讲解：6CCS3PRE、SVMs、Matlab、MatlabJava|Java

Department of Informatics, King’s College London PatternRecognition (6CCS3PRE/7CCSMPNN).Assignment: Support Vector Machines (SVMs) and EnsembleMethodsThis coursework is assessed. A type-written report needs to be submitted onlinethrough KEATS by the deadline specified on the module’s KEATS webpage. In thiscoursework, we consider (before Q8) a classification problem of 3 classes. A multi-classSVM-based classifier formed by multiple SVMs is designed to deal with the classificationproblem. And after Q8 (included Q8) considers your “own created” dataset toinvestigate the classification performance using the techniques of Bagging and Boosting.Some simple “weak” classifiers will be designed and combined to achieve an improvedclassification performance for a two-class classification problem.Q1. Write down your 7-digit student ID denoted as s1s2s3s4s5s6s7. (5 Marks)Q2. Find R1 which is the remainder of . Table 1 showsthe multi-class methods to be used corresponding to the value of R1 obtained.(5 Marks)R1 Method0 One against one1 One against all2 Binary decision tree3 Binary codedTable 1: R1 and its corresponding multi-class method.Q3. Create a linearly separable two-dimensional dataset of your own, which consists of3 classes. List the dataset in the format as shown in Table 2. Each class should contain atleast 10 samples and all three classes have the same number of samples. Note: This isyour own created dataset. The chance of having the same dataset in other submissions isslim. Do not share your dataset with others to avoid any plagiarism/collusion issues.(10 Marks) Table 2: Samples of three classes.Q4. Plot the dataset in Q3 to show that the samples are linearly separable. Explain whyyour dataset is linearly separable. Hint: the Matlab built-in function plot can be used andshow some example hyperplanes which can linearly separable the datasets. Identifywhich hyperplane is for which classes. (20 Marks)Q5. According to the method obtained in Q2, draw a block diagram at SVM level toshow the structure of the multi-class classifier constructed by linear SVMs. Explain thedesign (e.g., number of inputs, number of outputs, number f SVMs used, class labelassignment, etc.) and describe how this multi-class classifier works.Remark: A blocking diagram is a diagram which is used to, say, show a concept or astructure, etc. Here in this question, a diagram is used to show the structure of the multiclassSVM classifier, i.e., how to put binary SVM classifiers together to work as a multiclassSVM classifier. For example, Q5 of tutorial 9 is an example of a block diagram atSVM level. Neural network diagram is a kind of diagram to show its structure at neuronlevel. The block diagrams in lecture 9 are to show the architecture of ensembleclassifier, etc. (20 Marks)Q6. According to your dataset in Q3 and the design of your multi-class classifier in Q5,identify the support vectors of the linear SVMs by “inspection” and design theirhyperplanes by hand. Show the calculations and explain the details of your design.(20 Marks)Q7. Produce a test dataset by averaging the samples for each row in Table 2, i.e.,(sample of class 1 + sample of class 2 + sample of class 3)/3. Summarise the results inthe form of Table 3, where N is the number of SVMs in your design and “Classification” isthe class determined by your multi-class classifier. Explain how to get the“Classification” column using one test sample. Show the calculations for one or twosamples to demonstrate how to get the contents in the table. (20 Marks)Table 3: Summary of classification accuracy.Marking: The learning outcomes of this assignment are that student understands thefundamental principle and theory of support vector machine (SVM) classifier; is able todesign multi-class SVM classifier for linearly separable dataset and knows how todetermine the classification of test samples with the designed classifier. The assessmentwill look into the knowledge and understanding on the topic. When answering thequestions, show/explain/describe clearly the steps/design/concepts with reference tothe equations/theory/algorithms (stated in the lecture slides). When making comments(if necessary), provide statements with the support from the results obtained.Purposes of Assignment: This assignment provides the overall classification idea fromsamples to design to classification. It helps you to make clear the concept, workingprinciple, theory, classification of samples, design procedure and multiple-classclassification techniques for SVM.Q8. Create a non-linearly separable dataset consisting of at least 20 two-dimensionaldataset. Each data is characterised by tw代做6CCS3PRE作业、代写SVMs留学生作业、Matlab程序设计作业调试、代写Matlab语言作业 代做Java程o points x1 ∈ [?10, 10] and x2 ∈ [?10, 10] andassociated with a class y ∈ {?1, +1}. List the data in a table in a format as shown in Table1 where the first column is for the data points of class “?1” and the second column is forthe data points of class “+1”. (20 Marks)Q9. Plot the dataset (x axis is x1 and y axis is x2) and show that the dataset is nonlinearlyseparable. Represent class “?1” and class “+1” using “×” and ‘?”, respectively.Explain why your dataset is non-linearly separable. Hint: the Matlab built-in functionplot can be used. (20 Marks)Q10. Design Bagging classifiers consisting of 3, 4 and 5 weak classifiers using the stepsshown in Appendix 1. A linear classifier should be used as the weak classifier. Ex- plainand show the design of the hyperplanes of weak classifiers. List the parameters of thedesign hyperplanes.After designing the weak classifiers, apply the designed weak classifiers and baggingclassifier to all the samples in Table 1. Present the classification results in a table asshown in Table 2. The columns “Weak classifier 1” to ‘Weak classifier n” list the outputclass ({?1, +1}) of the corresponding weak classifiers. The column “Overall classifier” listthe output class ({?1, +1}) of the bagging classifier. The last row lists the classificationaccuracy in percentage for all classifiers, i.e., .Explain how to determine the class (for each weak classifier and over all classifier) using one test sample. You will have 3 tables (for 3, 4 and 5 weak classifiers) for this question.Comment on the results (in terms of classification performance when different numberof weak classifiers are used). (30 Marks)Table 2: Classification results using Bagging technique combining n weak classifiers. Thefirst row “Data” are the samples (both classes 1 and 2) in Table 1.Q11. Design a Boosting classifier consisting of 3 weak classifiers using the steps shownin Appendix 2. A linear classifier should be used as a weak classifier. Explain and showthe design of the hyperplanes of weak classifiers. List the parameters of the designhyperplanes. After designing the weak classifiers, apply the designed weak classifiersand boosting classifier to all the samples in Table 1. Present the classification results in atable as shown in Table 2. Explain how to determine the class (for each weak classifierand boosting classifier) using one test sample. Comment on the results of the overallclassifier in terms of classification performance when comparing with the 1st, 2nd andthe 3rd weak classifiers, and with the bagging classifier with 3-weak classifiers in Q.3.(30 Marks)Appendix 1: Bagging1Q1. Start with dataset D.Q2. Generate M dataset D1, D2, . . ., DM . Each distribution is created by drawing n′ replacement.? Some samples can appear more than once while others do not appear at. all.Q3. Learn weak classifier for each dataset.weak classifiers fi(x) for dataset Di, i = 1, 2, ..., M.Q4. Combine all weak. classifiers using a majority voting scheme. Appendix 2: Boosting 2 Dataset D with n patterns Training procedure:(1Details can be found in Section “Bagging” in the Lecture notes2Details can be found in Section “Boosting” in the Lecture notes. )Step 1: Randomly select a set of n1 ≤ n patterns (without replacement) from D tocreate dataset D1. Train a weak classifier C1 using D1 (C1 should have at least 50%classification accuracy).Step 2: Create an “informative” dataset D2 (n2 ≤ n) from D of which roughly. half ofthe patterns should be correctly classified by C1 and the rest is wrongly classified.Train a weak classifier C2 using D2.Step 3: Create an “informative” dataset D3 from D of which the patterns are not wellclassified by C1 and C2 (C1 and C2 disagree). Train a weak classifier C3 using D3. The final decision of classification is based on the votes of the weak classifiers.– e.g.,by the first two weak classifiers if they agree, and by the third weak classifier if thefirst two disagree.Marking: The learning outcomes of this assignment are that student understands thefundamental principle and concepts of ensemble methods (Bagging and Boosting); isable to design weak classifies; knows the way to form Bagging/Boosting classifier andknows how to determine the classification of test samples with the designedBagging/Boosting classifiers. The assessment will look into the knowledge andunderstanding on the topic. When answering the questions, show/explain/describeclearly the steps/design/concepts with reference to the equations/theory/algorithms(stated in the lecture slides). When making comments, provide statements with thesupport from the results obtained. 转自：http://ass.3daixie.com/2019030458440330.html