CS6716 Pattern Recognition
|
|
- Darrell Boyd
- 5 years ago
- Views:
Transcription
1 CS6716 Pattern Recognition Prototype Methods Aaron Bobick School of Interactive Computing
2 Administrivia Problem 2b was extended to March 25. Done? PS3 will be out this real soon (tonight) due April 10. Today chapter 13 of the Hastie book. (Save SVMs for after break) Slides from Sam Brown (who took them from Vipin Kumar), Jia Lee,
3 Outline K-means as the prototypical prototype method LVQ as a better version of K-means K-NN revisited Comparison to Bayes error Problem with dimensionality Discriminant Adaptive K-NN method
4 K-means (no classes yet) (R-means???) Assume a known number of clusters R (yes really, K is taken for number of classes). Start with some initial set of centers Repeat until tired: 1. For each center, find the training points closets to it (its cluster) 2. Re-estimate the center based upon the cluster.
5 K-means (with classes) Assume a known number of clusters R prototypes per class. Apply K-means to each class of data separately. Assign class label to each of the K*R prototypes (see?) Classify each new instance xx ii according to the nearest prototype label Start with some initial set of centers Repeat until tired: 1. For each center, find the training points closets to it (its cluster) 2. Re-estimate the center based upon the cluster.
6 Fixing K-Means The prototypes are not influenced by the other classes and can end up near the class boundary. Fix this by adjusting the prototypes by considering the training data: Kohonen s Learned Vector Quantization
7 Learned Vector Quantization 1. Asssume set of inputs xx ii and labels yy ii. Start from a set of initial prototypes with classes assigned. Denote the MM prototypes by ZZ = {zz 1,, zz MM } and their associated classes by CC zz mm, mm = 1, 2,, MM > The initial prototypes can be provided by k-means. 2. Sweep through the training samples and update zz mm after visiting each sample: 1. Suppose xx ii is assigned to the mm ttt prototype zz mm by the nearest neighbor rule: xx ii zz mm xx ii zz mm, mm mm, 1 mm MM 2. If yy ii = CC zz mm, move zz mm towards the training example. zz mm zz mm + εε xx ii zz mm where εε is the learning rate 3. Otherwise move zz mm away the training example. zz mm zz mm εε xx ii zz mm 3. Step 2 can be repeated a number of times.
8 Learned Vector Quantization
9 Some experiments Synthetic data 3-classes generated by mixture of Gaussians Bayesian boundaries known
10 Some experiments Real data: Use the diabetes data set Use prototypes obtained by k-means as initial prototypes. Use LVQ with εε = 0.1. Results obtained after 1, 2, and 5 passes are shown. Classification is not guaranteed to improve after adjusting prototypes. One pass with a small E usually helps. But don t over do it. Comments: Fine tuning often helps: Select initial prototypes. Adjust learning rate E. Read the package documents for details.
11 Diabetes k-means vslvq results (0) Error rate: 27.74% (1) Error rate: 27.61% (2) Error rate: 27.86% (5) Error rate: 32.37%
12 Is LVQ really any better Classification is not guaranteed to improve after adjusting prototypes. According to Jia Lee: One pass with a small εε usually helps. But don t over do it. Learning rate can be important Problem according to Hastie: the problem with [LVQ] methods is that they are defined by algorithms, rather than optimization of some fixed criteria; this makes it difficult to understand their properties
13 K-NN again???? We discussed K-NN in the overview of supervised learning and especially with respect to bias and variance. Now think about prototype/memory methods generally. Next time, maybe I ll do less early and more here
14 Why nearest neighbor? Used to classify objects based on closest training examples in the feature space Top 10 Data Mining Algorithm ICDM paper December 2007 A simple but sophisticated approach to classification? 14
15 K-Nearest Neighbor Compute the distance between two points: Euclidean distance: dd pp, qq = pp ii qq ii 2 Hamming distance (symbol overlap metric) bat (distance = 1) toned (distance = 3) cat roses Determine the class from nearest neighbor list Take the majority vote of class labels among the k-nearest neighbors Can be weighted by factor ww = 1/ (dd 2 ) Scaling issues can be a problem e.g. weight and height in very different units. 16
16 K-Nearest Neighbor different K k = 1: Belongs to square class? k = 3: Belongs to triangle class k = 7: Belongs to square class Choosing the value of k: If k is too small, sensitive to noise points If k is too large, neighborhood may include points from other classes Choose an odd value for k, to eliminate ties 17
17 K-Nearest Neighbor advantages Simple technique that is easily implemented by lazy computer scientists Building the model is cheap (but using it less so). Extremely flexible classification scheme Well suited for Multi-modal classes Records with multiple or ambigious class labels Can sometimes be the best method Michihiro Kuramochi and George Karypis, Gene Classification using Expression Profiles: A Feasibility Study, International Journal on Artificial Intelligence Tools. Vol. 14, No. 4, pp , 2005 K nearest neighbor outperformed SVM for protein function prediction using expression profiles 18
18 K-Nearest Neighbor advantages (more) Error rate of 1-NN in asymptotically at most twice that of Bayes error rate (Cover & Hart paper (1967) ) First way to see: Assume an underlying known (Bayes) densities and some variance added to that. Then the error rate on a sample point is just due to Bayes error plus the variance of one point. In 1-NN as NN the test point matches some training point. But the error from the Bayes rule is due to variances of both that training point and the new target point. Second way. At some point xx let kk be the dominant class and pp kk xx is the true conditional probability for class kk. Then:
19 K-Nearest Neighbor advantages (more) (cont) For K=2, pp 1 xx = 1 pp 2 xx so: 1-NN error = 2 pp kk xx 1 pp kk xx < [2 1 pp kk xx ] = 2*Bayes rate ie the 1-NN error rate is no worse than twice Bayes. See Duda and Hart for more complete proof.
20 A nice example: LANDSAT Pixel and 8 neighbors => 36 dimensions. 7 Possible labels Use 5-NN
21 A nice example: LANDSAT (1994)
22 A nice extension Problem: recognize digits. Input 16x16 gray values, so xx: R 256
23 Addressing systematic variation Consider slight rotations of the image, one connected to the other: That s just some curve in the 256 dimensional space. You might think you d have all these examples, but that s hard if multiple such variations, e.g. rotation and scale. To address this you could find the NN in terms of these curves. But that s painful.
24 Tangent method Instead, since only want small variations, just do a local tangent. Not perfect, but pretty good?
25 Tangent method Only need to find closest distance between two lines in d-dimensional space. Very good results but too slow to compute. Runtime matters for post office! Remember: boosted Neural Nest and SVM now around 0.8%
26 Why K>1 is usually a good idea
27 Cross-validation wants neighbors
28 K-Nearest Neighbor disadvantages Classifying unknown records are relatively expensive Requires distance computation of k-nearest neighbors Computationally intensive, especially when the size of the training set grows You can fix this you re computer people More fundamental: Problems in high dimensions Accuracy can be severely degraded by the presence of noisy or irrelevant features Hastie and Tibshirani, KDD 95 to the rescue: Discriminative Adaptive Nearest Neighbor 29
29 The dimensionality problem The size of the neighborhood we need to get K neighbors grows annoyingly. In Hastie: Why?
30 See, even at 1:30am I can do math Consider the unit cube in p dimensions centered at the origin. Assume a sphere with radius R about the origin. Assume it has a volume VV RR The probability that the distance d to the closest point of the N points is greater than R: NN Pr dd > RR = 1 VV RR Median => Pr dd > RR = 1 = 1 VV 2 RR NN So: ( 1 2 )1 NN= 1 VV RR VV RR = 1 ( 1 2 )1 NN If VV RR = vv pp RR pp vv pp RR PP = 1 ( 1 2 )1 NN => RR = vv pp 1 pp NN 1 pp
31 Neighborhood size goes up pretty fast
32 An motivating example Suppose two dimensions. But that classes only vary in x:? Class 1 Class 2 Devise a method that does this. Basically the neighborhood should be anisotropic. 33
33 Finding the right stretch (and dimensions) Goal: Adjust distance metric locally, so that the resulting neighborhoods stretch out in directions for which the class probabilities don t change much. Method: At each query point, a neighborhood of say 50 points is formed. Class probabilities are NOT assumed constant in this neighborhood. This neighborhood is used only to decide how to define the adapted metric. After the metric is decided, a normal k-nearest neighbor rule is applied to classify the query. The metric changes with the query.
34 Discriminant adaptive nearest neighbor classification (DANN) DANN: Discriminant sensitive to the set of classes Adaptive Capability of being able to adapt or adjust to fit the situation Nearest Neighbor classification based on a locality metric selected by the majority of adjacent neighbor s class DANN uses local linear discriminant analysis to estimate an effective metric for computing neighborhoods. DANN posterior probabilities tend to be more homogeneous in the modified neighborhoods. 35
35 DISCRIMINANT ADAPTIVE NEAREST NEIGHBOR CLASSIFICATION (DANN)? Class 1 Class 2 Using k -NN, we misclassify by crossing the boundary between classes. Standard linear discriminants extend infinitely in any direction. This is dangerous to local classification. 36
36 DISCRIMINANT ADAPTIVE NEAREST NEIGHBOR CLASSIFICATION (DANN)? Class 1 Class 2 DANN utilizes a small tuning parameter to shrink or stretch neighborhoods. 37
37 DISCRIMINANT ADAPTIVE NEAREST NEIGHBOR CLASSIFICATION (DANN)? The process of tuning can be done iteratively allowing stretching in all axis 38
38 DISCRIMINANT ADAPTIVE NEAREST NEIGHBOR CLASSIFICATION (DANN) 1. Initialize Σ to be the identity II 2. Given a test point xx 0 spread out a nearest neighborhood of K M points in the Σ metric around the xx 0 : DD xx, xx 0 = xx xx 0 TT Σ (xx xx 0 ) 3. Calculate the weighted within and between sum of squares matrices W and B using the points in the neighborhood (Remember LDA?) W = kk 1 WW kk, WW kk within class covariance And B is between class: Define a new metric: 1.Iterate steps 1, 2, and 3. 2.At completion, use the metric for k-nearest neighbor classification at the test point x o. 39
39 The magic What does WW 1 do? (W stands for something beyond within ) What is BB? It is the between matrix for the sphered (whitened)-data. It typically has some (many) zero eigenvalues. (Why?) If you left B alone, you would completely ignore distance in the zero-eigenvalue directions. I.E. you d use data arbitrarily far away. The εεεε term prevents that.
40 DISCRIMINANT ADAPTIVE NEAREST NEIGHBOR CLASSIFICATION (DANN) The DANN procedure has a number of adjustable tuning parameters: K M The number of nearest neighbors in the neighborhood N for estimation of the metric. K The number of neighbors in the final nearest neighbor rule. ε the softening parameter in the metric. Similar to Evolutionary Strategies Adjusts search space over a fitness landscape to find optimal solution. 41
41
42 Global approach to DANN
Instance-based Learning CE-717: Machine Learning Sharif University of Technology. M. Soleymani Fall 2015
Instance-based Learning CE-717: Machine Learning Sharif University of Technology M. Soleymani Fall 2015 Outline Non-parametric approach Unsupervised: Non-parametric density estimation Parzen Windows K-Nearest
More informationMachine Learning and Pervasive Computing
Stephan Sigg Georg-August-University Goettingen, Computer Networks 17.12.2014 Overview and Structure 22.10.2014 Organisation 22.10.3014 Introduction (Def.: Machine learning, Supervised/Unsupervised, Examples)
More informationNearest Neighbor Classification. Machine Learning Fall 2017
Nearest Neighbor Classification Machine Learning Fall 2017 1 This lecture K-nearest neighbor classification The basic algorithm Different distance measures Some practical aspects Voronoi Diagrams and Decision
More informationCS 584 Data Mining. Classification 1
CS 584 Data Mining Classification 1 Classification: Definition Given a collection of records (training set ) Each record contains a set of attributes, one of the attributes is the class. Find a model for
More informationAdaptive Metric Nearest Neighbor Classification
Adaptive Metric Nearest Neighbor Classification Carlotta Domeniconi Jing Peng Dimitrios Gunopulos Computer Science Department Computer Science Department Computer Science Department University of California
More informationCase-Based Reasoning. CS 188: Artificial Intelligence Fall Nearest-Neighbor Classification. Parametric / Non-parametric.
CS 188: Artificial Intelligence Fall 2008 Lecture 25: Kernels and Clustering 12/2/2008 Dan Klein UC Berkeley Case-Based Reasoning Similarity for classification Case-based reasoning Predict an instance
More informationCS 188: Artificial Intelligence Fall 2008
CS 188: Artificial Intelligence Fall 2008 Lecture 25: Kernels and Clustering 12/2/2008 Dan Klein UC Berkeley 1 1 Case-Based Reasoning Similarity for classification Case-based reasoning Predict an instance
More informationFigure (5) Kohonen Self-Organized Map
2- KOHONEN SELF-ORGANIZING MAPS (SOM) - The self-organizing neural networks assume a topological structure among the cluster units. - There are m cluster units, arranged in a one- or two-dimensional array;
More informationSVM-KNN : Discriminative Nearest Neighbor Classification for Visual Category Recognition
SVM-KNN : Discriminative Nearest Neighbor Classification for Visual Category Recognition Hao Zhang, Alexander Berg, Michael Maire Jitendra Malik EECS, UC Berkeley Presented by Adam Bickett Objective Visual
More informationK Nearest Neighbor Wrap Up K- Means Clustering. Slides adapted from Prof. Carpuat
K Nearest Neighbor Wrap Up K- Means Clustering Slides adapted from Prof. Carpuat K Nearest Neighbor classification Classification is based on Test instance with Training Data K: number of neighbors that
More informationSupervised vs unsupervised clustering
Classification Supervised vs unsupervised clustering Cluster analysis: Classes are not known a- priori. Classification: Classes are defined a-priori Sometimes called supervised clustering Extract useful
More informationECG782: Multidimensional Digital Signal Processing
ECG782: Multidimensional Digital Signal Processing Object Recognition http://www.ee.unlv.edu/~b1morris/ecg782/ 2 Outline Knowledge Representation Statistical Pattern Recognition Neural Networks Boosting
More informationThe Curse of Dimensionality
The Curse of Dimensionality ACAS 2002 p1/66 Curse of Dimensionality The basic idea of the curse of dimensionality is that high dimensional data is difficult to work with for several reasons: Adding more
More informationFeature Extractors. CS 188: Artificial Intelligence Fall Some (Vague) Biology. The Binary Perceptron. Binary Decision Rule.
CS 188: Artificial Intelligence Fall 2008 Lecture 24: Perceptrons II 11/24/2008 Dan Klein UC Berkeley Feature Extractors A feature extractor maps inputs to feature vectors Dear Sir. First, I must solicit
More informationIntro to Artificial Intelligence
Intro to Artificial Intelligence Ahmed Sallam { Lecture 5: Machine Learning ://. } ://.. 2 Review Probabilistic inference Enumeration Approximate inference 3 Today What is machine learning? Supervised
More informationTopics in Machine Learning
Topics in Machine Learning Gilad Lerman School of Mathematics University of Minnesota Text/slides stolen from G. James, D. Witten, T. Hastie, R. Tibshirani and A. Ng Machine Learning - Motivation Arthur
More informationData Mining and Data Warehousing Classification-Lazy Learners
Motivation Data Mining and Data Warehousing Classification-Lazy Learners Lazy Learners are the most intuitive type of learners and are used in many practical scenarios. The reason of their popularity is
More informationTopic 1 Classification Alternatives
Topic 1 Classification Alternatives [Jiawei Han, Micheline Kamber, Jian Pei. 2011. Data Mining Concepts and Techniques. 3 rd Ed. Morgan Kaufmann. ISBN: 9380931913.] 1 Contents 2. Classification Using Frequent
More informationCS 340 Lec. 4: K-Nearest Neighbors
CS 340 Lec. 4: K-Nearest Neighbors AD January 2011 AD () CS 340 Lec. 4: K-Nearest Neighbors January 2011 1 / 23 K-Nearest Neighbors Introduction Choice of Metric Overfitting and Underfitting Selection
More informationData mining. Classification k-nn Classifier. Piotr Paszek. (Piotr Paszek) Data mining k-nn 1 / 20
Data mining Piotr Paszek Classification k-nn Classifier (Piotr Paszek) Data mining k-nn 1 / 20 Plan of the lecture 1 Lazy Learner 2 k-nearest Neighbor Classifier 1 Distance (metric) 2 How to Determine
More informationUnsupervised Learning : Clustering
Unsupervised Learning : Clustering Things to be Addressed Traditional Learning Models. Cluster Analysis K-means Clustering Algorithm Drawbacks of traditional clustering algorithms. Clustering as a complex
More informationAnnouncements. CS 188: Artificial Intelligence Spring Generative vs. Discriminative. Classification: Feature Vectors. Project 4: due Friday.
CS 188: Artificial Intelligence Spring 2011 Lecture 21: Perceptrons 4/13/2010 Announcements Project 4: due Friday. Final Contest: up and running! Project 5 out! Pieter Abbeel UC Berkeley Many slides adapted
More informationClassification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University
Classification Vladimir Curic Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Outline An overview on classification Basics of classification How to choose appropriate
More informationCSE 573: Artificial Intelligence Autumn 2010
CSE 573: Artificial Intelligence Autumn 2010 Lecture 16: Machine Learning Topics 12/7/2010 Luke Zettlemoyer Most slides over the course adapted from Dan Klein. 1 Announcements Syllabus revised Machine
More informationRecap: Gaussian (or Normal) Distribution. Recap: Minimizing the Expected Loss. Topics of This Lecture. Recap: Maximum Likelihood Approach
Truth Course Outline Machine Learning Lecture 3 Fundamentals (2 weeks) Bayes Decision Theory Probability Density Estimation Probability Density Estimation II 2.04.205 Discriminative Approaches (5 weeks)
More information7. Nearest neighbors. Learning objectives. Foundations of Machine Learning École Centrale Paris Fall 2015
Foundations of Machine Learning École Centrale Paris Fall 2015 7. Nearest neighbors Chloé-Agathe Azencott Centre for Computational Biology, Mines ParisTech chloe agathe.azencott@mines paristech.fr Learning
More informationMS1b Statistical Data Mining Part 3: Supervised Learning Nonparametric Methods
MS1b Statistical Data Mining Part 3: Supervised Learning Nonparametric Methods Yee Whye Teh Department of Statistics Oxford http://www.stats.ox.ac.uk/~teh/datamining.html Outline Supervised Learning: Nonparametric
More informationCISC 4631 Data Mining
CISC 4631 Data Mining Lecture 03: Nearest Neighbor Learning Theses slides are based on the slides by Tan, Steinbach and Kumar (textbook authors) Prof. R. Mooney (UT Austin) Prof E. Keogh (UCR), Prof. F.
More informationEquation to LaTeX. Abhinav Rastogi, Sevy Harris. I. Introduction. Segmentation.
Equation to LaTeX Abhinav Rastogi, Sevy Harris {arastogi,sharris5}@stanford.edu I. Introduction Copying equations from a pdf file to a LaTeX document can be time consuming because there is no easy way
More informationWhy Do Nearest-Neighbour Algorithms Do So Well?
References Why Do Nearest-Neighbour Algorithms Do So Well? Brian D. Ripley Professor of Applied Statistics University of Oxford Ripley, B. D. (1996) Pattern Recognition and Neural Networks. CUP. ISBN 0-521-48086-7.
More informationUsing Machine Learning to Optimize Storage Systems
Using Machine Learning to Optimize Storage Systems Dr. Kiran Gunnam 1 Outline 1. Overview 2. Building Flash Models using Logistic Regression. 3. Storage Object classification 4. Storage Allocation recommendation
More informationCS 343: Artificial Intelligence
CS 343: Artificial Intelligence Kernels and Clustering Prof. Scott Niekum The University of Texas at Austin [These slides based on those of Dan Klein and Pieter Abbeel for CS188 Intro to AI at UC Berkeley.
More informationData Mining. Lecture 03: Nearest Neighbor Learning
Data Mining Lecture 03: Nearest Neighbor Learning Theses slides are based on the slides by Tan, Steinbach and Kumar (textbook authors) Prof. R. Mooney (UT Austin) Prof E. Keogh (UCR), Prof. F. Provost
More informationKernels and Clustering
Kernels and Clustering Robert Platt Northeastern University All slides in this file are adapted from CS188 UC Berkeley Case-Based Learning Non-Separable Data Case-Based Reasoning Classification from similarity
More informationCS249: ADVANCED DATA MINING
CS249: ADVANCED DATA MINING Classification Evaluation and Practical Issues Instructor: Yizhou Sun yzsun@cs.ucla.edu April 24, 2017 Homework 2 out Announcements Due May 3 rd (11:59pm) Course project proposal
More informationLecture 3. Oct
Lecture 3 Oct 3 2008 Review of last lecture A supervised learning example spam filter, and the design choices one need to make for this problem use bag-of-words to represent emails linear functions as
More informationBayes Risk. Classifiers for Recognition Reading: Chapter 22 (skip 22.3) Discriminative vs Generative Models. Loss functions in classifiers
Classifiers for Recognition Reading: Chapter 22 (skip 22.3) Examine each window of an image Classify object class within each window based on a training set images Example: A Classification Problem Categorize
More informationNon-Parametric Modeling
Non-Parametric Modeling CE-725: Statistical Pattern Recognition Sharif University of Technology Spring 2013 Soleymani Outline Introduction Non-Parametric Density Estimation Parzen Windows Kn-Nearest Neighbor
More informationNearest Neighbor Methods
Nearest Neighbor Methods Nicholas Ruozzi University of Texas at Dallas Based on the slides of Vibhav Gogate and David Sontag Nearest Neighbor Methods Learning Store all training examples Classifying a
More informationData Mining Classification: Alternative Techniques. Lecture Notes for Chapter 4. Instance-Based Learning. Introduction to Data Mining, 2 nd Edition
Data Mining Classification: Alternative Techniques Lecture Notes for Chapter 4 Instance-Based Learning Introduction to Data Mining, 2 nd Edition by Tan, Steinbach, Karpatne, Kumar Instance Based Classifiers
More informationLearning to Learn: additional notes
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.034 Artificial Intelligence, Fall 2008 Recitation October 23 Learning to Learn: additional notes Bob Berwick
More informationStatistical Learning Part 2 Nonparametric Learning: The Main Ideas. R. Moeller Hamburg University of Technology
Statistical Learning Part 2 Nonparametric Learning: The Main Ideas R. Moeller Hamburg University of Technology Instance-Based Learning So far we saw statistical learning as parameter learning, i.e., given
More informationClassifiers for Recognition Reading: Chapter 22 (skip 22.3)
Classifiers for Recognition Reading: Chapter 22 (skip 22.3) Examine each window of an image Classify object class within each window based on a training set images Slide credits for this chapter: Frank
More informationMIT 801. Machine Learning I. [Presented by Anna Bosman] 16 February 2018
MIT 801 [Presented by Anna Bosman] 16 February 2018 Machine Learning What is machine learning? Artificial Intelligence? Yes as we know it. What is intelligence? The ability to acquire and apply knowledge
More informationClassification: Feature Vectors
Classification: Feature Vectors Hello, Do you want free printr cartriges? Why pay more when you can get them ABSOLUTELY FREE! Just # free YOUR_NAME MISSPELLED FROM_FRIEND... : : : : 2 0 2 0 PIXEL 7,12
More informationDATA MINING LECTURE 10B. Classification k-nearest neighbor classifier Naïve Bayes Logistic Regression Support Vector Machines
DATA MINING LECTURE 10B Classification k-nearest neighbor classifier Naïve Bayes Logistic Regression Support Vector Machines NEAREST NEIGHBOR CLASSIFICATION 10 10 Illustrating Classification Task Tid Attrib1
More informationLecture 9. Support Vector Machines
Lecture 9. Support Vector Machines COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture Support vector machines (SVMs) as maximum
More informationMachine Learning Lecture 3
Machine Learning Lecture 3 Probability Density Estimation II 19.10.2017 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Announcements Exam dates We re in the process
More informationSupervised vs. Unsupervised Learning
Clustering Supervised vs. Unsupervised Learning So far we have assumed that the training samples used to design the classifier were labeled by their class membership (supervised learning) We assume now
More information7. Nearest neighbors. Learning objectives. Centre for Computational Biology, Mines ParisTech
Foundations of Machine Learning CentraleSupélec Paris Fall 2016 7. Nearest neighbors Chloé-Agathe Azencot Centre for Computational Biology, Mines ParisTech chloe-agathe.azencott@mines-paristech.fr Learning
More informationMachine Learning Techniques for Data Mining
Machine Learning Techniques for Data Mining Eibe Frank University of Waikato New Zealand 10/25/2000 1 PART VII Moving on: Engineering the input and output 10/25/2000 2 Applying a learner is not all Already
More informationSYDE Winter 2011 Introduction to Pattern Recognition. Clustering
SYDE 372 - Winter 2011 Introduction to Pattern Recognition Clustering Alexander Wong Department of Systems Design Engineering University of Waterloo Outline 1 2 3 4 5 All the approaches we have learned
More informationSlides for Data Mining by I. H. Witten and E. Frank
Slides for Data Mining by I. H. Witten and E. Frank 7 Engineering the input and output Attribute selection Scheme-independent, scheme-specific Attribute discretization Unsupervised, supervised, error-
More informationCS6375: Machine Learning Gautam Kunapuli. Mid-Term Review
Gautam Kunapuli Machine Learning Data is identically and independently distributed Goal is to learn a function that maps to Data is generated using an unknown function Learn a hypothesis that minimizes
More informationInstance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University February 19 th, 2007 2005-2007 Carlos Guestrin 1 Why not just use Linear Regression? 2005-2007 Carlos Guestrin
More informationMachine Learning Lecture 3
Many slides adapted from B. Schiele Machine Learning Lecture 3 Probability Density Estimation II 26.04.2016 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Course
More informationData Mining and Machine Learning: Techniques and Algorithms
Instance based classification Data Mining and Machine Learning: Techniques and Algorithms Eneldo Loza Mencía eneldo@ke.tu-darmstadt.de Knowledge Engineering Group, TU Darmstadt International Week 2019,
More informationMachine Learning Lecture 3
Course Outline Machine Learning Lecture 3 Fundamentals (2 weeks) Bayes Decision Theory Probability Density Estimation Probability Density Estimation II 26.04.206 Discriminative Approaches (5 weeks) Linear
More informationToday. Lecture 4: Last time. The EM algorithm. We examine clustering in a little more detail; we went over it a somewhat quickly last time
Today Lecture 4: We examine clustering in a little more detail; we went over it a somewhat quickly last time The CAD data will return and give us an opportunity to work with curves (!) We then examine
More informationCS4495/6495 Introduction to Computer Vision. 8C-L1 Classification: Discriminative models
CS4495/6495 Introduction to Computer Vision 8C-L1 Classification: Discriminative models Remember: Supervised classification Given a collection of labeled examples, come up with a function that will predict
More informationInstance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University October 15 th, 2007 2005-2007 Carlos Guestrin 1 1-Nearest Neighbor Four things make a memory based learner:
More informationSupervised Learning: K-Nearest Neighbors and Decision Trees
Supervised Learning: K-Nearest Neighbors and Decision Trees Piyush Rai CS5350/6350: Machine Learning August 25, 2011 (CS5350/6350) K-NN and DT August 25, 2011 1 / 20 Supervised Learning Given training
More informationMachine Learning in Biology
Università degli studi di Padova Machine Learning in Biology Luca Silvestrin (Dottorando, XXIII ciclo) Supervised learning Contents Class-conditional probability density Linear and quadratic discriminant
More information10-701/15-781, Fall 2006, Final
-7/-78, Fall 6, Final Dec, :pm-8:pm There are 9 questions in this exam ( pages including this cover sheet). If you need more room to work out your answer to a question, use the back of the page and clearly
More informationClustering. Supervised vs. Unsupervised Learning
Clustering Supervised vs. Unsupervised Learning So far we have assumed that the training samples used to design the classifier were labeled by their class membership (supervised learning) We assume now
More informationPattern Recognition ( , RIT) Exercise 1 Solution
Pattern Recognition (4005-759, 20092 RIT) Exercise 1 Solution Instructor: Prof. Richard Zanibbi The following exercises are to help you review for the upcoming midterm examination on Thursday of Week 5
More informationCS 229 Midterm Review
CS 229 Midterm Review Course Staff Fall 2018 11/2/2018 Outline Today: SVMs Kernels Tree Ensembles EM Algorithm / Mixture Models [ Focus on building intuition, less so on solving specific problems. Ask
More informationCS246: Mining Massive Datasets Jure Leskovec, Stanford University
CS246: Mining Massive Datasets Jure Leskovec, Stanford University http://cs246.stanford.edu [Kumar et al. 99] 2/13/2013 Jure Leskovec, Stanford CS246: Mining Massive Datasets, http://cs246.stanford.edu
More informationContent-based image and video analysis. Machine learning
Content-based image and video analysis Machine learning for multimedia retrieval 04.05.2009 What is machine learning? Some problems are very hard to solve by writing a computer program by hand Almost all
More informationINF 4300 Classification III Anne Solberg The agenda today:
INF 4300 Classification III Anne Solberg 28.10.15 The agenda today: More on estimating classifier accuracy Curse of dimensionality and simple feature selection knn-classification K-means clustering 28.10.15
More informationLast week. Multi-Frame Structure from Motion: Multi-View Stereo. Unknown camera viewpoints
Last week Multi-Frame Structure from Motion: Multi-View Stereo Unknown camera viewpoints Last week PCA Today Recognition Today Recognition Recognition problems What is it? Object detection Who is it? Recognizing
More informationCSE 5526: Introduction to Neural Networks Radial Basis Function (RBF) Networks
CSE 5526: Introduction to Neural Networks Radial Basis Function (RBF) Networks Part IV 1 Function approximation MLP is both a pattern classifier and a function approximator As a function approximator,
More informationPattern Recognition. Kjell Elenius. Speech, Music and Hearing KTH. March 29, 2007 Speech recognition
Pattern Recognition Kjell Elenius Speech, Music and Hearing KTH March 29, 2007 Speech recognition 2007 1 Ch 4. Pattern Recognition 1(3) Bayes Decision Theory Minimum-Error-Rate Decision Rules Discriminant
More informationCOMPUTATIONAL INTELLIGENCE SEW (INTRODUCTION TO MACHINE LEARNING) SS18. Lecture 6: k-nn Cross-validation Regularization
COMPUTATIONAL INTELLIGENCE SEW (INTRODUCTION TO MACHINE LEARNING) SS18 Lecture 6: k-nn Cross-validation Regularization LEARNING METHODS Lazy vs eager learning Eager learning generalizes training data before
More informationAnnouncements. CS 188: Artificial Intelligence Spring Classification: Feature Vectors. Classification: Weights. Learning: Binary Perceptron
CS 188: Artificial Intelligence Spring 2010 Lecture 24: Perceptrons and More! 4/20/2010 Announcements W7 due Thursday [that s your last written for the semester!] Project 5 out Thursday Contest running
More informationK- Nearest Neighbors(KNN) And Predictive Accuracy
Contact: mailto: Ammar@cu.edu.eg Drammarcu@gmail.com K- Nearest Neighbors(KNN) And Predictive Accuracy Dr. Ammar Mohammed Associate Professor of Computer Science ISSR, Cairo University PhD of CS ( Uni.
More informationText classification II CE-324: Modern Information Retrieval Sharif University of Technology
Text classification II CE-324: Modern Information Retrieval Sharif University of Technology M. Soleymani Fall 2015 Some slides have been adapted from: Profs. Manning, Nayak & Raghavan (CS-276, Stanford)
More information6. Object Identification L AK S H M O U. E D U
6. Object Identification L AK S H M AN @ O U. E D U Objects Information extracted from spatial grids often need to be associated with objects not just an individual pixel Group of pixels that form a real-world
More informationCLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS
CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS CHAPTER 4 CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS 4.1 Introduction Optical character recognition is one of
More informationInstance-based Learning
Instance-based Learning Nearest Neighbor 1-nearest neighbor algorithm: Remember all your data points When prediction needed for a new point Find the nearest saved data point Return the answer associated
More informationPerceptron as a graph
Neural Networks Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University October 10 th, 2007 2005-2007 Carlos Guestrin 1 Perceptron as a graph 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0-6 -4-2
More informationLazy Decision Trees Ronny Kohavi
Lazy Decision Trees Ronny Kohavi Data Mining and Visualization Group Silicon Graphics, Inc. Joint work with Jerry Friedman and Yeogirl Yun Stanford University Motivation: Average Impurity = / interesting
More informationCIS 520, Machine Learning, Fall 2015: Assignment 7 Due: Mon, Nov 16, :59pm, PDF to Canvas [100 points]
CIS 520, Machine Learning, Fall 2015: Assignment 7 Due: Mon, Nov 16, 2015. 11:59pm, PDF to Canvas [100 points] Instructions. Please write up your responses to the following problems clearly and concisely.
More informationCPSC 340: Machine Learning and Data Mining. Non-Parametric Models Fall 2016
CPSC 340: Machine Learning and Data Mining Non-Parametric Models Fall 2016 Assignment 0: Admin 1 late day to hand it in tonight, 2 late days for Wednesday. Assignment 1 is out: Due Friday of next week.
More informationNearest Neighbors Classifiers
Nearest Neighbors Classifiers Raúl Rojas Freie Universität Berlin July 2014 In pattern recognition we want to analyze data sets of many different types (pictures, vectors of health symptoms, audio streams,
More informationData Preprocessing. Supervised Learning
Supervised Learning Regression Given the value of an input X, the output Y belongs to the set of real values R. The goal is to predict output accurately for a new input. The predictions or outputs y are
More informationUnsupervised Learning
Outline Unsupervised Learning Basic concepts K-means algorithm Representation of clusters Hierarchical clustering Distance functions Which clustering algorithm to use? NN Supervised learning vs. unsupervised
More informationCS 4495 Computer Vision A. Bobick. CS 4495 Computer Vision. Features 2 SIFT descriptor. Aaron Bobick School of Interactive Computing
CS 4495 Computer Vision Features 2 SIFT descriptor Aaron Bobick School of Interactive Computing Administrivia PS 3: Out due Oct 6 th. Features recap: Goal is to find corresponding locations in two images.
More informationSYDE 372 Introduction to Pattern Recognition. Distance Measures for Pattern Classification: Part I
SYDE 372 Introduction to Pattern Recognition Distance Measures for Pattern Classification: Part I Alexander Wong Department of Systems Design Engineering University of Waterloo Outline Distance Measures
More informationNetwork Traffic Measurements and Analysis
DEIB - Politecnico di Milano Fall, 2017 Introduction Often, we have only a set of features x = x 1, x 2,, x n, but no associated response y. Therefore we are not interested in prediction nor classification,
More informationMachine Learning Classifiers and Boosting
Machine Learning Classifiers and Boosting Reading Ch 18.6-18.12, 20.1-20.3.2 Outline Different types of learning problems Different types of learning algorithms Supervised learning Decision trees Naïve
More informationNearest neighbor classification DSE 220
Nearest neighbor classification DSE 220 Decision Trees Target variable Label Dependent variable Output space Person ID Age Gender Income Balance Mortgag e payment 123213 32 F 25000 32000 Y 17824 49 M 12000-3000
More informationBiometrics Technology: Image Processing & Pattern Recognition (by Dr. Dickson Tong)
Biometrics Technology: Image Processing & Pattern Recognition (by Dr. Dickson Tong) References: [1] http://homepages.inf.ed.ac.uk/rbf/hipr2/index.htm [2] http://www.cs.wisc.edu/~dyer/cs540/notes/vision.html
More informationSearch Engines. Information Retrieval in Practice
Search Engines Information Retrieval in Practice All slides Addison Wesley, 2008 Classification and Clustering Classification and clustering are classical pattern recognition / machine learning problems
More informationFeature Extractors. CS 188: Artificial Intelligence Fall Nearest-Neighbor Classification. The Perceptron Update Rule.
CS 188: Artificial Intelligence Fall 2007 Lecture 26: Kernels 11/29/2007 Dan Klein UC Berkeley Feature Extractors A feature extractor maps inputs to feature vectors Dear Sir. First, I must solicit your
More informationNearest Neighbor Classification
Nearest Neighbor Classification Charles Elkan elkan@cs.ucsd.edu October 9, 2007 The nearest-neighbor method is perhaps the simplest of all algorithms for predicting the class of a test example. The training
More informationCombined Weak Classifiers
Combined Weak Classifiers Chuanyi Ji and Sheng Ma Department of Electrical, Computer and System Engineering Rensselaer Polytechnic Institute, Troy, NY 12180 chuanyi@ecse.rpi.edu, shengm@ecse.rpi.edu Abstract
More informationClustering. CS294 Practical Machine Learning Junming Yin 10/09/06
Clustering CS294 Practical Machine Learning Junming Yin 10/09/06 Outline Introduction Unsupervised learning What is clustering? Application Dissimilarity (similarity) of objects Clustering algorithm K-means,
More informationR (2) Data analysis case study using R for readily available data set using any one machine learning algorithm.
Assignment No. 4 Title: SD Module- Data Science with R Program R (2) C (4) V (2) T (2) Total (10) Dated Sign Data analysis case study using R for readily available data set using any one machine learning
More informationFunction approximation using RBF network. 10 basis functions and 25 data points.
1 Function approximation using RBF network F (x j ) = m 1 w i ϕ( x j t i ) i=1 j = 1... N, m 1 = 10, N = 25 10 basis functions and 25 data points. Basis function centers are plotted with circles and data
More information