In the beginning, let's have some common terminologies overview, A cluster is a group of objects that lie under the same class, or in other words, objects with similar properties are grouped in one cluster, and dissimilar objects are collected in another cluster. And, clustering is the process of classifying objects into a number of groups wherein each group, objects are very similar to each other than those objects in other groups. Simply, segmenting groups with similar properties/behaviour and assign them into clusters. Being an important analysis method in machine learning, clustering is used for identifying patterns and structure in labelled and unlabelled datasets. Clustering is exploratory data analysis techniques that can identify subgroups in data such that data points in each same subgroup (cluster) are very similar to each other and data points in separate clusters have different characteristics.

In this study, we examine a clustering problem in which the covariates of each individual element in a dataset are associated with an uncertainty specific to that element. More specifically, we consider a clustering approach in which a pre-processing applying a non-linear transformation to the covariates is used to capture the hidden data structure. To this end, we approximate the sets representing the propagated uncertainty for the pre-processed features empirically. To exploit the empirical uncertainty sets, we propose a greedy and optimistic clustering (GOC) algorithm that finds better feature candidates over such sets, yielding more condensed clusters. As an important application, we apply the GOC algorithm to synthetic datasets of the orbital properties of stars generated through our numerical simulation mimicking the formation process of the Milky Way. The GOC algorithm demonstrates an improved performance in finding sibling stars originating from the same dwarf galaxy. These realistic datasets have also been made publicly available.

This article explains what data engineers are and what their varied tasks and duties are. Seaborn is a very prominent library used during Exploratory Data Analysis of any data science project you are working upon. At times, this cohort could feel overwhelming due to the sheer volume of material I would need to learn and practice.

The Yellowbrick library also contains a set of visualisation tools for analysing clustering algorithms. A common way to evaluate the performance of clustering models is with an intercluster distance map. The intercluster distance map plots an embedding of each cluster centre and visualises both the distance between the clusters and the relative size of each cluster based on membership. We can turn the diabetes dataset into a clustering problem by only using the features (X). Before we cluster the data we can use the popular elbow method to find the optimal number of clusters.

This is part numero tres of the Explaining Machine Learning Algorithms to a 10-Year Old series. If you read the two previous ones about XGBoost Regression and K-Means Clustering, then you know the drill. We have a scary-sounding algorithm, so let's strip it of its scary bits and understand the simple intuition behind it. In the same vein as K-Means Clustering, today we are going to talk about another popular clustering algorithm -- Hierarchical Clustering. Let's say a clothing store has collected the ages of 9 of its customers, labeled C1-C9, and the amount each of them spent at the store in the last month.

Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may face challenges for discovering repeated geographic patterns with spatial contiguity maintained. In this paper, we propose a Spatial Toeplitz Inverse Covariance-Based Clustering (STICC) method that considers both attributes and spatial relationships of geographic objects for multivariate spatial clustering. A subregion is created for each geographic object serving as the basic unit when performing clustering. A Markov random field is then constructed to characterize the attribute dependencies of subregions. Using a spatial consistency strategy, nearby objects are encouraged to belong to the same cluster. To test the performance of the proposed STICC algorithm, we apply it in two use cases. The comparison results with several baseline methods show that the STICC outperforms others significantly in terms of adjusted rand index and macro-F1 score. Join count statistics is also calculated and shows that the spatial contiguity is well preserved by STICC. Such a spatial clustering method may benefit various applications in the fields of geography, remote sensing, transportation, and urban planning, etc.

Dynamic networks are ubiquitous for modelling sequential graph-structured data, e.g., brain connectome, population flows and messages exchanges. In this work, we consider dynamic networks that are temporal sequences of graph snapshots, and aim at detecting abrupt changes in their structure. This task is often termed network change-point detection and has numerous applications, such as fraud detection or physical motion monitoring. Leveraging a graph neural network model, we design a method to perform online network change-point detection that can adapt to the specific network domain and localise changes with no delay. The main novelty of our method is to use a siamese graph neural network architecture for learning a data-driven graph similarity function, which allows to effectively compare the current graph and its recent history. Importantly, our method does not require prior knowledge on the network generative distribution and is agnostic to the type of change-points; moreover, it can be applied to a large variety of networks, that include for instance edge weights and node attributes. We show on synthetic and real data that our method enjoys a number of benefits: it is able to learn an adequate graph similarity function for performing online network change-point detection in diverse types of change-point settings, and requires a shorter data history to detect changes than most existing state-of-the-art baselines.

If the groups under investigation are pre-specified, i.e., not a function of the observed data, then classical hypothesis tests will control the Type I error rate. However, it is increasingly common to want to test for a difference in means between groups that are defined through the observed data, e.g., via the output of a clustering algorithm. For instance, in single-cell RNA-sequencing analysis, researchers often first cluster the cells, and then test for a difference in the expected gene expression levels between the clusters to quantify up-or down-regulation of genes, annotate known cell types, and identify new cell types (Grün et al., 2015; Aizarani et al., 2019; Lähnemann et al., 2020; Zhang et al., 2019; Doughty & Kerkhoven, 2020). In fact, the inferential challenges resulting from testing data-guided hypotheses have been described as a "grand challenge" in the field of genomics (Lähnemann et al., 2020), and papers in the field continue to overlook this issue: as an example, seurat (Stuart et al., 2019), the state-of-the-art single-cell RNA sequencing analysis tool, tests for differential gene expression between groups obtained via clustering, with a note that "p-values [from these hypotheses] should be interpreted cautiously, as the genes used for clustering are the same genes tested for differential expression." Testing data-guided hypothesis also arises in the field of neuroscience (Kriegeskorte et al., 2009; Button, 2019), social psychology (Hung & Fithian, 2020), and physical sciences (Friederich et al., 2020; Pollice

Among the methods offered by machine learning and artificial intelligence, clustering methods are among the most interesting. These methods belong to the class of unsupervised methods, and as such do not suffer from bias or presuppositions, since they do not seek to learn a known rule, but rather to identify unknown links. Their appeal, therefore, lies in their ability to make sense of data whose volume and/or cardinality exceed the processing capabilities of a human. There are in the field of artificial intelligence, two major classes of methods: the supervised approach and the unsupervised approach. They are distinguished by the form of the problem that is submitted to machine learning.

In this paper we provide the quantum version of the Convex Non-negative Matrix Factorization algorithm (Convex-NMF) by using the D-wave quantum annealer. More precisely, we use D-wave 2000Q to find the low rank approximation of a fixed real-valued matrix X by the product of two non-negative matrices factors W and G such that the Frobenius norm of the difference X-XWG is minimized. In order to solve this optimization problem we proceed in two steps. In the first step we transform the global real optimization problem depending on W,G into two quadratic unconstrained binary optimization problems (QUBO) depending on W and G respectively. In the second step we use an alternative strategy between the two QUBO problems corresponding to W and G to find the global solution. The running of these two QUBO problems on D-wave 2000Q need to use an embedding to the chimera graph of D-wave 2000Q, this embedding is limited by the number of qubits of D-wave 2000Q. We perform a study on the maximum number of real data to be used by our approach on D-wave 2000Q. The proposed study is based on the number of qubits used to represent each real variable. We also tested our approach on D-Wave 2000Q with several randomly generated data sets to prove that our approach is faster than the classical approach and also to prove that it gets the best results.