There are 2 major kinds of machine learning models: supervised and unsupervised. In supervised learning, you have input data X and output data y, then the model finds a map from X to y. In unsupervised learning, you only have input data X. The goal of unsupervised learning varies: clustering observations in X, reducing the dimensionality of X, anomaly detection in X, etc. As supervised learning has been discussed extensively in Part 1 and Part 2 of the series, this story is focused on unsupervised learning.

Mining the latent intentions from large volumes of natural language inputs is a key step to help data analysts design and refine Intelligent Virtual Assistants (IVAs) for customer service and sales support. We created a flexible and scalable clustering pipeline within the Verint Intent Manager (VIM) that integrates the fine-tuning of language models, a high performing k-NN library and community detection techniques to help analysts quickly surface and organize relevant user intentions from conversational texts. The fine-tuning step is necessary because pre-trained language models cannot encode texts to efficiently surface particular clustering structures when the target texts are from an unseen domain or the clustering task is not topic detection. We describe the pipeline and demonstrate its performance and ability to scale on three real-world text mining tasks. As deployed in the VIM application, this clustering pipeline produces high quality results, improving the performance of data analysts and reducing the time it takes to surface intentions from customer service data, thereby reducing the time it takes to build and deploy IVAs in new domains.

A common problem in data science is "use this function defined over this small set to generate predictions over that larger set." Extrapolation, interpolation, statistical inference and forecasting all reduce to this problem. The Kan extension is a powerful tool in category theory that generalizes this notion. In this work we explore several applications of Kan extensions to data science. We begin by deriving a simple classification algorithm as a Kan extension and experimenting with this algorithm on real data. Next, we use the Kan extension to derive a procedure for learning clustering algorithms from labels and explore the performance of this procedure on real data. We then investigate how Kan extensions can be used to learn a general mapping from datasets of labeled examples to functions and to approximate a complex function with a simpler one.

Process mining provides various algorithms to analyze process executions based on event data. Process discovery, the most prominent category of process mining techniques, aims to discover process models from event logs, however, it leads to spaghetti models when working with real-life data. Therefore, several clustering techniques have been proposed on top of traditional event logs (i.e., event logs with a single case notion) to reduce the complexity of process models and discover homogeneous subsets of cases. Nevertheless, in real-life processes, particularly in the context of Business-to-Business (B2B) processes, multiple objects are involved in a process. Recently, Object-Centric Event Logs (OCELs) have been introduced to capture the information of such processes, and several process discovery techniques have been developed on top of OCELs. Yet, the output of the proposed discovery techniques on real OCELs leads to more informative but also more complex models. In this paper, we propose a clustering-based approach to cluster similar objects in OCELs to simplify the obtained process models. Using a case study of a real B2B process, we demonstrate that our approach reduces the complexity of the process models and generates coherent subsets of objects which help the end-users gain insights into the process.

Despite the recent advances in out-of-distribution(OOD) detection, anomaly detection, and uncertainty estimation tasks, there do not exist a task-agnostic and post-hoc approach. To address this limitation, we design a novel clustering-based ensembling method, called Task Agnostic and Post-hoc Unseen Distribution Detection (TAPUDD) that utilizes the features extracted from the model trained on a specific task. Explicitly, it comprises of TAP-Mahalanobis, which clusters the training datasets' features and determines the minimum Mahalanobis distance of the test sample from all clusters. Further, we propose the Ensembling module that aggregates the computation of iterative TAP-Mahalanobis for a different number of clusters to provide reliable and efficient cluster computation. Through extensive experiments on synthetic and real-world datasets, we observe that our approach can detect unseen samples effectively across diverse tasks and performs better or on-par with the existing baselines. To this end, we eliminate the necessity of determining the optimal value of the number of clusters and demonstrate that our method is more viable for large-scale classification tasks.

Integrated Development Environments (IDEs) provide tool support to automate many source code editing tasks. Traditionally, IDEs use only the spatial context, i.e., the location where the developer is editing, to generate candidate edit recommendations. However, spatial context alone is often not sufficient to confidently predict the developer's next edit, and thus IDEs generate many suggestions at a location. Therefore, IDEs generally do not actively offer suggestions and instead, the developer is usually required to click on a specific icon or menu and then select from a large list of potential suggestions. As a consequence, developers often miss the opportunity to use the tool support because they are not aware it exists or forget to use it. To better understand common patterns in developer behavior and produce better edit recommendations, we can additionally use the temporal context, i.e., the edits that a developer was recently performing. To enable edit recommendations based on temporal context, we present Overwatch, a novel technique for learning edit sequence patterns from traces of developers' edits performed in an IDE. Our experiments show that Overwatch has 78% precision and that Overwatch not only completed edits when developers missed the opportunity to use the IDE tool support but also predicted new edits that have no tool support in the IDE.

In this paper we propose an adaptive approach for clustering and visualization of data by an orthogonalization process. Starting with the data points being represented by a Markov process using the diffusion map framework, the method adaptively increase the orthogonality of the clusters by applying a feedback mechanism inspired by the Gromov-Wasserstein distance. This mechanism iteratively increases the spectral gap and refines the orthogonality of the data to achieve a clustering with high specificity. By using the diffusion map framework and representing the relation between data points using transition probabilities, the method is robust with respect to both the underlying distance, noise in the data and random initialization. We prove that the method converges globally to a unique fixpoint for certain parameter values. We also propose a related approach where the transition probabilities in the Markov process are required to be doubly stochastic, in which case the method generates a minimizer to a nonconvex optimization problem. We apply the method on cryo-electron microscopy image data from biopharmaceutical manufacturing where we can confirm biologically relevant insights related to therapeutic efficacy. We consider an example with morphological variations of gene packaging and confirm that the method produces biologically meaningful clustering results consistent with human expert classification.

Boolean Matrix Factorization (BMF) aims to find an approximation of a given binary matrix as the Boolean product of two low-rank binary matrices. Binary data is ubiquitous in many fields, and representing data by binary matrices is common in medicine, natural language processing, bioinformatics, computer graphics, among many others. Unfortunately, BMF is computationally hard and heuristic algorithms are used to compute Boolean factorizations. Very recently, the theoretical breakthrough was obtained independently by two research groups. Ban et al. (SODA 2019) and Fomin et al. (Trans. Algorithms 2020) show that BMF admits an efficient polynomial-time approximation scheme (EPTAS). However, despite the theoretical importance, the high double-exponential dependence of the running times from the rank makes these algorithms unimplementable in practice. The primary research question motivating our work is whether the theoretical advances on BMF could lead to practical algorithms. The main conceptional contribution of our work is the following. While EPTAS for BMF is a purely theoretical advance, the general approach behind these algorithms could serve as the basis in designing better heuristics. We also use this strategy to develop new algorithms for related $\mathbb{F}_p$-Matrix Factorization. Here, given a matrix $A$ over a finite field GF($p$) where $p$ is a prime, and an integer $r$, our objective is to find a matrix $B$ over the same field with GF($p$)-rank at most $r$ minimizing some norm of $A-B$. Our empirical research on synthetic and real-world data demonstrates the advantage of the new algorithms over previous works on BMF and $\mathbb{F}_p$-Matrix Factorization.

In this note we introduce a novel clustering preserving transformation of cluster sets obtained from k-means algorithm. It may be considered as a contribution towards formulation of clustering axiomatic system. From the practical point of view, this clustering preserving transformation can be used for purposes of: generating new labeled datasets from existent ones, which may be of use in testing algorithms from k-means family in their stability on cluster perturbations which d not change the theoretical clustering, generating new labeled datasets from existent ones, obfuscating sensitive data From the theoretical standpoint, the contribution of this paper consists in proposing a less rigid cluster preserving transformation than centric consistency, known so far as the only cluster preserving transformation for k-means family of algorithms.

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote interpretability of the clustering process has become a hot research topic at the intersection of mathematical optimization and machine learning research. The problem of taking advantage of background information in data clustering is called semi-supervised or constrained clustering. In this paper, we present a branch-and-cut algorithm for semi-supervised MSSC, where background knowledge is incorporated as pairwise must-link and cannot-link constraints. For the lower bound procedure, we solve the semidefinite programming relaxation of the MSSC discrete optimization model, and we use a cutting-plane procedure for strengthening the bound. For the upper bound, instead, by using integer programming tools, we use an adaptation of the k-means algorithm to the constrained case. For the first time, the proposed global optimization algorithm efficiently manages to solve real-world instances up to 800 data points with different combinations of must-link and cannot-link constraints and with a generic number of features. This problem size is about four times larger than the one of the instances solved by state-of-the-art exact algorithms.