Clustering is a fundamental procedure in the analysis of scientific data. It is used ubiquitously across the sciences. Despite decades of research, existing clustering algorithms have limited effectiveness in high dimensions and often require tuning parameters for different domains and datasets. We present a clustering algorithm that achieves high accuracy across multiple domains and scales efficiently to high dimensions and large datasets. The presented algorithm optimizes a smooth continuous objective, which is based on robust statistics and allows heavily mixed clusters to be untangled. The continuous nature of the objective also allows clustering to be integrated as a module in end-to-end feature learning pipelines. We demonstrate this by extending the algorithm to perform joint clustering and dimensionality reduction by efficiently optimizing a continuous global objective. The presented approach is evaluated on large datasets of faces, handwritten digits, objects, newswire articles, sensor readings from the Space Shuttle, and protein expression levels. Our method achieves high accuracy across all datasets, outperforming the best prior algorithm by a factor of 3 in average rank.clustering | data analysis | unsupervised learning C lustering is one of the fundamental experimental procedures in data analysis. It is used in virtually all natural and social sciences and has played a central role in biology, astronomy, psychology, medicine, and chemistry. Data-clustering algorithms have been developed for more than half a century (1). Significant advances in the last two decades include spectral clustering (2-4), generalizations of classic center-based methods (5, 6), mixture models (7, 8), mean shift (9), affinity propagation (10), subspace clustering (11-13), nonparametric methods (14, 15), and feature selection (16)(17)(18)(19)(20).Despite these developments, no single algorithm has emerged to displace the k -means scheme and its variants (21). This is despite the known drawbacks of such center-based methods, including sensitivity to initialization, limited effectiveness in high-dimensional spaces, and the requirement that the number of clusters be set in advance. The endurance of these methods is in part due to their simplicity and in part due to difficulties associated with some of the new techniques, such as additional hyperparameters that need to be tuned, high computational cost, and varying effectiveness across domains. Consequently, scientists who analyze large high-dimensional datasets with unknown distribution must maintain and apply multiple different clustering algorithms in the hope that one will succeed. Books have been written to guide practitioners through the landscape of data-clustering techniques (22).We present a clustering algorithm that is fast, easy to use, and effective in high dimensions. The algorithm optimizes a clear continuous objective, using standard numerical methods that scale to massive datasets. The number of clusters need not be known in advance.The operation of the algorithm ...

Semidefinite programming (SDP) is an indispensable tool in computer vision, but general-purpose solvers for SDPs are often too slow and memory intensive for large-scale problems. Our framework, referred to as biconvex relaxation (BCR), transforms an SDP consisting of PSD constraint matrices into a specific biconvex optimization problem, which can then be approximately solved in the original, low-dimensional variable space at low complexity. The resulting problem is solved using an efficient alternating minimization (AM) procedure. Since AM has the potential to get stuck in local minima, we propose a general initialization scheme that enables BCR to start close to a global optimum-this is key for BCR to quickly converge to optimal or near-optimal solutions. We showcase the efficacy of our approach on three applications in computer vision, namely segmentation, co-segmentation, and manifold metric learning. BCR achieves solution quality comparable to state-of-the-art SDP methods with speedups between 4× and 35×.

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Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not minimizers, of the loss function. The alternating stochastic gradient methods typically used for such problems do not reliably converge to saddle points, and when convergence does happen it is often highly sensitive to learning rates. We propose a simple modification of stochastic gradient descent that stabilizes adversarial networks. We show, both in theory and practice, that the proposed method reliably converges to saddle points, and is stable with a wider range of training parameters than a non-prediction method. This makes adversarial networks less likely to "collapse," and enables faster training with larger learning rates.

SnO 2 is a promising material for photovoltaic and photocatalytic applications because it exhibits high electron mobility, its conduction band lies at a convenient energy to act as an electron acceptor, and it can be easily grown in a variety of different nanostructures including nanoparticles, nanorods, and nanosheets. However, strategies for surface functionalization of SnO 2 are much less well developed than alternative oxides. Here, we demonstrate the growth and subsequent chemical functionalization of SnO 2 nanorods to enable the chemically directed assembly of SnO 2 nanorod-TiO 2 nanoparticle heterojunctions, and we characterize the charge-transfer properties using time-resolved surface photovoltage measurements. Vertically aligned SnO 2 nanorods were grown via a high-pressure chemical synthesis method. The SnO 2 nanorods were square in cross-section, exposing sidewalls consisting of {110}-type crystal planes. Functionalization via photochemical grafting with butenol yielded nanorods terminated with a high density of -OH groups that were converted to azide groups. The azide groups were linked with alkyne-modified TiO 2 nanoparticles via the Cu(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAC) reaction, a form of ''click'' chemistry, thereby covalently grafting the TiO 2 nanoparticles to the SnO 2 nanorods. Time-resolved surface photovoltage measurements of the resulting adducts showed that the covalent bonding of TiO 2 nanoparticles to the SnO 2 nanorods enhances the interfacial charge transfer compared to the unmodified SnO 2 nanorods, leading to an increased accumulation of holes at the surface.