Clustering and Latent Semantic Indexing Aspects of the Nonnegative Matrix Factorization

This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering objective, so clustering aspect of the NMF has a solid justification. Different from previous approaches which usually discard the nonnegativity constraints, our approach guarantees the stationary point being used in deriving the equivalence is located on the feasible region in the nonnegative orthant. Additionally, since clustering capability of a matrix decomposition technique can sometimes imply its latent semantic indexing (LSI) aspect, we will also evaluate LSI aspect of the NMF by showing its capability in solving the synonymy and polysemy problems in synthetic datasets. And more extensive evaluation will be conducted by comparing LSI performances of the NMF and the singular value decomposition (SVD), the standard LSI method, using some standard datasets.Comment: 28 pages, 5 figure

A Short Survey on Data Clustering Algorithms

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial analysis. Formally speaking, given a set of data instances, a clustering algorithm is expected to divide the set of data instances into the subsets which maximize the intra-subset similarity and inter-subset dissimilarity, where a similarity measure is defined beforehand. In this work, the state-of-the-arts clustering algorithms are reviewed from design concept to methodology; Different clustering paradigms are discussed. Advanced clustering algorithms are also discussed. After that, the existing clustering evaluation metrics are reviewed. A summary with future insights is provided at the end

Recent Developments in Document Clustering

This report aims to give a brief overview of the current state of document clustering research and present recent developments in a well-organized manner. Clustering algorithms are considered with two hypothetical scenarios in mind: online query clustering with tight efficiency constraints, and offline clustering with an emphasis on accuracy. A comparative analysis of the algorithms is performed along with a table summarizing important properties, and open problems as well as directions for future research are discussed

Unsupervised Human Activity Recognition Using the Clustering Approach: A Review

Currently, many applications have emerged from the implementation of softwaredevelopment and hardware use, known as the Internet of things. One of the most importantapplication areas of this type of technology is in health care. Various applications arise daily inorder to improve the quality of life and to promote an improvement in the treatments of patients athome that suffer from different pathologies. That is why there has emerged a line of work of greatinterest, focused on the study and analysis of daily life activities, on the use of different data analysistechniques to identify and to help manage this type of patient. This article shows the result of thesystematic review of the literature on the use of the Clustering method, which is one of the mostused techniques in the analysis of unsupervised data applied to activities of daily living, as well asthe description of variables of high importance as a year of publication, type of article, most usedalgorithms, types of dataset used, and metrics implemented. These data will allow the reader tolocate the recent results of the application of this technique to a particular area of knowledg

Unsupervised learning-based approach for detecting 3D edges in depth maps

3D edge features, which represent the boundaries between different objects or surfaces in a 3D scene, are crucial for many computer vision tasks, including object recognition, tracking, and segmentation. They also have numerous real-world applications in the field of robotics, such as vision-guided grasping and manipulation of objects. To extract these features in the noisy real-world depth data, reliable 3D edge detectors are indispensable. However, currently available 3D edge detection methods are either highly parameterized or require ground truth labelling, which makes them challenging to use for practical applications. To this extent, we present a new 3D edge detection approach using unsupervised classification. Our method learns features from depth maps at three different scales using an encoder-decoder network, from which edge-specific features are extracted. These edge features are then clustered using learning to classify each point as an edge or not. The proposed method has two key benefits. First, it eliminates the need for manual fine-tuning of data-specific hyper-parameters and automatically selects threshold values for edge classification. Second, the method does not require any labelled training data, unlike many state-of-the-art methods that require supervised training with extensive hand-labelled datasets. The proposed method is evaluated on five benchmark datasets with single and multi-object scenes, and compared with four state-of-the-art edge detection methods from the literature. Results demonstrate that the proposed method achieves competitive performance, despite not using any labelled data or relying on hand-tuning of key parameters.</p