data classification
play

Data Classification Linear Classifier II Latent Differential - PowerPoint PPT Presentation

Sep 19, 2023 •271 likes •637 views

Data Classification Linear Classifier II Latent Differential Analysis Mean Classification Memory If youre here, you are RED If youre here, you are BLUE 2 Back Linear Classifier A classifier that assigns a class to a new point

  1. Data Classification Linear Classifier II Latent Differential Analysis

  2. Mean Classification Memory If you’re here, you are RED If you’re here, you are BLUE 2 – Back

  3. Linear Classifier A classifier that assigns a class to a new point based on a separation hyperplane is called a linear classifier . The criterion for a linear classifier can be written as vector product, ie., there is a vector w and a number c such that a new data vector x is classified as being in group one exactly if

  4. Limitations of Mean Classifier Memory LOO accuracy: 66.6 % 2 – Back

  5. Linear Classifier Works Memory LOO performance: 100 % 2 – Back

  6. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix.

  7. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix.

  8. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix.

  9. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix.

  10. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix. Why doesn’t the mean classifier work here? Q1 1 The points are not linearly separable. 2 The covariance matrix is far from the identity matrix.

  11. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix. Observation 2: Mean Classification works great if the variables really are distributed with unit covariance matrix, but badly otherwise.

  12. Linear Discriminant Analysis Observation 1: Mean Classification is equivalent to classifying according to a Gaussian likelihood with identity as covariance matrix. Observation 2: Mean Classification works great if the variables really are distributed with unit covariance matrix, but badly otherwise. Linear Discriminant Analysis (LDA): Implement Observation 1, but using real data covariance matrix!

  13. Linear Discriminant Analysis Linear Discriminant Analysis (LDA): Classify according to a Gaussian likelihood with covariance matrix of the data. Which color does LDA classify this point to? Q2 1 RED 2 Blue

  14. Linear Discriminant Analysis Linear Discriminant Analysis (LDA): Classify according to a Gaussian likelihood with covariance matrix of the data.

  15. Linear Discriminant Analysis Linear Discriminant Analysis: Classify according to Gaussian, That is: Classify x as blue if >

  16. Linear Discriminant Analysis > Q3 Q4 Q5

  17. Linear Discriminant Analysis

  18. Linear Discriminant Analysis Let µ 1 and µ 2 be the two group means in the training set, and Σ the covariance matrix. The linear classifier that classifies each item x to the group with higher Gaussian likelihood under these means and the common covariance matrix, is called Linear Discriminant Analysis . Note: The common covariance matrix is the average squared distance from the mean in each group , not from the total mean!

  19. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2)

  20. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2) 1 Q6 2

  21. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2)

  22. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2)

  23. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2)

  24. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2)

  25. Example for LDA Control Group Treatment Group

  26. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) ID 1 = (1,2,1) ID 6 = (4,1,1) ID 2 = (2,1,0) ID 7 = (0,2,0) ID 3 = (1,1,1) ID 8 = (1,0,2) ID 4 = (0,0,2) Filter

  27. Example for LDA Treatment Group Control Group ID 5 = (3,1,1) 2.1 ID 1 = (1,2,1) -0.1 ID 6 = (4,1,1) 5.4 ID 2 = (2,1,0) 1.5 ID 7 = (0,2,0) -0.7 ID 3 = (1,1,1) -0.7 ID 8 = (1,0,2) -2.1 ID 4 = (0,0,2) -3.5

  28. Example for LDA ID 1 = (1,2,1) ID 5 = (3,1,1) ID 2 = (2,1,0) ID 6 = (4,1,1) ID 3 = (1,1,1) ID 7 = (0,2,0) ID 4 = (0,0,2) ID 8 = (1,0,2) 1 1 0 1

  29. Example for LDA ID 1 = (1,2,1) ID 5 = (3,1,1) ID 2 = (2,1,0) ID 6 = (4,1,1) ID 3 = (1,1,1) ID 7 = (0,2,0) ID 4 = (0,0,2) ID 8 = (1,0,2) 1 1 0 1

  30. Example for LDA ID 1 = (1,2,1) ID 5 = (3,1,1) ID 2 = (2,1,0) ID 6 = (4,1,1) ID 3 = (1,1,1) ID 7 = (0,2,2) ID 4 = (0,0,2) ID 8 = (1,0,0) 1 1 0 1

  31. Example for LDA miss – classified ID 1 = (1,2,1) ID 5 = (3,1,1) ID 2 = (2,1,0) ID 6 = (4,1,1) ID 3 = (1,1,1) ID 7 = (0,2,2) ID 4 = (0,0,2) ID 8 = (1,0,0) 1 1 separation plane 0 1

  32. Geometry of Linear Classifier

  33. Linear Regression x t ID 1 = (1,2,1), -1 ID 2 = (2,1,0), -1 ID 3 = (1,1,1), -1 ID 4 = (0,0,2), -1 ID 5 = (3,1,1), 1 ID 6 = (4,1,1), 1 ID 7 = (0,2,2), 1 ID 8 = (1,0,0), 1 Make it as close as possible minimize:

  34. Linear Regression x t ID 1 = (1,1,2,1), -1 ID 2 = (1,2,1,0), -1 ID 3 = (1,1,1,1), -1 ID 4 = (1,0,0,2), -1 = ID 5 = (1,3,1,1), 1 ID 6 = (1,4,1,1), 1 ID 7 = (1,0,2,2), 1 ID 8 = (1,1,0,0), 1 minimize:

  35. Linear Regression minimize: Minimization is the same as setting the 1 st derivative to zero: =

  36. Answer Form Working with Linear Classifier II 1 2 Q1 1 2 Q2 Q3 Q4 Q5 1 2 Q6

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Data Classification Data Classification While not (explicitly) on the CCNA Security (640-553

Data Classification Data Classification While not (explicitly) on the CCNA Security (640-553

Data Classification Data Classification While not (explicitly) on the CCNA Security (640-553 IINS) blueprint, all of the Cisco Press books for the CCNA Security exam that I reviewed included data classification (specifically US data

255 views • 9 slides
(a) Quantitative classification (b) Qualitative classification (c) Area classification (d) Simple

(a) Quantitative classification (b) Qualitative classification (c) Area classification (d) Simple

MCQS OF PRESENTATION OF DATA MCQ No 2.1: When data are classified according to a single characteristic, it is called: (a) Quantitative classification (b) Qualitative classification (c) Area classification (d) Simple classification MCQ No 2.2:

535 views • 9 slides
Automatic Classification of Automatic Classification of Audio Data Audio Data Carlos H. C.

Automatic Classification of Automatic Classification of Audio Data Audio Data Carlos H. C.

Automatic Classification of Automatic Classification of Audio Data Audio Data Carlos H. C. Lopes, Jaime D. Valle Jr. & Alessandro L. Koerich IEEE International Conference on Systems, Man and Cybernetics The Hague, The Netherlands October

1.17k views • 24 slides
CS145: INTRODUCTION TO DATA MINING 08: Classification Evaluation and Practical Issues

CS145: INTRODUCTION TO DATA MINING 08: Classification Evaluation and Practical Issues

CS145: INTRODUCTION TO DATA MINING 08: Classification Evaluation and Practical Issues Instructor: Yizhou Sun yzsun@cs.ucla.edu October 24, 2017 Learnt Prediction and Classification Methods Vector Data Set Data Sequence Data Text Data

635 views • 24 slides
CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 1 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 1 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 1 Instructor: Yizhou Sun yzsun@ccs.neu.edu September 14, 2014 Matrix Data: Classification: Part 1 Classification: Basic Concepts Decision Tree Induction Model

904 views • 44 slides
CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 1 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 1 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 1 Instructor: Yizhou Sun yzsun@ccs.neu.edu September 16, 2013 Matrix Data: Classification: Part 1 Classification: Basic Concepts Decision Tree Induction Model

779 views • 48 slides
CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 3 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 3 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 3 Instructor: Yizhou Sun yzsun@ccs.neu.edu September 28, 2014 Methods to Learn Matrix Data Set Data Sequence Time Series Graph & Data Network Classification Decision

858 views • 70 slides
DATA MINING LECTURE 10 Classification Nearest Neighbor Classification Support Vector Machines

DATA MINING LECTURE 10 Classification Nearest Neighbor Classification Support Vector Machines

DATA MINING LECTURE 10 Classification Nearest Neighbor Classification Support Vector Machines Logistic Regression Nave Bayes Classifier Supervised Learning Illustrating Classification Task Learning Tid Attrib1 Attrib2 Attrib3 Class

954 views • 79 slides
DATA MINING LECTURE 11 Classification Nearest Neighbor Classification Support Vector Machines

DATA MINING LECTURE 11 Classification Nearest Neighbor Classification Support Vector Machines

DATA MINING LECTURE 11 Classification Nearest Neighbor Classification Support Vector Machines Logistic Regression Nave Bayes Classifier Supervised Learning Illustrating Classification Task Learning Tid Attrib1 Attrib2 Attrib3 Class

1.03k views • 75 slides
Support Vector Machines for Classification of Flow Data Classification of Flow Data Funded by

Support Vector Machines for Classification of Flow Data Classification of Flow Data Funded by

Support Vector Machines for Classification of Flow Data Classification of Flow Data Funded by SBIR Grant # R43 RR024094-01A1 FlowCap 2010 p John Quinn Ph.D. Treestar john@treestar.com Our Objective Our Objective Demonstrate that

312 views • 18 slides
Classification Comparisons Math 3220 Data Mining Methods Angelo Parker Overview

Classification Comparisons Math 3220 Data Mining Methods Angelo Parker Overview

Classification Comparisons Math 3220 Data Mining Methods Angelo Parker Overview Classification C5.0 Rpart SVM The example datasets Classification comparisons Classification The method of taking data and breaking it

318 views • 18 slides
Classification and feat u re engineering MAC H IN E L E AR N IN G FOR TIME SE R IE S DATA IN

Classification and feat u re engineering MAC H IN E L E AR N IN G FOR TIME SE R IE S DATA IN

Classification and feat u re engineering MAC H IN E L E AR N IN G FOR TIME SE R IE S DATA IN P YTH ON Chris Holdgraf Fello w, Berkele y Instit u te for Data Science Al w a y s v is u ali z e ra w data before fitting models MACHINE LEARNING

579 views • 37 slides
Classification from Pairwise Similarity and Unlabeled Data Han Bao 1,2 , Gang Niu 2 , Masashi

Classification from Pairwise Similarity and Unlabeled Data Han Bao 1,2 , Gang Niu 2 , Masashi

Classification from Pairwise Similarity and Unlabeled Data Han Bao 1,2 , Gang Niu 2 , Masashi Sugiyama 2,1 1 The University of Tokyo, Japan / 2 RIKEN, Japan July 13 th , 2018 Gentle Start: Binary Classification 2 Boundary Training data

264 views • 13 slides
Learning From Data Lecture 8 Linear Classification and Regression Linear Classification Linear

Learning From Data Lecture 8 Linear Classification and Regression Linear Classification Linear

Learning From Data Lecture 8 Linear Classification and Regression Linear Classification Linear Regression M. Magdon-Ismail CSCI 4100/6100 recap: Approximation Versus Generalization VC Analysis Bias-Variance Analysis E out E in + ( d

390 views • 23 slides
P ( X | Y ) P ( Y ) P ( Y | X ) P ( X ) Introduction to Data Mining, 2 nd

P ( X | Y ) P ( Y ) P ( Y | X ) P ( X ) Introduction to Data Mining, 2 nd

Data Mining Classification: Alternative Techniques Bayesian Classifiers Introduction to Data Mining, 2 nd Edition by Tan, Steinbach, Karpatne, Kumar 1 Bayes Classifier A probabilistic framework for solving classification

169 views • 13 slides
CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 2 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 2 Instructor: Yizhou Sun

CS6220: DATA MINING TECHNIQUES Matrix Data: Classification: Part 2 Instructor: Yizhou Sun yzsun@ccs.neu.edu September 27, 2015 Methods to Learn Matrix Data Text Set Data Sequence Time Series Graph & Images Data Data Network

551 views • 38 slides
The Kalman Filter An Algorithm for Dealing with Uncertainty Steven Janke May 2011 Steven Janke

The Kalman Filter An Algorithm for Dealing with Uncertainty Steven Janke May 2011 Steven Janke

The Kalman Filter An Algorithm for Dealing with Uncertainty Steven Janke May 2011 Steven Janke (Seminar) The Kalman Filter May 2011 1 / 29 Autonomous Robots Steven Janke (Seminar) The Kalman Filter May 2011 2 / 29 The Problem Steven

535 views • 29 slides
Nested logit models Michel Bierlaire michel.bierlaire@epfl.ch Transport and Mobility Laboratory

Nested logit models Michel Bierlaire michel.bierlaire@epfl.ch Transport and Mobility Laboratory

Nested logit models Michel Bierlaire michel.bierlaire@epfl.ch Transport and Mobility Laboratory Nested logit models p. 1/23 Red bus/Blue bus paradox Mode choice example Two alternatives: car and bus There are red buses and blue

238 views • 23 slides
compsci 514: algorithms for data science Cameron Musco University of Massachusetts Amherst.

compsci 514: algorithms for data science Cameron Musco University of Massachusetts Amherst.

compsci 514: algorithms for data science Cameron Musco University of Massachusetts Amherst. Spring 2020. Lecture 16 0 summary Last Class: Low-Rank Approximation, Eigendecomposition, and PCA by projecting data points into that space. (PCA).

822 views • 24 slides
PLUGIN CLASSIFIERS: NAIVE BAYES, LDA, PLUGIN CLASSIFIERS: NAIVE BAYES, LDA, LOGISTIC REGRESSION

PLUGIN CLASSIFIERS: NAIVE BAYES, LDA, PLUGIN CLASSIFIERS: NAIVE BAYES, LDA, LOGISTIC REGRESSION

PLUGIN CLASSIFIERS: NAIVE BAYES, LDA, PLUGIN CLASSIFIERS: NAIVE BAYES, LDA, LOGISTIC REGRESSION LOGISTIC REGRESSION Matthieu R Bloch Tuesday, January 28, 2020 1 LOGISTICS LOGISTICS TAs and Office hours Monday: Mehrdad (TSRB 523a) -

261 views • 11 slides
1 Random vectors I Some experiments produce outcomes that are vectors. Such a vector is

1 Random vectors I Some experiments produce outcomes that are vectors. Such a vector is

Advanced topics from statistics Anders Ringgaard Kristensen Advanced Herd Management Slide 1 Outline Covariance and correlation Random vectors and multivariate distributions The multinomial distribution The multivariate

443 views • 9 slides
Chapter 2: Video 4 - Supplementary Slides Stationarity To obtain parsimony in a time series model

Chapter 2: Video 4 - Supplementary Slides Stationarity To obtain parsimony in a time series model

Chapter 2: Video 4 - Supplementary Slides Stationarity To obtain parsimony in a time series model we often assume some form of distributional invariance over time, or stationarity. For observed time series: Fluctuations appear random.

61 views • 5 slides
Stochastic Signals Overview Introduction Discrete-time stochastic processes provides a

Stochastic Signals Overview Introduction Discrete-time stochastic processes provides a

Stochastic Signals Overview Introduction Discrete-time stochastic processes provides a mathematical Definitions framework for working with non-deterministic signals Second order statistics Signals that have an exact functional

363 views • 12 slides
x t + h 1 , 1 ( h ) 1 , 2 ( h ) 1 ,p ( h ) . . . 2 , 1 ( h ) 2 , 2

x t + h 1 , 1 ( h ) 1 , 2 ( h ) 1 ,p ( h ) . . . 2 , 1 ( h ) 2 , 2

Vector-Valued SeriesNotation Studies of time series data often involve p > 1 series. E.g. Southern Oscillation Index and recruitment in a fish population ( p = 2). Treated as a p 1 column vector: x t, 1 x t, 2

326 views • 8 slides

More recommend