We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and $\rm W_{H\alpha}$ vs. [NII]/H$\alpha$ (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLIGHT datasets. We apply a GMM to empirically define classes of galaxies in a three-dimensional space spanned by the $\log$ [OIII]/H$\beta$, $\log$ [NII]/H$\alpha$, and $\log$ EW(H${\alpha}$), optical parameters. The best-fit GMM based on several statistical criteria suggests a solution around four Gaussian components (GCs), which are capable to explain up to 97 per cent of the data variance. Using elements of information theory, we compare each GC to their respective astronomical counterpart. GC1 and GC4 are associated with star-forming galaxies, suggesting the need to define a new starburst subgroup. GC2 is associated with BPT's Active Galaxy Nuclei (AGN) class and WHAN's weak AGN class. GC3 is associated with BPT's composite class and WHAN's strong AGN class. Conversely, there is no statistical evidence -- based on four GCs -- for the existence of a Seyfert/LINER dichotomy in our sample. Notwithstanding, the inclusion of an additional GC5 unravels it. The GC5 appears associated to the LINER and Passive galaxies on the BPT and WHAN diagrams respectively. Subtleties aside, we demonstrate the potential of our methodology to recover/unravel different objects inside the wilderness of astronomical datasets, without lacking the ability to convey physically interpretable results. The probabilistic classifications from the GMM analysis are publicly available within the COINtoolbox (https://cointoolbox.github.io/GMM\_Catalogue/).

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.

We investigate statistical properties of a clustering algorithm that receives level set estimates from a kernel density estimator and then estimates the first split in the density level cluster tree if such a split is present or detects the absence of such a split. Key aspects of our analysis include finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for chosing the kernel bandwidth. For the rates and the adaptivity we do not need continuity assumptions on the density such as H\"older continuity, but only require intuitive geometric assumptions of non-parametric nature.

A Dirichlet $k$-partition of a domain $U \subseteq \mathbb{R}^d$ is a collection of $k$ pairwise disjoint open subsets such that the sum of their first Laplace-Dirichlet eigenvalues is minimal. A discrete version of Dirichlet partitions has been posed on graphs with applications in data analysis. Both versions admit variational formulations: solutions are characterized by minimizers of the Dirichlet energy of mappings from $U$ into a singular space $\Sigma_k \subseteq \mathbb{R}^k$. In this paper, we extend results of N.\ Garc\'ia Trillos and D.\ Slep\v{c}ev to show that there exist solutions of the continuum problem arising as limits to solutions of a sequence of discrete problems. Specifically, a sequence of points $\{x_i\}_{i \in \mathbb{N}}$ from $U$ is sampled i.i.d.\ with respect to a given probability measure $\nu$ on $U$ and for all $n \in \mathbb{N}$, a geometric graph $G_n$ is constructed from the first $n$ points $x_1, x_2, \ldots, x_n$ and the pairwise distances between the points. With probability one with respect to the choice of points $\{x_i\}_{i \in \mathbb{N}}$, we show that as $n \to \infty$ the discrete Dirichlet energies for functions $G_n \to \Sigma_k$ $\Gamma$-converge to (a scalar multiple of) the continuum Dirichlet energy for functions $U \to \Sigma_k$ with respect to a metric coming from the theory of optimal transport. This, along with a compactness property for the aforementioned energies that we prove, implies the convergence of minimizers. When $\nu$ is the uniform distribution, our results also imply the statistical consistency statement that Dirichlet partitions of geometric graphs converge to partitions of the sampled space in the Hausdorff sense.

Malaria is a serious infectious disease that is responsible for over half million deaths yearly worldwide. The major cause of these mortalities is late or inaccurate diagnosis. Manual microscopy is currently considered as the dominant diagnostic method for malaria. However, it is time consuming and prone to human errors. The aim of this paper is to automate the diagnosis process and minimize the human intervention. We have developed the hardware and software for a cost-efficient malaria diagnostic system. This paper describes the manufactured hardware and also proposes novel software to handle parasite detection and life-stage identification. A motorized microscope is developed to take images from Giemsa-stained blood smears. A patch-based unsupervised statistical clustering algorithm is proposed which offers a novel method for classification of different regions within blood images. The proposed method provides better robustness against different imaging settings. The core of the proposed algorithm is a model called Mixture of Independent Component Analysis. A manifold based optimization method is proposed that facilitates the application of the model for high dimensional data usually acquired in medical microscopy. The method was tested on 600 blood slides with various imaging conditions. The speed of the method is higher than current supervised systems while its accuracy is comparable to or better than them.

You don't need to know K-NN to understand this article -- but click here if you want to learn more about it. You don't need a background in statistical science either. Let's describe this new algorithm and its various components, in simple English We are dealing here with a supervised learning problem, and more specifically, clustering (also called supervised classification.). In particular, we want to assign a class label to a new observation that does not belong to the training set. Instead of checking out individual points (the nearest neighbors) and using a majority (voting) rule to assign the new observation to a cluster based on nearest neighbor counts, we are checking out cliques of points, and focus on the nearest cliques rather than on the nearest points.

You don't need to know K-NN to understand this article -- but click here if you want to learn more about it. You don't need a background in statistical science either. Let's describe this new algorithm and its various components, in simple English We are dealing here with a supervised learning problem, and more specifically, clustering (also called supervised classification.). In particular, we want to assign a class label to a new observation that does not belong to the training set. Instead of checking out individual points (the nearest neighbors) and using a majority (voting) rule to assign the new observation to a cluster based on nearest neighbor counts, we are checking out cliques of points, and focus on the nearest cliques rather than on the nearest points. The cliques considered here are defined by circles (in two dimensions) or spheres (in three dimensions.)

You don't need to know K-NN to understand this article -- but click here if you want to learn more about it. You don't need a background in statistical science either. Let's describe this new algorithm and its various components, in simple English We are dealing here with a supervised learning problem, and more specifically, clustering (also called supervised classification.). In particular, we want to assign a class label to a new observation that does not belong to the training set. Instead of checking out individual points (the nearest neighbors) and using a majority (voting) rule to assign the new observation to a cluster based on nearest neighbor counts, we are checking out cliques of points, and focus on the nearest cliques rather than on the nearest points.

Clustering, or cluster analysis, is used for analyzing data which does not include pre-labeled classes. Data instances are grouped together using the concept of maximizing intraclass similarity and minimizing the similarity between differing classes. This translates to the clustering algorithm identifying and grouping instances which are very similar, as opposed to ungrouped instances which are much less-similar to one another. As clustering does not require the pre-labeling of classes, it is a form of unsupervised learning. At the core of cluster analysis is the concept of measuring distances between a variety of different data point dimensions.

Typical decisions: • Grant credit/not to new applicants • Increasing/Decreasing spending limits • Increasing/Decreasing lending rates • What new products can be given to existing applicants? Step 2: Assign every entity to its closest medoid (using the distance matrix we have calculated). Step 3: For each cluster, identify the observation that would yield the lowest average distance if it were to be re-assigned as the medoid. If so, make this observation the new medoid. Step 4: If at least one medoid has changes, return to step 2. Otherwise, end the algorithm.