Which of the following best describes the K-means algorithm?

Question

BlackTom AI · Accepted Answer

K-means partitions data into K groups by iteratively assigning points to the nearest cluster centroid and updating those centroids to minimize within-cluster variance.

Relevant knowledge points:
- K-means is an unsupervised clustering algorithm (no labels used).
- It aims to minimize the within-cluster sum of squared distances: J = Σ_{j=1..K} Σ_{x∈C_j} ||x − μ_j||^2, where μ_j is the centroid of cluster C_j.
- The algorithm alternates between assignment and update steps until convergence.

Step-by-step reasoning and procedure:
1. Choose K, the number of clusters, and initialize K centroids (random or via k-means++).  
2. Assignment step: for each data point x, assign it to cluster j* where j* = argmin_j ||x − μ_j||^2 (closest centroid).  
3. Update step: recompute each centroid μ_j as the mean of all points assigned to cluster j: μ_j = (1/|C_j|) Σ_{x∈C_j} x.  
4. Repeat steps 2–3 until assignments do not change or the decrease in J is below a threshold.  
Intermediate calculations include computing Euclidean distances from each point to all centroids and averaging assigned points to get new centroids. The objective J strictly decreases (or remains) at each iteration, leading to a local minimum.

Why the correct option is correct:
- "A technique for grouping similar data points into clusters" directly matches K-means’ goal and mechanics: grouping by proximity to centroids and minimizing intra-cluster variance.

Why the other options are incorrect:
- "A method that predicts continuous numeric values" describes regression (e.g., linear regression), a supervised task using labeled outputs.  
- "A model that creates decision boundaries using margins" describes Support Vector Machines (SVMs), which are supervised classifiers maximizing margins.  
- "A deep learning architecture used for image recognition" refers to convolutional neural networks (CNNs), a class of deep models for feature learning and classification, not K-means clustering.

Conclusion: The correct answer is "A technique for grouping similar data points into clusters," which matches the provided answer.

Which of the following best describes the K-means algorithm?单项选择题

类似问题

In K Means, what does the value of K represent?

Why is scaling often important before using K Means?

In K Means, what does the value of K represent?

What does K Means try to do?

What is K Means?

True or False: In a K-Means clustering algorithm where K = 3, there will always be 3 iterations of the algorithm performed.

Q37. You create an elbow plot for different values of k. The curve decreases smoothly, but there is no clear “elbow” point. Which of the following is the most likely explanation?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单