This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and accordingly weighs informative features while discovering biclusters. Moreover, the method is adaptive to the data, and is accompanied by an efficient algorithm based on proximal alternating minimization, complete with detailed guidance on hyperparameter tuning and efficient solutions to optimization subproblems. These contributions are theoretically grounded; we establish finite-sample bounds on the objective function under sub-Gaussian errors, and generalize these guarantees to cases where input affinities need not be uniform. Extensive simulation results reveal our method consistently recovers underlying biclusters while weighing and selecting features appropriately, outperforming peer methods. An application to a gene microarray dataset of lymphoma samples recovers biclusters matching an underlying classification, while giving additional interpretation to the mRNA samples via the column groupings and fitted weights.

Given samples lying on any of a number of subspaces, subspace clustering is the task of grouping the samples based on the their corresponding subspaces. Many subspace clustering methods operate by assigning a measure of affinity to each pair of points and feeding these affinities into a graph clustering algorithm. This paper proposes a new paradigm for subspace clustering that computes affinities based on the corresponding conic geometry. The proposed conic subspace clustering (CSC) approach considers the convex hull of a collection of normalized data points and the corresponding tangent cones. The union of subspaces underlying the data imposes a strong association between the tangent cone at a sample $x$ and the original subspace containing $x$. In addition to describing this novel geometric perspective, this paper provides a practical algorithm for subspace clustering that leverages this perspective, where a tangent cone membership test is used to estimate the affinities. This algorithm is accompanied with deterministic and stochastic guarantees on the properties of the learned affinity matrix, on the true and false positive rates and spread, which directly translate into the overall clustering accuracy.

Graph clustering is a fundamental task in many data-mining and machine-learning pipelines. In particular, identifying a good hierarchical structure is at the same time a fundamental and challenging problem for several applications. The amount of data to analyze is increasing at an astonishing rate each day. Hence there is a need for new solutions to efficiently compute effective hierarchical clusterings on such huge data. The main focus of this paper is on minimum spanning tree (MST) based clusterings. In particular, we propose affinity, a novel hierarchical clustering based on Boruvka's MST algorithm. We prove certain theoretical guarantees for affinity (as well as some other classic algorithms) and show that in practice it is superior to several other state-of-the-art clustering algorithms.

To remedy this, most robust fine-tuning methods aim to preserve the pre-trained features.

MolGroup achieves this by utilizing a routing mechanismoptimized through abi-level optimization framework.

Fighting with thecurse of dimensionalityby leveraging low-dimensional intrinsic structures has become an important guiding principle in modern data science.