Subspace clustering is a crucial task in data analysis, where the goal is to group similar data points into clusters. Traditional methods rely on hand-crafted features or heuristics, which can limit their effectiveness. In this paper, we propose a framework that utilizes the Minimum Description Length (MDL) principle to overcome these limitations. MDL is a powerful technique that helps find the optimal representation of data with the fewest possible bits. Our approach combines MDL with parameter-free methods, such as k-means and spectral clustering, to automatically determine the number of subspaces and clusters.
MDL and Subspace Clustering
To understand how MDL works, imagine you have a big box full of different toys. Each toy has a unique name, but some names are longer than others. The length of the name represents the complexity or richness of the toy’s features. Now, imagine you want to describe this box of toys to someone else without showing them the toys themselves. You can use shorter names (descriptors) to represent each toy, but some descriptors will be better at describing the toys than others. The goal is to find the best descriptors that can accurately convey the information about the toys with the fewest possible bits.
In subspace clustering, we face a similar problem. We have a dataset with many features, and our task is to identify meaningful clusters within the data. Traditional methods often rely on hand-crafted features or heuristics that can lead to inaccurate cluster assignments. By using MDL, we can find the optimal descriptors that capture the essential information of each feature and group similar data points into clusters.
Our framework consists of two stages: (1) parameter selection, and (2) subspace clustering. In the first stage, we use MDL to select the optimal parameters for the clustering algorithm. This includes choosing the number of subspaces and the dimensionality of each subspace. Once these parameters are selected, we enter the second stage, where we apply the selected clustering algorithm to find the clusters within each subspace.
Results
We evaluated our framework on several datasets and compared it with existing methods. Our approach consistently outperformed other methods in terms of accuracy and computational efficiency. We also demonstrated that our method can handle non-linear cluster structures and identify outliers more effectively than traditional methods.
Conclusion
In summary, this paper presents a novel framework for subspace clustering based on the MDL principle. By leveraging the power of MDL, we can automatically determine the optimal parameters for clustering algorithms and identify meaningful clusters within the data. Our approach outperforms existing methods in terms of accuracy and efficiency, making it a valuable tool for data analysts and researchers.
