**k-Means Clustering** is a clustering algorithm that divides a training set into $k$ different clusters of examples that are near each other. It works by initializing $k$ different centroids {$\mu\left(1\right),\ldots,\mu\left(k\right)$} to different values, then alternating between two steps until convergence:

(i) each training example is assigned to cluster $i$ where $i$ is the index of the nearest centroid $\mu^{(i)}$

(ii) each centroid $\mu^{(i)}$ is updated to the mean of all training examples $x^{(j)}$ assigned to cluster $i$.

Text Source: Deep Learning, Goodfellow et al

Image Source: [scikit-learn](https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_digits.html)

CPE is an effective collaborative metric learning to effectively address the problem of sparse and insufficient preference supervision from the margin distribution point-of-view.

Collaborative Preference Embedding against Sparse Labels

k-Means Clustering

A **convolution** is a type of matrix operation, consisting of a kernel, a small matrix of weights, that slides over input data performing element-wise multiplication with the part of the input it is on, then summing the results into an output.

Intuitively, a convolution allows for weight sharing - reducing the number of effective parameters - and image translation (allowing for the same feature to be detected in different parts of the input space).

Image Source: [https://arxiv.org/pdf/1603.07285.pdf](https://arxiv.org/pdf/1603.07285.pdf)

Year	2000
Data Source	CC BY-SA - https://paperswithcode.com