A modified principal component technique based on the LASSO

In many multivariate statistical techniques, a set of linear functions of the original p variables is produced. One of the more difŽ cult aspects of these techniques is the interpretation of the linear functions, as these functions usually have nonzero coefŽ cients on all p variables.A common approach is to effectively ignore (treat as zero) any coefŽ cients less than some threshold value, so that the function becomes simple and the interpretation becomes easier for the users. Such a procedure can be misleading.There are alternatives to principal component analysis which restrict the coefficients to a smaller number of possible values in the derivationof the linear functions,or replace the principal components by “principal variables.” This article introduces a new technique, borrowing an idea proposed by Tibshirani in the context of multiple regressionwhere similar problemsarise in interpreting regression equations. This approach is the so-called LASSO, the “least absolute shrinkage and selection operator,” in which a bound is introduced on the sum of the absolute values of the coefficients, and in which some coefficients consequently become zero.We explore some of the propertiesof the newtechnique,both theoreticallyand using simulationstudies, and apply it to an example

The alternating least-squares algorithm for CDPCA

Clustering and Disjoint Principal Component Analysis (CDP CA) is a constrained principal component analysis recently proposed for clustering of objects and partitioning of variables, simultaneously, which we have implemented in R language. In this paper, we deal in detail with the alternating least-squares algorithm for CDPCA and highlight its algebraic features for constructing both interpretable principal components and clusters of objects. Two applications are given to illustrate the capabilities of this new methodology

Police Officers Arrested for Driving Under the Influence, 2005-2017

Presentation at the Annual Meeting of the Midwestern Criminal Justice Association in Chicago, IL, on September 22, 2022

An Exploratory Study of Police Officers Arrested for Sex-Related Crimes, 2005-2017

Presentation at the Annual Meeting of the Academy of Criminal Justice Sciences in National Harbor, MD, on March 17, 2023

Significance analysis and statistical mechanics: an application to clustering

This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements? The computation of this cluster p-value for randomly distributed vectors is mapped onto a well-defined problem of statistical mechanics. We solve this problem analytically, establishing a connection between the physics of quenched disorder and multiple testing statistics in clustering and related problems. In an application to gene expression data, we find a remarkable link between the statistical significance of a cluster and the functional relationships between its genes.Comment: to appear in Phys. Rev. Let

Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism

A method is presented for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy, i.e.\ materials such that $c_{ijkl}= c_{ijkl}(r)$ in a spherical coordinate system ${r,\theta,\phi}$. The time harmonic displacement field $\mathbf{u}(r,\theta ,\phi)$ is expanded in a separation of variables form with dependence on $\theta,\phi$ described by vector spherical harmonics with $r$-dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as $\mathbf{u}(r,\theta)$, admit this type of separation of variables solutions for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.Comment: 15 page

High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that Maximum Lik elihood inference is deeply related to Principal Component Analysis when the amp litude of the pattern components, xi, is negligible compared to N^1/2. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in xi/N^1/2. We stress that it is important to generalize the Hopfield model and include both attractive and repulsive patterns, to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size, N and of the amplitude, xi. The inference approach is illustrated on synthetic and biological data.Comment: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2011) to appea

Precision control of an invasive ant on an ecologically sensitive tropical island: a principle with wide applicability

Effective management of invasive ants is an important priority for many conservation programs but can be difficult to achieve, especially within ecologically sensitive habitats. This study assesses the efficacy and nontarget risk of a precision ant baiting method aiming to reduce a population of the invasive big-headed ant Pheidole megacephala on a tropical island of great conservation value. Area-wide application of a formicidal bait, delivered in bait stations, resulted in the rapid decline of 8 ha of P. megacephala. Effective suppression remained throughout the succeeding 11-month monitoring period. We detected no negative effects of baiting on nontarget arthropods. Indeed, species richness of nontarget ants and abundance of other soil-surface arthropods increased significantly after P. megacephala suppression. This bait station method minimized bait exposure to nontarget organisms and was cost effective and adaptable to target species density. However, it was only effective over short distances and required thorough bait placement. This method would therefore be most appropriate for localized P. megacephala infestations where the prevention of nontarget impacts is essential. The methodology used here would be applicable to other sensitive tropical environments.This work was funded by DST-NRF Centre of Excellence for Invasion Biology (C•I•B) and the Working for Water Programme through their collaborative research project on “Integrated Management of Invasive Alien Species”

Neuronal assembly dynamics in supervised and unsupervised learning scenarios

The dynamic formation of groups of neurons—neuronal assemblies—is believed to mediate cognitive phenomena at many levels, but their detailed operation and mechanisms of interaction are still to be uncovered. One hypothesis suggests that synchronized oscillations underpin their formation and functioning, with a focus on the temporal structure of neuronal signals. In this context, we investigate neuronal assembly dynamics in two complementary scenarios: the first, a supervised spike pattern classification task, in which noisy variations of a collection of spikes have to be correctly labeled; the second, an unsupervised, minimally cognitive evolutionary robotics tasks, in which an evolved agent has to cope with multiple, possibly conflicting, objectives. In both cases, the more traditional dynamical analysis of the system’s variables is paired with information-theoretic techniques in order to get a broader picture of the ongoing interactions with and within the network. The neural network model is inspired by the Kuramoto model of coupled phase oscillators and allows one to fine-tune the network synchronization dynamics and assembly configuration. The experiments explore the computational power, redundancy, and generalization capability of neuronal circuits, demonstrating that performance depends nonlinearly on the number of assemblies and neurons in the network and showing that the framework can be exploited to generate minimally cognitive behaviors, with dynamic assembly formation accounting for varying degrees of stimuli modulation of the sensorimotor interactions

Song variation of the South Eastern Indian Ocean pygmy blue whale population in the Perth Canyon, Western Australia

Sea noise collected over 2003 to 2017 from the Perth Canyon, Western Australia was analysed for variation in the South Eastern Indian Ocean pygmy blue whale song structure. The primary song-types were: P3, a three unit phrase (I, II and III) repeated with an inter-song interval (ISI) of 170–194 s; P2, a phrase consisting of only units II & III repeated every 84–96 s; and P1 with a phrase consisting of only unit II repeated every 45–49 s. The different ISI values were approximate multiples of each other within a season. When comparing data from each season, across seasons, the ISI value for each song increased significantly through time (all fits had p < 0.001), at 0.30 s/Year (95%CI 0.217–0.383), 0.8 s/Year (95% CI 0.655–1.025) and 1.73 s/Year (95%CI 1.264–2.196) for the P1, P2 and P3 songs respectively. The proportions of each song-type averaged at 21.5, 24.2 and 56% for P1, P2 and P3 occurrence respectively and these ratios could vary by up to ± 8% (95% CI) amongst years. On some occasions animals changed the P3 ISI to be significantly shorter (120–160 s) or longer (220–280 s). Hybrid song patterns occurred where animals combined multiple phrase types into a repeated song. In recent years whales introduced further complexity by splitting song units. This variability of song-type and proportions implies abundance measure for this whale sub population based on song detection needs to factor in trends in song variability to make data comparable between seasons. Further, such variability in song production by a sub population of pygmy blue whales raises questions as to the stability of the song types that are used to delineate populations. The high level of song variability may be driven by an increasing number of background whale callers creating ‘noise’ and so forcing animals to alter song in order to ‘stand out’ amongst the crowd