Efficient Parameter-free Clustering Using First Neighbor Relations (1902.11266v1)

Abstract: We present a new clustering method in the form of a single clustering equation that is able to directly discover groupings in the data. The main proposition is that the first neighbor of each sample is all one needs to discover large chains and finding the groups in the data. In contrast to most existing clustering algorithms our method does not require any hyper-parameters, distance thresholds and/or the need to specify the number of clusters. The proposed algorithm belongs to the family of hierarchical agglomerative methods. The technique has a very low computational overhead, is easily scalable and applicable to large practical problems. Evaluation on well known datasets from different domains ranging between 1077 and 8.1 million samples shows substantial performance gains when compared to the existing clustering techniques.

• The paper introduces FINCH, a novel parameter-free algorithm that uses first neighbor relationships to identify natural clusters without manual tuning.
• The paper demonstrates that FINCH efficiently constructs a hierarchical clustering structure, enabling scalable analysis with low computational overhead.
• The paper validates FINCH through theoretical analysis and empirical testing, showing superior clustering accuracy and normalized mutual information across diverse datasets.

Overview of "Efficient Parameter-free Clustering Using First Neighbor Relations"

The paper introduces an innovative clustering algorithm, "FINCH," which stands for First Integer Neighbor Clustering Hierarchy. This method is parameter-free, meaning it does not require user-defined inputs, such as the number of clusters, similarity thresholds, or extensive domain-specific pre-knowledge. The core of this method is built upon a straightforward principle: leveraging the first neighbor of each data point to establish direct connectivity and discern natural groupings in data.

Key Contributions

1. Parameter-Free Clustering: The algorithm distinguishes itself by eliminating the need for any hyper-parameters. Traditional methods like Kmeans demand specification of the number of clusters, while hierarchical agglomerative clustering (HAC) relies on predefined distance thresholds. FINCH circumvents these constraints by utilizing an adjacency link matrix produced from the first neighbors of data points.
2. Hierarchical Agglomeration: FINCH offers a hierarchical clustering structure akin to HAC methods. This property allows it to provide a set of partitions that reveal data organization at different granularity levels, which can be preferable to single-flat cluster solutions.
3. Scalability and Efficiency: The computational simplicity of FINCH, owing to the use of integer indices from first neighbor relationships, facilitates its application on large datasets with low computational overhead. This advantage is clearly demonstrated by the algorithm's capability to handle datasets with up to 8.1 million samples.
4. Theoretical Foundations and Empirical Validation: The paper establishes the theoretical basis of FINCH by relating it to concepts like 1-nearest neighbor (1-nn) and shared nearest neighbor (SNN) graphs. Empirical assessments on diverse datasets—including biological data, text, image data, and face datasets—show high performance in terms of clustering accuracy (ACC) and normalized mutual information (NMI).

Numerical Results

The results obtained from experimental evaluations underscore the efficacy of FINCH across multiple datasets. Notably, FINCH attains near-perfect clustering accuracy on datasets like MNIST when features are learned using the same labels. On the evaluation metrics such as NMI, FINCH not only provides a parameter-free clustering solution but also surpasses existing state-of-the-art methods in many cases. Furthermore, its performance on the BBTs01 and BFs05 video face clustering datasets showcases its strong adaptive capacity beyond typical static datasets.

Implications and Future Directions

The introduction of FINCH can bear significant implications in areas where minimal intervention and parameter tuning are necessary to discover data patterns. Since it scales well and provides hierarchical clustering solutions, it has potential utility in large-scale data analytics, including genomics, image recognition, and natural language processing.

In future developments, extending FINCH with a more rigorous theoretical analysis could further reinforce its utility in clustering research. Integrating deeper connections with graph theory and exploring its robust applications in non-linear embedding learning could expand its scope. With the advent of ever-larger datasets in contemporary research domains, FINCH represents a promising direction in unsupervised learning and data organization methods.

Ultimately, by allowing a seamless transition from understanding small clusters to large-scale data distributions without human intervention, FINCH might redefine conventional clustering paradigms across scientific and industrial applications.