Georgia Institute Of Technology ISYE 6501 Midterm 1 Study Guide (Complete Solution)

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ISYE Midterm 1 Notes: Week 1 Classification: - Two main types of classifiers: o Hard Classifier: A classifier that perfectly separates data into 2 (or more) correct classes. This type of classifie... r is rigid and is only applicable to perfectly separable datasets. o Soft Classifier: A classifier that does not perfectly separate data into perfectly correct classes. This type is used when a dataset it not realistically separable by class thus we use a more flexible classifier that gives us not a perfect, but optimal solution given the constraint of a-separability. - If a given model uses a soft classifier, we can further tune it to fit our needs based on factors such as the cost of misclassification. - Semantics on the types of data: o Columns: Attribute / Features / Response / Covariates / Predictor o Rows: Observations / Data point o Structured Data: data that is described and stored in a structured way o Unstructured Data: data cannot be described or easily stored. The most common example is written language. o Quantitative Values: Numbers that have meaning in a numerical sense o Categorical Data: can be numeric representing a category or non-numeric indicating a category o Unrelated Data: No relationships between datapoints o Timeseries Data: Same data recorded over time typically in regular intervals - Hyperplane: In a p-dimensional coordinate space, a hyperplane is the flat affine subspace of that dimension such that it takes a dimensionality of (p-1). In this context affine indicates that the subspace need not pass through the origin. This equation will be in general linear form. o Equation of p dimensional general form:  β0 + β1X1 + β2X2 + … + βpXp = 0 - Linear Separable Hyperplane: Given a set of datapoints with given signed classes and perfectly linearly separable classes, there will be an infinite number of hyperplanes equations that satisfy all points being classified correctly. This is demonstrated in the constraints below. If a point is above the hyperplane it will have a positive value and if it is below the separating hyperplane it will have a value less than zero. Furthermore, if the class is correctly predicted via the result of the equation it will share the sign of its respective yi value. Given these two properties of the hyperplanes we can infer the following constraints [Show More]

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