第1个回答 2024-10-14
Clustering is a common unsupervised learning method, which involves categorizing similar data samples into groups (clusters). This process doesn't involve predefined labels; instead, it aims to group similar samples based on their inherent distribution patterns.
Clustering algorithms can be broadly categorized into traditional clustering algorithms and deep clustering algorithms. Among them, K-means clustering is one of the most widely used techniques, which relies on the partitioning method. The core idea is to initialize k cluster centers and then categorize samples based on their distances to these centers, iteratively minimizing the distance between each sample and its respective cluster center (as defined by a target function).
The optimization algorithm for K-means clustering comprises several steps:
1. Randomly select k samples as initial cluster centers (where k is the hyperparameter representing the number of clusters. Its value can be determined by prior knowledge or validation techniques).
2. For each data point, calculate its distance to k cluster centers and assign it to the cluster with the closest center.
3. Recalculate the position of each cluster center based on the newly assigned cluster memberships.
4. Repeat steps 2 and 3 until a stopping condition is met (like a predetermined number of iterations or when cluster centers stabilize).
It's worth noting that K-means clustering's iterative algorithm is closely related to the Expectation-Maximization (EM) algorithm. The EM algorithm tackles the issue of parameter estimation in probabilistic models with unobservable latent variables. In the K-means context, the latent variables are the cluster assignments for each data point. The K-means algorithm's steps of assigning data points to clusters and recalculating cluster centers correspond to the E-step and M-step of the EM algorithm, respectively.
One of the critical challenges in K-means clustering is the selection of the distance metric. The algorithm relies on measuring the similarity between samples based on distance, which determines their assignment to the nearest cluster center. Commonly used metrics include Manhattan distance and Euclidean distance, as discussed in the article "Comprehensive Overview of Distance and Similarity Methods (7 Types)."
The Manhattan and Euclidean distances are straightforward to compute, involving the sum of the differences between each feature of two samples. For instance, in a two-dimensional feature space, the blue line represents the Manhattan distance (akin to driving from one intersection to another in the Manhattan grid system), and the red line represents the Euclidean distance.
Deciding the value of k, or the number of clusters, is a crucial aspect of K-means clustering. The outcome can vary significantly with different k values. Determining k can be done through various methods, such as the prior knowledge approach, elbow method, or other techniques like:
Firstly, the prior approach is relatively simple and relies on domain expertise to determine the value of k. For example, using the iris flower dataset, which typically contains three categories, one can set k=3 for clustering validation. The below image illustrates that the clustering prediction aligns well with the actual iris categories.
The elbow method's limitation lies in its subjective nature, lacking automation. Other methods include:
The limitations of K-means clustering include:
One significant issue is the initialization of cluster centers, which can significantly impact the final results. To address this, the K-means++ algorithm was introduced, which initializes centers by selecting points that are as far as possible from each other, based on the distances to existing centers. The probability of selecting a point as a new center is proportional to its distance from the already determined centers, squared.
Another limitation is the assumption of spherical and isotropic data clusters in Euclidean space, which doesn't always hold in real-world scenarios. To tackle this, we can employ kernel functions, leading to the kernel K-means algorithm, a variant of kernel clustering. This method involves mapping input data points into a higher-dimensional feature space using a nonlinear transformation, where clustering is performed. This transformation increases the likelihood of linear separability, thus enabling more accurate clustering in cases where classical algorithms fail.
K-means is designed for numerical features, necessitating encoding techniques for categorical features. Alternative algorithms like K-Modes and K-Prototypes are tailored for mixed data types, where the cluster centers for numerical features are averages, for categorical features are modes, and the distance metric is the Hamming distance.
Another challenge is the handling of feature scaling, as larger features can disproportionately influence distance calculations. To mitigate this, data is typically standardized or normalized to ensure all numerical features are on a comparable scale. For instance, in a dataset with age and salary features, the squared difference in age will be vastly smaller than that in salary, potentially biasing the clustering results. To address this, feature scaling methods like normalization or standardization are employed.
For assigning weights to features, K-means calculates distances based on feature similarity. To incorporate feature weights, normalization can be adjusted by multiplying each feature's value by the appropriate weight. For Manhattan distance, simply multiplying the feature value by the weight accomplishes this. When dealing with categorical features represented through embeddings, scaling each embedding dimension by the square root of its size ensures that the clustering is not disproportionately influenced by these high-dimensional features.
Feature selection is crucial in unsupervised clustering, as it can dramatically affect the outcome. Including irrelevant or noisy features can lead to misleading results. For instance, in clustering bank customers based on quality, transaction frequency and deposit amount are significant features, whereas gender and age might introduce noise, leading to clusters based on similarities in gender and age rather than customer quality.
For guidance on unsupervised clustering feature selection, consult the following references:
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