Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
CSE 8392 SPRING 1999 DATA MINING: CORE TOPICS Classification Professor Margaret H. Dunham Department of Computer Science and Engineering Southern Methodist University Dallas, Texas 75275 (214) 768-3087 fax: (214) 768-3085 email: [email protected] www: http://www.seas.smu.edu/~mhd January 1999 CSE 8392 Spring 1999 51 Classification • “Classify a set of data based on their values in certain attributes” (R[2],p868) • Each grouping is a class • Equivalence Class • Given a set K = {k1, k2, k3 …ky} kx -> (A, B, C, D, E…) where this mapping partitions K • Similar to estimation CSE 8392 Spring 1999 52 Classification Examples • • • • • Financial market trends (bull, bear) Images (raster, vector) Loan approval (yes, no) Medical diagnosis Detecting faults in industry applications CSE 8392 Spring 1999 53 Basic Classification Techniques (Kennedy,Ch3) • Boundaries for decision regions – Ex: Loan threshold • Probability Techniques – p(x|C) – Figure 3-4, p 3-5, Kennedy – May also use prior knowledge of class membership probabilities P(C) – Select class that maximizes P(C)p(x|C) – Probability x is in class C is proportional to the probability that any input is in C and class C contains x CSE 8392 Spring 1999 54 Supervised Induction Techniques • Output the probability of class membership based on input values using some estimation technique (Decision Trees, Neural Nets) – – – – Use a sample database as a training set Analyze training data Develop model using attributes of data Use these class descriptions on rest of data • Note: May be many different class descriptions CSE 8392 Spring 1999 55 Posterior Probabilities (Kennedy) • P(C|x) - Probability input x belongs to class C • Suppose m classes, look at: P(C1|x), … , P(Cm|x) • Classification by assigning x to the class with the highest posterior probability • Look at training data and assign posterior probabilities to example patterns • May not work well with complex tuples in large databases • Fig 3-7, p3-9 CSE 8392 Spring 1999 56 Linear Regression • Linear mapping of input attributes to desired output • Error may exist: y w0 w1 x1 ... wn xn error Here xi are input attributes • Least-Squares Minimization: Sum of the squared error terms is minimized over database (training set) • Find weights: EQ3,EQ4 Kennedy, p 10-14 • May be used as baseline comparison approach • May not work well with complex databases : Not all data values known & May not be numeric values CSE 8392 Spring 1999 57 Similarity Measures • Describe each input tuple as vector D1 = <d11, … , d1n> • Define Sim(D1,D2) where: – Normalize (0-no similarity, 1- identical) – Usually assumes all values are numeric only • Represent each class with vector Ci – May be determined as centroid of vectors from training set • Assign each tuple Dj to class i where Sim(Dj,Ci) is minimized CSE 8392 Spring 1999 58 K Nearest Neighbors (Kennedy) • Store all input-output pairs in training set • Define distance function • When a tuple needs to be classified, determine distance between it and all items in the training set • Fig 10-12, p10-38 • Base answer on K nearest items in training set. Algorithm p 10-39 • Memory intensive & Slow CSE 8392 Spring 1999 59 Decision Trees (Kennedy, Section 10.4.10) • Similar to Twenty Questions: Fig 8-5, p144, Barquin • Internal Nodes: Decision Points based on one attribute • Leaves: Identify classes • Classification Process: Input tuple and move through tree based on attribute values • Difficult Part - Constructing tree (so that it is efficient) (Try playing twenty questions with a young child!) • Training Set used to build tree CSE 8392 Spring 1999 60 Decision Tree Issues • • • • • • Attributes Splits (Categorical, Discrete, Continuous) Ordering of attributes in tree Determining when to stop Must perform perfectly on training set Pruning of tree (remove branches) CSE 8392 Spring 1999 61 Decision Tree Advantages/Disadvantages • Advantages – Easy to understand – Efficient (time) • Disadvantages – May be difficult to use with continuous data – Limited to problems solved by dividing into subrectangles – Not flexible (no automatic revisions if incorrect) – No way to handle missing data – May have overfitting – Pruning combats overfitting (but it may induce other errors) CSE 8392 Spring 1999 62 ID-3 (R[2]) • Decision Tree learning system based on information theory • Attempts to minimize expected number of tests on a tuple • Formalizes the approach adults have to twenty questions! • Picks attributes with highest information gain first • Entropy i ( pi ln( pi )) CSE 8392 Spring 1999 63 CART (Kennedy,p10-56) • Builds binary decision tree • Exhaustive search to determine best tree where best defined by goodness of split : ( s / t ) 2 PL PR classes P( j / t j 1 L ) P( j / t R ) • Optimal splitting: (s' / t ) Maxi ((si / t )) CSE 8392 Spring 1999 64 Neural Networks • Determine “predictions using ‘neurons’ (computations) and their interconnections (weighted inputs).” (p142,Barquin) • Example: Fig 8-4, p143, Barquin Input values of attributes at left Weight associated with links between nodes Classification produced at output on right • Neural Net and Decision Tree Peter Cabena, Pablo Hadjinian, Rolf Stadler, Jaap Verhees, and Alessandro Zanasi, Discovering Data Mining From Concept to Implementation, Prentice-Hall, 1998, p71,p74. CSE 8392 Spring 1999 65 Neural Nets • Number of processing layers between input and output • Each processing unit (node) connected to all in the next layer • Construct neural net: Determine network structure (modeler) Weights “learned” by applying tree to training set Backpropagation used to adjust weights Desired output provided with training data Actual network output subtracted from desired output and error produced Connection weights changed based on a minimization method called gradient descent CSE 8392 Spring 1999 66 Historical Note: • Neural network weights are adjusted based on whether or not the prediction is good. • Earlier IR systems uses “feedback” to adjust weights in document vectors based on precision/recall values CSE 8392 Spring 1999 67 Neural Nets Advantages/Disadvantages • Advantages – Low classification error rates – Robust in noisy environments – Rules may be more concise if strong relationships in attributes – Provides high degree of accuracy • Disadvantages – Multiple passes over database - Very expensive – Classification process not apparent - “Black Box” • Embedded within graph structure and link weights • May be difficult to generate rules • Difficult to infuse domain knowledge in neural net – May have overfitting – May fail to converge CSE 8392 Spring 1999 68 Rule Extraction (RX) Algorithm (R[4]) • • • • • • Cluster Enumerate ruleset for network outputs Enumerate ruleset for network inputs Merge input and output rulesets Algorithm p958 Neural Net Mining Example – Lu, section 2.2 CSE 8392 Spring 1999 69 Neural Net Data Mining Research Issues • Network training time • Possible methods for incremental training of network • Use of domain experts • Reduction of inputs to network CSE 8392 Spring 1999 70 Bayesian Classification (Fayyad,Ch6) • In Bayesian statistics, we measure the likelihood of observed data y given each value of x, e.g. f(y|x) • Data mining goal: find the most probable set of class descriptions • NASA AutoClass(Fayyad,Ch6) – – – – Discover automatic classifications in data Like clustering No prior definition of classes Classes may be unknown to experts CSE 8392 Spring 1999 71 AutoClass • Records represented as vectors of values • pdf: Gives “probability of observing an instance possessing any particular attribute value vector.” (p156,Cheeseman) • Model: finite mixture distribution Interclass Mixture Probability P = (Xi Cj | Vc, Tc, S, I) • Two levels of search: maximum posterior parameter (MAP), most probable density function • Each model a product of independent probability distributions of attribute subsets CSE 8392 Spring 1999 72 AutoClass Case Studies • IRAS: Spectra Classification – “Minimum” information vs. full access – “Good” outputs are domain specific • DNA Codes – Results may extend beyond limits of database • LandSat Pixels – Parallelization – Undocumented preprocessing CSE 8392 Spring 1999 73 AutoClass Issues • Interaction between domain experts and machine – Essential for good results – Experts and machine each have unique strengths – Iterative process • Ockham Factor – If a particular parameter does not noticeably improve model, reject models with this parameter CSE 8392 Spring 1999 74 Classification Summary • Watch out for preprocessing: key words: – – – – – – – – – Calibration Corrected Averaged Normalized Adjusted Compressed Subsets Partitioned Representative • Uncover biases in data collection • Engage in full partnership with experts and obtain domain specific results! CSE 8392 Spring 1999 75