Numerically stable locality-preserving partial least squares discriminant analysis for efficient dimensionality reduction and classification of high-dimensional data.

Dimensionality reduction plays a pivotal role in preparing high-dimensional data for classification and discrimination tasks by eliminating redundant features and enhancing the efficiency of classifiers. The effectiveness of a dimensionality reduction algorithm hinges on its numerical stability. When data projections are numerically stable, they lead to enhanced class separability in the lower-dimensional embedding, consequently yielding higher classification accuracy. This paper investigates the numerical attributes of dimensionality reduction and discriminant subspace learning, with a specific focus on Locality-Preserving Partial Least Squares Discriminant Analysis (LPPLS-DA). High-dimensional data frequently introduce singularity in the scatter matrices, posing a significant challenge. To tackle this issue, the paper explores two robust implementations of LPPLS-DA. These approaches not only optimize data projections but also capture more discriminative features, resulting in a marked improvement in classification accuracy. Empirical evidence supports these findings through numerical experiments conducted on synthetic and spectral datasets. The results demonstrate the superior performance of the proposed methods when compared to several state-of-the-art dimensionality reduction techniques in terms of both classification accuracy and dimension reduction.

Measuring Time-Varying Effective Reproduction Numbers for COVID-19 and Their Relationship with Movement Control Order in Malaysia.

To curb the spread of SARS-CoV-2 virus (COVID-19) in Malaysia, the government imposed a nationwide movement control order (MCO) from 18 March 2020 to 3 May 2020. It was enforced in four phases (i.e., MCO 1, MCO 2, MCO 3 and MCO 4). In this paper, we propose an initiative to assess the impact of MCO by using time-varying reproduction number (Rt). We used data from the Johns Hopkins University Centre for Systems Science and Engineering Coronavirus repository. Day 1 was taken from the first assumed local transmission of COVID-19. We estimated Rt by using the EpiEstim package and plotted the epidemic curve and Rt. Then, we extracted the mean Rt at day 1, day 5 and day 10 for all MCO phases and compared the differences. The Rt values peaked around day 43, which was shortly before the start of MCO 1. The means for Rt at day 1, day 5, and day 10 for all MCOs ranged between 0.665 and 1.147. The average Rt gradually decreased in MCO 1 and MCO 2. Although spikes in the number of confirmed cases were observed when restrictions were gradually relaxed in the later MCO phases, the situation remained under control with Rt values being stabilised to below unity level (Rt value less than one).

Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan).

The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article. First, we formulate the model without control and study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Furthermore, we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host population. In order to do this, we use two control variables. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system. Taking into account the central manifold theory the bifurcation analysis is also incorporated. The numerical simulations are performed in order to show the feasibility of the control strategy and effectiveness of the theoretical results.

Modelling COVID-19 Scenarios for the States and Federal Territories of Malaysia.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causes COVID-19 disease, which has become pandemic since December 2019. In the recent months, among five countries in the Southeast Asia, Malaysia has the highest per-capita daily new cases and daily new deaths. A mathematical modelling approach using a Singular Spectrum Analysis (SSA) technique was used to generate data-driven 30-days ahead forecasts for the number of daily cases in the states and federal territories in Malaysia at four consecutive time points between 27 July 2021 and 26 August 2021. Each forecast was produced using SSA prediction model of the current major trend at each time point. The objective is to understand the transition dynamics of COVID-19 in each state by analysing the direction of change of the major trends during the period of study. The states and federal territories in Malaysia were grouped in four categories based on the nature of the transition. Overall, it was found that the COVID-19 spread has progressed unevenly across states and federal territories. Major regions like Selangor, Kuala Lumpur, Putrajaya and Negeri Sembilan were in Group 3 (fast decrease in infectivity) and Labuan was in Group 4 (possible eradication of infectivity). Other states e.g. Pulau Pinang, Sabah, Sarawak, Kelantan and Johor were categorised in Group 1 (very high infectivity levels) with Perak, Kedah, Pahang, Terengganu and Melaka were classified in Group 2 (high infectivity levels). It is also cautioned that SSA provides a promising avenue for forecasting the transition dynamics of COVID-19; however, the reliability of this technique depends on the availability of good quality data.

Complex Chemical Data Classification and Discrimination Using Locality Preserving Partial Least Squares Discriminant Analysis.

Partial least squares discriminant analysis (PLS-DA) is a well-known technique for feature extraction and discriminant analysis in chemometrics. Despite its popularity, it has been observed that PLS-DA does not automatically lead to extraction of relevant features. Feature learning and extraction depends on how well the discriminant subspace is captured. In this paper, discriminant subspace learning of chemical data is discussed from the perspective of PLS-DA and a recent extension of PLS-DA, which is known as the locality preserving partial least squares discriminant analysis (LPPLS-DA). The objective is twofold: (a) to introduce the LPPLS-DA algorithm to the chemometrics community and (b) to demonstrate the superior discrimination capabilities of LPPLS-DA and how it can be a powerful alternative to PLS-DA. Four chemical data sets are used: three spectroscopic data sets and one that contains compositional data. Comparative performances are measured based on discrimination and classification of these data sets. To compare the classification performances, the data samples are projected onto the PLS-DA and LPPLS-DA subspaces, and classification of the projected samples into one of the different groups (classes) is done using the nearest-neighbor classifier. We also compare the two techniques in data visualization (discrimination) task. The ability of LPPLS-DA to group samples from the same class while at the same time maximizing the between-class separation is clearly shown in our results. In comparison with PLS-DA, separation of data in the projected LPPLS-DA subspace is more well defined.

A stochastic total least squares solution of adaptive filtering problem.

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence analysis of the algorithm is given to show the global convergence of the proposed algorithm, provided that the stepsize parameter is appropriately chosen. The TLMS algorithm is computationally simpler than the other TLS algorithms and demonstrates a better performance as compared with the least mean square (LMS) and normalized least mean square (NLMS) algorithms. It provides minimum mean square deviation by exhibiting better convergence in misalignment for unknown system identification under noisy inputs.