Fair clustering aims to divide data into distinct clusters while preventing sensitive attributes (\textit{e.g.}, gender, race, RNA sequencing technique) from dominating the clustering. Although a number of works have been conducted and achieved huge success recently, most of them are heuristical, and there lacks a unified theory for algorithm design. In this work, we fill this blank by developing a mutual information theory for deep fair clustering and accordingly designing a novel algorithm, dubbed FCMI. In brief, through maximizing and minimizing mutual information, FCMI is designed to achieve four characteristics highly expected by deep fair clustering, \textit{i.e.}, compact, balanced, and fair clusters, as well as informative features. Besides the contributions to theory and algorithm, another contribution of this work is proposing a novel fair clustering metric built upon information theory as well. Unlike existing evaluation metrics, our metric measures the clustering quality and fairness as a whole instead of separate manner. To verify the effectiveness of the proposed FCMI, we conduct experiments on six benchmarks including a single-cell RNA-seq atlas compared with 11 state-of-the-art methods in terms of five metrics. The code could be accessed from \url{ https://pengxi.me}.

As black-box models increasingly power high-stakes applications, a variety of data-driven explanation methods have been introduced. Meanwhile, machine learning models are constantly challenged by distributional shifts. A question naturally arises: Are data-driven explanations robust against out-of-distribution data? Our empirical results show that even though predict correctly, the model might still yield unreliable explanations under distributional shifts. How to develop robust explanations against out-of-distribution data? To address this problem, we propose an end-to-end model-agnostic learning framework Distributionally Robust Explanations (DRE). The key idea is, inspired by self-supervised learning, to fully utilizes the inter-distribution information to provide supervisory signals for the learning of explanations without human annotation. Can robust explanations benefit the model's generalization capability? We conduct extensive experiments on a wide range of tasks and data types, including classification and regression on image and scientific tabular data. Our results demonstrate that the proposed method significantly improves the model's performance in terms of explanation and prediction robustness against distributional shifts.

In this paper, we study how to achieve two characteristics highly-expected by incomplete multi-view clustering (IMvC). Namely, i) instance commonality refers to that within-cluster instances should share a common pattern, and ii) view versatility refers to that cross-view samples should own view-specific patterns. To this end, we design a novel dual-stream model which employs a dual attention layer and a dual contrastive learning loss to learn view-specific prototypes and model the sample-prototype relationship. When the view is missed, our model performs data recovery using the prototypes in the missing view and the sample-prototype relationship inherited from the observed view. Thanks to our dual-stream model, both cluster- and view-specific information could be captured, and thus the instance commonality and view versatility could be preserved to facilitate IMvC. Extensive experiments demonstrate the superiority of our method on six challenging benchmarks compared with 11 approaches. The code will be released.

Urbanization has a strong impact on the health and wellbeing of populations across the world. Predictive spatial modeling of urbanization therefore can be a useful tool for effective public health planning. Many spatial urbanization models have been developed using classic machine learning and numerical modeling techniques. However, deep learning with its proven capacity to capture complex spatiotemporal phenomena has not been applied to urbanization modeling. Here we explore the capacity of deep spatial learning for the predictive modeling of urbanization. We treat numerical geospatial data as images with pixels and channels, and enrich the dataset by augmentation, in order to leverage the high capacity of deep learning. Our resulting model can generate end-to-end multi-variable urbanization predictions, and outperforms a state-of-the-art classic machine learning urbanization model in preliminary comparisons.

Data augmentation is a powerful technique for improving the performance of the few-shot classification task. It generates more samples as supplements, and then this task can be transformed into a common supervised learning issue for solution. However, most mainstream data augmentation based approaches only consider the single modality information, which leads to the low diversity and quality of generated features. In this paper, we present a novel multi-modal data augmentation approach named Dizygotic Conditional Variational AutoEncoder (DCVAE) for addressing the aforementioned issue. DCVAE conducts feature synthesis via pairing two Conditional Variational AutoEncoders (CVAEs) with the same seed but different modality conditions in a dizygotic symbiosis manner. Subsequently, the generated features of two CVAEs are adaptively combined to yield the final feature, which can be converted back into its paired conditions while ensuring these conditions are consistent with the original conditions not only in representation but also in function. DCVAE essentially provides a new idea of data augmentation in various multi-modal scenarios by exploiting the complement of different modality prior information. Extensive experimental results demonstrate our work achieves state-of-the-art performances on miniImageNet, CIFAR-FS and CUB datasets, and is able to work well in the partial modality absence case.

In this paper, we propose a one-stage online clustering method called Contrastive Clustering (CC) which explicitly performs the instance- and cluster-level contrastive learning. To be specific, for a given dataset, the positive and negative instance pairs are constructed through data augmentations and then projected into a feature space. Therein, the instance- and cluster-level contrastive learning are respectively conducted in the row and column space by maximizing the similarities of positive pairs while minimizing those of negative ones. Our key observation is that the rows of the feature matrix could be regarded as soft labels of instances, and accordingly the columns could be further regarded as cluster representations. By simultaneously optimizing the instance- and cluster-level contrastive loss, the model jointly learns representations and cluster assignments in an end-to-end manner. Extensive experimental results show that CC remarkably outperforms 17 competitive clustering methods on six challenging image benchmarks. In particular, CC achieves an NMI of 0.705 (0.431) on the CIFAR-10 (CIFAR-100) dataset, which is an up to 19\% (39\%) performance improvement compared with the best baseline.

Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance. This paper proposes a graph learning framework to preserve both the local and global structure of data. Specifically, our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Furthermore, most existing graph-based methods conduct clustering and semi-supervised classification on the graph learned from the original data matrix, which doesn't have explicit cluster structure, thus they might not achieve the optimal performance. By considering rank constraint, the achieved graph will have exactly $c$ connected components if there are $c$ clusters or classes. As a byproduct of this, graph learning and label inference are jointly and iteratively implemented in a principled way. Theoretically, we show that our model is equivalent to a combination of kernel k-means and k-means methods under certain condition. Extensive experiments on clustering and semi-supervised classification demonstrate that the proposed method outperforms other state-of-the-art methods.

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturing the structural information in a graph. We theoretically show that our formulation is as powerful as any positive semidefinite kernels. To efficiently learn the kernel, we propose a novel mechanism for node feature aggregation and a data-driven similarity metric employed during the training phase. More importantly, our framework is flexible and complementary to other graph-based deep learning models, e.g., Graph Convolutional Networks (GCNs). We empirically evaluate our approach on a number of standard node classification benchmarks, and demonstrate that our model sets the new state of the art.

In this paper, we study how to make clustering benefiting from differentiable programming whose basic idea is treating the neural network as a language instead of a machine learning method. To this end, we recast the vanilla $k$-means as a novel feedforward neural network in an elegant way. Our contribution is two-fold. On the one hand, the proposed \textit{k}-meansNet is a neural network implementation of the vanilla \textit{k}-means, which enjoys four advantages highly desired, i.e., robustness to initialization, fast inference speed, the capability of handling new coming data, and provable convergence. On the other hand, this work may provide novel insights into differentiable programming. More specifically, most existing differentiable programming works unroll an \textbf{optimizer} as a \textbf{recurrent neural network}, namely, the neural network is employed to solve an existing optimization problem. In contrast, we reformulate the \textbf{objective function} of \textit{k}-means as a \textbf{feedforward neural network}, namely, we employ the neural network to describe a problem. In such a way, we advance the boundary of differentiable programming by treating the neural network as from an alternative optimization approach to the problem formulation. Extensive experimental studies show that our method achieves promising performance comparing with 12 clustering methods on some challenging datasets.

The iterative hard-thresholding algorithm (ISTA) is one of the most popular optimization solvers to achieve sparse codes. However, ISTA suffers from following problems: 1) ISTA employs non-adaptive updating strategy to learn the parameters on each dimension with a fixed learning rate. Such a strategy may lead to inferior performance due to the scarcity of diversity; 2) ISTA does not incorporate the historical information into the updating rules, and the historical information has been proven helpful to speed up the convergence. To address these challenging issues, we propose a novel formulation of ISTA (named as adaptive ISTA) by introducing a novel \textit{adaptive momentum vector}. To efficiently solve the proposed adaptive ISTA, we recast it as a recurrent neural network unit and show its connection with the well-known long short term memory (LSTM) model. With a new proposed unit, we present a neural network (termed SC2Net) to achieve sparse codes in an end-to-end manner. To the best of our knowledge, this is one of the first works to bridge the $\ell_1$-solver and LSTM, and may provide novel insights in understanding model-based optimization and LSTM. Extensive experiments show the effectiveness of our method on both unsupervised and supervised tasks.