to

### Estimating mixed-memberships using the Symmetric Laplacian Inverse Matrix

Community detection has been well studied in network analysis, and one popular technique is spectral clustering which is fast and statistically analyzable for detect-ing clusters for given networks. But the more realistic case of mixed membership community detection remains a challenge. In this paper, we propose a new spectral clustering method Mixed-SLIM for mixed membership community detection. Mixed-SLIM is designed based on the symmetrized Laplacian inverse matrix (SLIM) (Jing et al. 2021) under the degree-corrected mixed membership (DCMM) model. We show that this algorithm and its regularized version Mixed-SLIM {\tau} are asymptotically consistent under mild conditions. Meanwhile, we provide Mixed-SLIM appro and its regularized version Mixed-SLIM {\tau}appro by approximating the SLIM matrix when dealing with large networks in practice. These four Mixed-SLIM methods outperform state-of-art methods in simulations and substantial empirical datasets for both community detection and mixed membership community detection problems.

### Discovering New Intents with Deep Aligned Clustering

Discovering new intents is a crucial task in a dialogue system. Most existing methods are limited in transferring the prior knowledge from known intents to new intents. These methods also have difficulties in providing high-quality supervised signals to learn clustering-friendly features for grouping unlabeled intents. In this work, we propose an effective method (Deep Aligned Clustering) to discover new intents with the aid of limited known intent data. Firstly, we leverage a few labeled known intent samples as prior knowledge to pre-train the model. Then, we perform k-means to produce cluster assignments as pseudo-labels. Moreover, we propose an alignment strategy to tackle the label inconsistency during clustering assignments. Finally, we learn the intent representations under the supervision of the aligned pseudo-labels. With an unknown number of new intents, we predict the number of intent categories by eliminating low-confidence intent-wise clusters. Extensive experiments on two benchmark datasets show that our method is more robust and achieves substantial improvements over the state-of-the-art methods.(Code available at https://github.com/hanleizhang/DeepAligned-Clustering)

### Clustering and Semi-Supervised Classification for Clickstream Data via Mixture Models

Finite mixture models have been used for unsupervised learning for some time, and their use within the semi-supervised paradigm is becoming more commonplace. Clickstream data is one of the various emerging data types that demands particular attention because there is a notable paucity of statistical learning approaches currently available. A mixture of first-order continuous time Markov models is introduced for unsupervised and semi-supervised learning of clickstream data. This approach assumes continuous time, which distinguishes it from existing mixture model-based approaches; practically, this allows account to be taken of the amount of time each user spends on each webpage. The approach is evaluated, and compared to the discrete time approach, using simulated and real data.

### Clustering Ensemble Meets Low-rank Tensor Approximation

This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a co-association matrix, which indicates the pairwise similarity between samples, as the weighted linear combination of the connective matrices from different base clusterings, and the resulting co-association matrix is then adopted as the input of an off-the-shelf clustering algorithm, e.g., spectral clustering. However, the co-association matrix may be dominated by poor base clusterings, resulting in inferior performance. In this paper, we propose a novel low-rank tensor approximation-based method to solve the problem from a global perspective. Specifically, by inspecting whether two samples are clustered to an identical cluster under different base clusterings, we derive a coherent-link matrix, which contains limited but highly reliable relationships between samples. We then stack the coherent-link matrix and the co-association matrix to form a three-dimensional tensor, the low-rankness property of which is further explored to propagate the information of the coherent-link matrix to the co-association matrix, producing a refined co-association matrix. We formulate the proposed method as a convex constrained optimization problem and solve it efficiently. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods. To the best of our knowledge, this is the first work to explore the potential of low-rank tensor on clustering ensemble, which is fundamentally different from previous approaches.

### Modeling Heterogeneous Statistical Patterns in High-dimensional Data by Adversarial Distributions: An Unsupervised Generative Framework

Since the label collecting is prohibitive and time-consuming, unsupervised methods are preferred in applications such as fraud detection. Meanwhile, such applications usually require modeling the intrinsic clusters in high-dimensional data, which usually displays heterogeneous statistical patterns as the patterns of different clusters may appear in different dimensions. Existing methods propose to model the data clusters on selected dimensions, yet globally omitting any dimension may damage the pattern of certain clusters. To address the above issues, we propose a novel unsupervised generative framework called FIRD, which utilizes adversarial distributions to fit and disentangle the heterogeneous statistical patterns. When applying to discrete spaces, FIRD effectively distinguishes the synchronized fraudsters from normal users. Besides, FIRD also provides superior performance on anomaly detection datasets compared with SOTA anomaly detection methods (over 5% average AUC improvement). The significant experiment results on various datasets verify that the proposed method can better model the heterogeneous statistical patterns in high-dimensional data and benefit downstream applications.

### Objective-Based Hierarchical Clustering of Deep Embedding Vectors

We initiate a comprehensive experimental study of objective-based hierarchical clustering methods on massive datasets consisting of deep embedding vectors from computer vision and NLP applications. This includes a large variety of image embedding (ImageNet, ImageNetV2, NaBirds), word embedding (Twitter, Wikipedia), and sentence embedding (SST-2) vectors from several popular recent models (e.g. ResNet, ResNext, Inception V3, SBERT). Our study includes datasets with up to $4.5$ million entries with embedding dimensions up to $2048$. In order to address the challenge of scaling up hierarchical clustering to such large datasets we propose a new practical hierarchical clustering algorithm B++&C. It gives a 5%/20% improvement on average for the popular Moseley-Wang (MW) / Cohen-Addad et al. (CKMM) objectives (normalized) compared to a wide range of classic methods and recent heuristics. We also introduce a theoretical algorithm B2SAT&C which achieves a $0.74$-approximation for the CKMM objective in polynomial time. This is the first substantial improvement over the trivial $2/3$-approximation achieved by a random binary tree. Prior to this work, the best poly-time approximation of $\approx 2/3 + 0.0004$ was due to Charikar et al. (SODA'19).

### Spectral Methods for Data Science: A Statistical Perspective

Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues (resp. singular values) and eigenvectors (resp. singular vectors) of some properly designed matrices constructed from data. A diverse array of applications have been found in machine learning, data science, and signal processing. Due to their simplicity and effectiveness, spectral methods are not only used as a stand-alone estimator, but also frequently employed to initialize other more sophisticated algorithms to improve performance. While the studies of spectral methods can be traced back to classical matrix perturbation theory and methods of moments, the past decade has witnessed tremendous theoretical advances in demystifying their efficacy through the lens of statistical modeling, with the aid of non-asymptotic random matrix theory. This monograph aims to present a systematic, comprehensive, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. In particular, our exposition gravitates around several central questions that span various applications: how to characterize the sample efficiency of spectral methods in reaching a target level of statistical accuracy, and how to assess their stability in the face of random noise, missing data, and adversarial corruptions? In addition to conventional $\ell_2$ perturbation analysis, we present a systematic $\ell_{\infty}$ and $\ell_{2,\infty}$ perturbation theory for eigenspace and singular subspaces, which has only recently become available owing to a powerful "leave-one-out" analysis framework.

### Efficient Clustering from Distributions over Topics

There are many scenarios where we may want to find pairs of textually similar documents in a large corpus (e.g. a researcher doing literature review, or an R&D project manager analyzing project proposals). To programmatically discover those connections can help experts to achieve those goals, but brute-force pairwise comparisons are not computationally adequate when the size of the document corpus is too large. Some algorithms in the literature divide the search space into regions containing potentially similar documents, which are later processed separately from the rest in order to reduce the number of pairs compared. However, this kind of unsupervised methods still incur in high temporal costs. In this paper, we present an approach that relies on the results of a topic modeling algorithm over the documents in a collection, as a means to identify smaller subsets of documents where the similarity function can then be computed. This approach has proved to obtain promising results when identifying similar documents in the domain of scientific publications. We have compared our approach against state of the art clustering techniques and with different configurations for the topic modeling algorithm. Results suggest that our approach outperforms (> 0.5) the other analyzed techniques in terms of efficiency.

### REDAT: Accent-Invariant Representation for End-to-End ASR by Domain Adversarial Training with Relabeling

Accents mismatching is a critical problem for end-to-end ASR. This paper aims to address this problem by building an accent-robust RNN-T system with domain adversarial training (DAT). We unveil the magic behind DAT and provide, for the first time, a theoretical guarantee that DAT learns accent-invariant representations. We also prove that performing the gradient reversal in DAT is equivalent to minimizing the Jensen-Shannon divergence between domain output distributions. Motivated by the proof of equivalence, we introduce reDAT, a novel technique based on DAT, which relabels data using either unsupervised clustering or soft labels. Experiments on 23K hours of multi-accent data show that DAT achieves competitive results over accent-specific baselines on both native and non-native English accents but up to 13% relative WER reduction on unseen accents; our reDAT yields further improvements over DAT by 3% and 8% relatively on non-native accents of American and British English.

### Clustering multivariate functional data using unsupervised binary trees

Motivated by a large number of applications ranging from sports to the automotive industry and healthcare, there is a great interest in modeling observation entities in the form of a sequence of possibly vector-valued measurements, recorded intermittently at several discrete points in time. Functional data analysis (FDA) considers such data as being values on the realizations of a stochastic process, recorded with some error, at discrete random times. The purpose of FDA is to study such trajectories, also called curves or functions. See, e.g., [37, 49, 21, 54, 19] for some recent references. The amount of such data collected grows rapidly as does the cost of their labeling. Thus, there is an increasing interest in methods that aim to identify homogeneous groups within functional datasets.