"The primary aim of clustering is not just to make clusters, but to make good and meaningful ones" – Analytics Vidhya (https://www.analyticsvidhya.com/). An optimal multi-objective clustering is one of the most popular, and, at the same time, curious supervised machine learning problems, that occurs in many fields of computer science such as data and knowledge mining, data compression, vector quantization, patterns detection and classification, Voronoi diagrams, recommender engines (RE), etc. The process of clustering analysis itself allows us to reveal various of trends and insights exhibited on the input dataset. The cluster analysis (CA) process allows us to determine the similarities and differences between specific data, partitioning the data in such as a way that the similar data normally belongs to a specific group or cluster. For example, we can perform the clustering analysis of the data on a credit card customer to reveal what special offers should be given to a specific customer, based on the balance and loan amount criteria. In this case, all that we have to do is to partition all customers data into the number of clusters, and, then give the same offer to the similar customers. This is typically done by performing the multi-variate numerical data the multi-variate numerical data clustering analysis. The main goal of performing the actual clustering is to arrange a set of data items having an associated numeric n-dimensional vector of features into the number of homogeneous groups, called - "clusters".

Such models have been shown to allow estimation and inference by regression clustering methods. This paper is motivated by the finding that the clustered heterogeneity models studied in this literature can be badly misspecified, even when the panel has significant discrete cross-sectional structure. To address this issue, we generalize previous approaches to discrete unobserved heterogeneity by allowing each unit to have multiple, imperfectly-correlated latent variables that describe its response-type to different covariates. We give inference results for a k-means style estimator of our model and develop information criteria to jointly select the number clusters for each latent variable. Monte Carlo simulations confirm our theoretical results and give intuition about the finite-sample performance of estimation and model selection. We also contribute to the theory of clustering with an over-specified number of clusters and derive new convergence rates for this setting. Our results suggest that over-fitting can be severe in k-means style estimators when the number of clusters is over-specified.

Originally posted by Michael Grogan. The below is an example of how sklearn in Python can be used to develop a k-means clustering algorithm. The purpose of k-means clustering is to be able to partition observations in a dataset into a specific number of clusters in order to aid in analysis of the data. From this perspective, it has particular value from a data visualisation perspective. The particular example used here is that of stock returns.

The identification of cyberattacks which target information and communication systems has been a focus of the research community for years. Network intrusion detection is a complex problem which presents a diverse number of challenges. Many attacks currently remain undetected, while newer ones emerge due to the proliferation of connected devices and the evolution of communication technology. In this survey, we review the methods that have been applied to network data with the purpose of developing an intrusion detector, but contrary to previous reviews in the area, we analyze them from the perspective of the Knowledge Discovery in Databases (KDD) process. As such, we discuss the techniques used for the capture, preparation and transformation of the data, as well as, the data mining and evaluation methods. In addition, we also present the characteristics and motivations behind the use of each of these techniques and propose more adequate and up-to-date taxonomies and definitions for intrusion detectors based on the terminology used in the area of data mining and KDD. Special importance is given to the evaluation procedures followed to assess the different detectors, discussing their applicability in current real networks. Finally, as a result of this literature review, we investigate some open issues which will need to be considered for further research in the area of network security.

Time series forecasting has gained lots of attention recently; this is because many real-world phenomena can be modeled as time series. The massive volume of data and recent advancements in the processing power of the computers enable researchers to develop more sophisticated machine learning algorithms such as neural networks to forecast the time series data. In this paper, we propose various neural network architectures to forecast the time series data using the dynamic measurements; moreover, we introduce various architectures on how to combine static and dynamic measurements for forecasting. We also investigate the importance of performing techniques such as anomaly detection and clustering on forecasting accuracy. Our results indicate that clustering can improve the overall prediction time as well as improve the forecasting performance of the neural network. Furthermore, we show that feature-based clustering can outperform the distance-based clustering in terms of speed and efficiency. Finally, our results indicate that adding more predictors to forecast the target variable will not necessarily improve the forecasting accuracy.

In the previous article, we studied the k-NN. One thing that I believe is that if we can correlate anything with us or our lives, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans. It tries to make the inter-cluster data points as similar as possible while also keeping the clusters as different or as far as possible. It assigns data points to a cluster such that the sum of the squared distance between the data points and the cluster's centroid is at the minimum.

Outlier detection has received special attention in various fields, mainly for those dealing with machine learning and artificial intelligence. As strong outliers, anomalies are divided into the point, contextual and collective outliers. The most important challenges in outlier detection include the thin boundary between the remote points and natural area, the tendency of new data and noise to mimic the real data, unlabelled datasets and different definitions for outliers in different applications. Considering the stated challenges, we defined new types of anomalies called Collective Normal Anomaly and Collective Point Anomaly in order to improve a much better detection of the thin boundary between different types of anomalies. Basic domain-independent methods are introduced to detect these defined anomalies in both unsupervised and supervised datasets. The Multi-Layer Perceptron Neural Network is enhanced using the Genetic Algorithm to detect newly defined anomalies with higher precision so as to ensure a test error less than that calculated for the conventional Multi-Layer Perceptron Neural Network. Experimental results on benchmark datasets indicated reduced error of anomaly detection process in comparison to baselines.

Clustering analysis has become a ubiquitous information retrieval tool in a wide range of domains, but a more automatic framework is still lacking. Though internal metrics are the key players towards a successful retrieval of clusters, their effectiveness on real-world datasets remains not fully understood, mainly because of their unrealistic assumptions underlying datasets. We hypothesized that capturing {\it traces of information gain} between increasingly complex clustering retrievals---{\it InfoGuide}---enables an automatic clustering analysis with improved clustering retrievals. We validated the {\it InfoGuide} hypothesis by capturing the traces of information gain using the Kolmogorov-Smirnov statistic and comparing the clusters retrieved by {\it InfoGuide} against those retrieved by other commonly used internal metrics in artificially-generated, benchmarks, and real-world datasets. Our results suggested that {\it InfoGuide} can enable a more automatic clustering analysis and may be more suitable for retrieving clusters in real-world datasets displaying nontrivial statistical properties.

A tensor provides a concise way to codify the interdependence of complex data. Treating a tensor as a d-way array, each entry records the interaction between the different indices. Clustering provides a way to parse the complexity of the data into more readily understandable information. Clustering methods are heavily dependent on the algorithm of choice, as well as the chosen hyperparameters of the algorithm. However, their sensitivity to data scales is largely unknown. In this work, we apply the discrete wavelet transform to analyze the effects of coarse-graining on clustering tensor data. We are particularly interested in understanding how scale effects clustering of the Earth's climate system. The discrete wavelet transform allows classification of the Earth's climate across a multitude of spatial-temporal scales. The discrete wavelet transform is used to produce an ensemble of classification estimates, as opposed to a single classification. Using information theory, we discover a sub-collection of the ensemble that span the majority of the variance observed, allowing for efficient consensus clustering techniques that can be used to identify climate biomes.

This work proposes an ensemble clustering method using transfer learning approach. We consider a clustering problem, in which in addition to data under consideration, "similar" labeled data are available. The datasets can be described with different features. The method is based on constructing meta-features which describe structural characteristics of data, and their transfer from source to target domain. An experimental study of the method using Monte Carlo modeling has confirmed its efficiency. In comparison with other similar methods, the proposed one is able to work under arbitrary feature descriptions of source and target domains; it has smaller complexity.