ppose we have a dataset of eight 3-bit binary vectors and their corresponding labels. Classify a new data point, 010,using a k-nearest neighbor classifier with k=3 and Hamming distance.Data 000 001 010 011 100 101 110 111 111 111point A A B B C C D D D D
Question
ppose we have a dataset of eight 3-bit binary vectors and their corresponding labels. Classify a new data point, 010,using a k-nearest neighbor classifier with k=3 and Hamming distance.Data 000 001 010 011 100 101 110 111 111 111point A A B B C C D D D D
Solution
To classify a new data point, 010, using a k-nearest neighbor classifier with k=3 and Hamming distance, we need to follow these steps:
Step 1: Calculate the Hamming distance between the new data point (010) and each of the existing data points in the dataset. The Hamming distance is the number of positions at which the corresponding bits are different.
- Hamming distance between 010 and 000: 2
- Hamming distance between 010 and 001: 1
- Hamming distance between 010 and 010: 0
- Hamming distance between 010 and 011: 1
- Hamming distance between 010 and 100: 2
- Hamming distance between 010 and 101: 1
- Hamming distance between 010 and 110: 2
- Hamming distance between 010 and 111: 3
Step 2: Select the k nearest neighbors based on the calculated Hamming distances. In this case, k=3, so we choose the three data points with the smallest Hamming distances:
- Nearest neighbors: 010, 001, 011
Step 3: Determine the majority class among the selected nearest neighbors. In this case, we have:
- Class A: 1 occurrence
- Class B: 1 occurrence
- Class C: 1 occurrence
Since each class occurs once, there is no clear majority.
Step 4: Make a prediction based on the majority class. In this case, since there is no clear majority, we cannot confidently classify the new data point 010.
Therefore, the classification of the new data point 010 using a k-nearest neighbor classifier with k=3 and Hamming distance is inconclusive.
Similar Questions
Consider a classification problem where the input space consists of 10 binary features (X₁, X₂, ..., X₁₀) and the output space consists of two classes (0 and 1). A dataset of 100 training examples is given, with the following feature values and corresponding class labels:Example 1: (0, 1, 1, 0, 1, 0, 1, 0, 0, 1) → Class: 0Example 2: (1, 0, 0, 1, 1, 1, 0, 1, 0, 1) → Class: 1Example 3: (1, 1, 1, 0, 0, 1, 0, 0, 1, 0) → Class: 1Example 100: (0, 0, 1, 0, 1, 0, 1, 1, 0, 1) → Class: 0You are tasked with building a supervised learning model using logistic regression. Each feature Xi is binary and can take values 0 or 1. You decide to use one-hot encoding to represent the input features. After applying one-hot encoding, how many features will the dataset have for training the logistic regression model?a)19b)20c)10d)18
#<GRADED> def knnclassifier(xTr,yTr,xTe,k): """ function preds=knnclassifier(xTr,yTr,xTe,k); k-nn classifier Input: xTr = nxd input matrix with n row-vectors of dimensionality d xTe = mxd input matrix with m row-vectors of dimensionality d k = number of nearest neighbors to be found Output: preds = 1xd vector of predicted labels, ie preds(i) is the predicted label of xTe(i,:) """ # fix array shapes yTr = yTr.flatten() # Your code goes here raise NotImplementedError('Your code goes here!') return preds #</GRADED> python code with no for loop and return preds
#<GRADED> def knnclassifier(xTr,yTr,xTe,k): """ function preds=knnclassifier(xTr,yTr,xTe,k); k-nn classifier Input: xTr = nxd input matrix with n row-vectors of dimensionality d xTe = mxd input matrix with m row-vectors of dimensionality d k = number of nearest neighbors to be found Output: preds = 1xd vector of predicted labels, ie preds(i) is the predicted label of xTe(i,:) """ # fix array shapes yTr = yTr.flatten() # Your code goes here raise NotImplementedError('Your code goes here!') return preds #</GRADED> use python without using for-loop
(3,7) hamming code represents
<p>(b) Implement the function <b><code>findknn</code></b>, which should find the $k$ nearest neighbors of a set of vectors within a given training data set. Break ties arbitrarily. The call of <pre> [I,D]=findknn(xTr,xTe,k); </pre> should result in two matrices $I$ and $D$, both of dimensions $k\times m$, where $m$ is the number of input vectors in <code>xTe</code>. The matrix $I(i,j)$ is the index of the $i^{th}$ nearest neighbor of the vector $xTe(j,:)$. So, for example, if we set <code>i=I(1,3)</code>, then <code>xTr(i,:)</code> is the first nearest neighbor of vector <code>xTe(3,:)</code>. The second matrix $D$ returns the corresponding distances. So $D(i,j)$ is the distance of $xTe(j,:)$ to its $i^{th}$ nearest neighbor. </p>
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.