Classifications organize entities into categories that identify similarities within a category and discern dissimilarities among categories, and they powerfully classify information in support of analysis. We propose a new classification scheme premised on the reality of imperfect data. Our computational model uses uncertain data envelopment analysis to define a classification's proximity to equitable efficiency, which is an aggregate measure of intra-similarity within a classification's categories. Our classification process has two overriding computational challenges, those being a loss of convexity and a combinatorially explosive search space. We overcome the first by establishing lower and upper bounds on the proximity value, and then by searching this range with a first-order algorithm. We overcome the second by adapting the p-median problem to initiate our exploration, and by then employing an iterative neighborhood search to finalize a classification. We conclude by classifying the thirty stocks in the Dow Jones Industrial average into performant tiers and by classifying prostate treatments into clinically effectual categories.

Clustering is a method that can help machine learning engineers understand unlabeled data by creating meaningful groups or clusters. This often reveals patterns in data, which can be a useful first step in machine learning. Since the data you are working with is unlabeled, clustering is an unsupervised machine learning task. Data is categorized into groups based on their similarity to each other through a metric known as the similarity measure, which is used to find out how similar the objects in the dataset are. To calculate this similarity measure, the feature data of the object in the dataset is used.

The open domain knowledge base is very important. It is usually extracted from encyclopedia websites and is widely used in knowledge retrieval systems, question answering systems, or recommendation systems. In practice, the key challenge is to maintain an up-to-date knowledge base. Different from Unwieldy fetching all of the data from the encyclopedia dumps, to enlarge the freshness of the knowledge base as big as possible while avoiding invalid fetching, the current knowledge base updating methods usually determine whether entities need to be updated by building a prediction model. However, these methods can only be defined in some specific fields and the result turns out to be obvious bias, due to the problem of data source and data structure. The users' query intentions are often diverse as to the open domain knowledge, so we construct a topic-aware graph network for knowledge updating based on the user query log. Our methods can be summarized as follow: 1. Extract entities through the user's log and select them as seeds 2. Scrape the attributes of seed entities in the encyclopedia website, and self-supervised construct the entity attribute graph for each entity. 3. Use the entity attribute graph to train the GNN entity update model to determine whether the entity needs to be synchronized. 4.Use the encyclopedia knowledge to match and update the filtered entity with the entity in the knowledge base according to the minimum edit times algorithm.

For companies with customer service, mapping intents inside their conversational data is crucial in building applications based on natural language understanding (NLU). Nevertheless, there is no established automated technique to gather the intents from noisy online chats or voice transcripts. Simple clustering approaches are not suited to intent-sparse dialogues. To solve this intent-landscape task, we propose an unsupervised pipeline that extracts the intents and the taxonomy of intents from real-world dialogues. Our pipeline mines intent-span candidates with an extractive Question-Answering Electra model and leverages sentence embeddings to apply a low-level density clustering followed by a top-level hierarchical clustering. Our results demonstrate the generalization ability of an ELECTRA large model fine-tuned on the SQuAD2 dataset to understand dialogues. With the right prompting question, this model achieves a rate of linguistic validation on intent spans beyond 85%. We furthermore reconstructed the intent schemes of five domains from the MultiDoGo dataset with an average recall of 94.3%.

This work proposes a clusterization algorithm called k-Morphological Sets (k-MS), based on morphological reconstruction and heuristics. k-MS is faster than the CPU-parallel k-Means in worst case scenarios and produces enhanced visualizations of the dataset as well as very distinct clusterizations. It is also faster than similar clusterization methods that are sensitive to density and shapes such as Mitosis and TRICLUST. In addition, k-MS is deterministic and has an intrinsic sense of maximal clusters that can be created for a given input sample and input parameters, differing from k-Means and other clusterization algorithms. In other words, given a constant k, a structuring element and a dataset, k-MS produces k or less clusters without using random/ pseudo-random functions. Finally, the proposed algorithm also provides a straightforward means for removing noise from images or datasets in general.

This article studies the estimation of latent community memberships from pairwise interactions in a network of $N$ nodes, where the observed interactions can be of arbitrary type, including binary, categorical, and vector-valued, and not excluding even more general objects such as time series or spatial point patterns. As a generative model for such data, we introduce a stochastic block model with a general measurable interaction space $\mathcal S$, for which we derive information-theoretic bounds for the minimum achievable error rate. These bounds yield sharp criteria for the existence of consistent and strongly consistent estimators in terms of data sparsity, statistical similarity between intra- and inter-block interaction distributions, and the shape and size of the interaction space. The general framework makes it possible to study temporal and multiplex networks with $\mathcal S = \{0,1\}^T$, in settings where both $N \to \infty$ and $T \to \infty$, and the temporal interaction patterns are correlated over time. For temporal Markov interactions, we derive sharp consistency thresholds. We also present fast online estimation algorithms which fully utilise the non-binary nature of the observed data. Numerical experiments on synthetic and real data show that these algorithms rapidly produce accurate estimates even for very sparse data arrays.

We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph. However, instead of using a fast Fourier transform (FFT) computation at every node, our proposed approach exploits the Koopman operator framework. Specifically, we show that propagating waves in the graph followed by a local dynamic mode decomposition (DMD) computation at every node is capable of retrieving the eigenvalues and the local eigenvector components of the graph Laplacian, thereby providing local cluster assignments for all nodes. We demonstrate that the DMD computation is more robust than the existing FFT based approach and requires 20 times fewer steps of the wave equation to accurately recover the clustering information and reduces the relative error by orders of magnitude. We demonstrate the decentralized approach on a range of graph clustering problems.

It is known that unsupervised nonlinear dimensionality reduction and clustering is sensitive to the selection of hyperparameters, particularly for deep learning based methods, which hinders its practical use. How to select a proper network structure that may be dramatically different in different applications is a hard issue for deep models, given little prior knowledge of data. In this paper, we aim to automatically determine the optimal network structure of a deep model, named multilayer bootstrap networks (MBN), via simple ensemble learning and selection techniques. Specifically, we first propose an MBN ensemble (MBN-E) algorithm which concatenates the sparse outputs of a set of MBN base models with different network structures into a new representation. Then, we take the new representation produced by MBN-E as a reference for selecting the optimal MBN base models. Moreover, we propose a fast version of MBN-E (fMBN-E), which is not only theoretically even faster than a single standard MBN but also does not increase the estimation error of MBN-E. Importantly, MBN-E and its ensemble selection techniques maintain the simple formulation of MBN that is based on one-nearest-neighbor learning. Empirically, comparing to a number of advanced deep clustering methods and as many as 20 representative unsupervised ensemble learning and selection methods, the proposed methods reach the state-of-the-art performance without manual hyperparameter tuning. fMBN-E is empirically even hundreds of times faster than MBN-E without suffering performance degradation. The applications to image segmentation and graph data mining further demonstrate the advantage of the proposed methods.

Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many realworld applications, and brings perverse influence on pattern analysis. As a consequence, the specific solutions to data imputation and handling are developed to conduct the missing values of data, and independent stage of knowledge exploitation is absorbed for information understanding. In this work, a novel approach to clustering of incomplete data, termed leachable component clustering, is proposed. Rather than existing methods, the proposed method handles data imputation with Bayes alignment, and collects the lost patterns in theory. Due to the simple numeric computation of equations, the proposed method can learn optimized partitions while the calculation efficiency is held. Experiments on several artificial incomplete data sets demonstrate that, the proposed method is able to present superior performance compared with other state-of-the-art algorithms.

We present a novel approach for relocalization or place recognition, a fundamental problem to be solved in many robotics, automation, and AR applications. Rather than relying on often unstable appearance information, we consider a situation in which the reference map is given in the form of localized objects. Our localization framework relies on 3D semantic object detections, which are then associated to objects in the map. Possible pair-wise association sets are grown based on hierarchical clustering using a merge metric that evaluates spatial compatibility. The latter notably uses information about relative object configurations, which is invariant with respect to global transformations. Association sets are furthermore updated and expanded as the camera incrementally explores the environment and detects further objects. We test our algorithm in several challenging situations including dynamic scenes, large view-point changes, and scenes with repeated instances. Our experiments demonstrate that our approach outperforms prior art in terms of both robustness and accuracy.