +4 5 4 0 bytes 0 0 0 -1 0 0 2 .2 4 0 0 .4 5 0 0 0 0 .8 9 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0 0 0 x x

slide 10:

The image compression example in http://journal.batard.info/post/2009/04/08/svd- fun-profit • Original size 384384 bytes 147456 bytes • k1: 3841+1+1384769 bytes • k10: 38410+10+103847690 bytes • k20: 38420+20+2038415380 bytes • k50: 38450+50+5038438450 bytes • k100: 384100+100+10038476900 bytes • k200: 384200+200+200384153800 bytes

authorStream Live Help