KNN algorithm is one of the simplest classification algorithm and it is one of the most used learning algorithms. So what is the KNN algorithm?
This is shown in the figure below, which depicts the examples instances with the plus and minus signs and the query point with a red circle. Our task is to estimate classify the outcome of the query point based on a selected number of its nearest neighbors. In other words, we want to know whether the query point can be classified as a plus or a minus sign.
It is clear that in this case KNN will predict the outcome of the query point with a plus since the closest point carries a plus sign. This time KNN will not be able to classify the outcome of the query point since the second closest point is a minus, and so both the plus and the minus signs achieve the same score i.
This will define a nearest neighbor region, which is indicated by the circle shown in the figure above. Since there are 2 and 3 plus and minus signs, respectively, in this circle KNN will assign a minus sign to the outcome of the query point. Regression In this section we will generalize the concept of k-nearest neighbors to include regression problems.
Regression problems are concerned with predicting the outcome of a dependent variable given a set of independent variables. To start with, we consider the schematic shown above, where a set of points green squares are drawn from the relationship between the independent variable x and the dependent variable y red curve.
Given the set of green objects known as examples we use the k-nearest neighbors method to predict the outcome of X also known as query point given the example set green squares.
In this case we search the example set green squares and locate the one closest to the query point X. For this particular case, this happens to be x4.
The outcome of x4 i. In this case, we locate the first two closest points to X, which happen to be y3 and y4.
Taking the average of their outcome, the solution for Y is then given by: The above discussion can be extended to an arbitrary number of nearest neighbors K.
To summarize, in a k-nearest neighbor method, the outcome Y of the query point X is taken to be the average of the outcomes of its k-nearest neighbors. Each example consists of a data case having a set of independent values labeled by a set of dependent outcomes.
The independent and dependent variables can be either continuous or categorical. For continuous dependent variables, the task is regression; otherwise it is a classification.
Given a new case of dependent values query pointwe would like to estimate the outcome based on the KNN examples. For regression problems, KNN predictions are based on averaging the outcomes of the K nearest neighbors; for classification problems, a majority of voting is used.
The choice of K is essential in building the KNN model.
In fact, k can be regarded as one of the most important factors of the model that can strongly influence the quality of predictions.AN IMPLEMENTATION OF ALGORITHM FOR SECURED OPTICAL CHANNEL FOR IMPLANTABLE MEDICAL DEVICES published in Although we simply concentrate on range and k - nearest - neighbor queries within this work, our bodies can be simply extended to aid other spatial queries without altering the cal culations operated by the semi - reliable 3rd party and.
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|Installing R package command||Algorithm[ edit ] Example of k-NN classification. The test sample green circle should be classified either to the first class of blue squares or to the second class of red triangles.|
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