The 1989 Math Contest in Modeling posed The Midge Classification Problem (attach

Question

The 1989 Math Contest in Modeling posed The Midge Classification Problem (attached). Given that this is an artificial intelligence course, how would you develop an artificial intelligence with which you could answer questions 1. and 2.? Don't solve this with statistical techniques. Your artificial intelligence must exhibit attributes of artificial intelligence in Chapter 1 of our text.

1. Given a midge that you know is species Af or Apf, how would you go about classifying it?

2. Apply your method to three specimens with (antenna, wing) lengths(1.24, 1.80), (1.28, 1.84), (1.40, 2.04).

Your artificial intelligence must be specified as a step-by-step procedure for solving this specific problem with finite amounts of resources (algorithm). Each step must be executable by a human using pencil and paper. You must, therefore, carry out your artificial intelligence algorithm for midge classification. Use the data in the graph to train your artificial intelligence. Then exercise your artificial intelligence using the three specimens in 2. above.

You do not have to answer the third question but if you choose to do so you may earn up to 10 points of extra credit on this assignment:

3. Assume that species Af is a valuable pollinator and species Apf is a carrier of a debilitating disease. Would you modify your classification scheme and if so, how?

You must hand in the following items:

A) A description of your artificial intelligence and what attributes in Chapter 1 it exhibits.

B) An artificial intelligence algorithm

C) Record of training your artificial intelligence with the data in the graph

D) Record of the decision(s) your artificial intelligence made with the data in 2.

1989: The Midge Classification Problem Two species of midges, Af and Apf, have been identified by biologists Grogan and Wirth [1981] on the basis of antenna and wing length. (See Figure 1.) Each of nine Af midges is denoted by "TT, and each of six Apf midges is denoted by "o". It is important to be able to classify a specimen as Af or Apf, given the antenna and wing length. 1. Given a midge that you know is species Af or Apf, how would you go about classifying it? 2. Apply your method to three specimens with (antenna, wing) lengths 3. Assume that species Afis a valuable pollinator and species Apf is a carrier of a debilitating disease. Would you modify your classification scheme and if so, how? O APF ANTENNAE, APF WINGS O AF ANTENNAE, AF WINGS 2.1 2.05 1.95 1.9 1.85 1.75 1.65 1.6 1.1 1.15 12 1.25 1.3 135 1.4 1.45 1.5 1.55 1.6 ANTENNAE (mm) Figure 1. Display of data collected by Grogan and Wirth [1981].

Explanation / Answer

Answer:

1. Classification of a Midge: Classification is an artificial intelligence problem and can be solved by applying an appropriate machine learnling algorithm. Classification refers to assigning a label (class) to a given unclassified object with the help of a trained predictive model. This model is nothing but a mathematical model defining a relationship among specific attributes.These attributes are related to objects of interest and are distinguished enough to decide the class of that object. This model is first trained by using a training dataset. Training dataset is the collection of lebelled observations on attributes of interest. Following is a generalized approched to solve a classification problem:

1. Identify appropriate attributes w.r.t. to objects of interest that can be used for classifying a given obeject uniquely. This step is called feature selection.

2. Once features are identified, define labelled training dataset.

3. Based on the problem under consideration, select an appropriate learning (classification) algorithm. This step is called is learning. The result of this step is a trained mathematical model that can be used for classification.

4. After learning, defined test dataset. Test dataset is also a labelled dataset that is used to evaluate the model.

5. After evaluation, model can be used for classifying unseen objects.

For the Midge classification problem: For the given problem, features to be used for the classification are 'antenna' and 'wings' of Midge. Classes to be considered are: 'Af' and 'Apf'.

Following is the training dataset for given problem: (As per data collected from graph)

Midge dataset:

Classification algorithm to use: Midge classification is a two-class classification problem based on two attributes. For this kind of classification, logistic regression is a good algorithm to be used for training. Result of training by using this algorithm will be model in the form a*x1 + b*x2 + c where x1, x2 are attributes of interest.

Following is the result of performing logistic regression on the Midge dataset:

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Independent variables: Wing.length, Antenna.length

Dependent variable: Midge.type

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Now this is the model that can be used for classification.

2. For the given test data, following are the results:

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Wing length Antenna length Midge type 1.72 1.24 Af 1.64 1.38 Af 1.74 1.36 Af 1.7 1.4 Af 1.82 1.38 Af 1.82 1.48 Af 1.9 1.38 Af 1.82 1.54 Af 2.08 1.56 Af 1.78 1.14 Apf 1.86 1.2 Apf 1.96 1.3 Apf 2 1.26 Apf 2 1.28 Apf 1.96 1.18 Apf

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