2.2 One versus all classifier (OVA) A OVA
classifier involves training a binary classifier for each class that discriminates between one class and all the remaining classes. Thus in total there will be C classifiers, each with their own set of parameters.
(a) (5 points) Does the dataset (Figure 1) fulfill the assumptions of LDA, if we were to construct a binary classifier between each class and all other classes? Justify your answer!
(b) (10 points) Suppose we were to construct hOVA in a similar way as the hOVO classifier presented above, i.e. we try to classify samples via majority vote. With the help of the example in Figure 1 and a rough sketch, explain in your own words, why this approach does not work. Hint: Try separating the feature space into different regions, like in exercise 2.1
(c). As we have seen in the previous exercise, we need more information than simply the class assigned by each of the C classifiers, in order to uniquely classify each possible input. Instead of only looking at which side of the hyperplane an input xi is on, we are now interested in how confident the classifier is in its decision. We train a binary classifier for each class j ∈ Y against all other classes hj (x) = 1{w> j x+bj−cj≥0} . We then obtain the probability of xi belonging to class j via P(y = j|x = xi) = σ(w> j xi + bj − cj ), (3) where σ(t) = 1 1+e−t is the sigmoid function. We can interpret this probability as the confidence of the binary classifier for each class. We thus define the multi-class OVA-LDA classifier as hOVA(x) = argmax j∈Y [σ(w> j x + bj − cj )] (4) where wj , bj and cj are parameters of classifier hj . (c) (10 points) From the definition of the binary LDA classifier in the lecture notes, derive equation (3).
(d) (10 points) Make a sketch of the dataset in Figure 2 and shade the regions of the feature space according to the class that equation (4) would assign them to.
(e) (5 points) Sketch an example of a dataset in which the OVA method cannot provide an optimal classifier, but the OVO method can. Justify your answer with a brief explanation! Hints: • Compare your answers to exercises 2.1 (a) and 2.2 (a). Can you find a distribution of classes, where the OVA classifier violates the LDA assumptions to an extreme extent? • You need not perform calculations, but instead use your intuition to make rough sketches.
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
