Automatic classification of nuclear physics data via a Constrained Evolutionary Clustering approach

https://doi.org/10.1016/j.cpc.2020.107667Get rights and content

Highlights

  • Automatic nuclear physics data classification at low and intermediate incident energies.

  • Charged particle identification in nucleus–nucleus collisions via longitudinally stacked detectors.

  • Evolutionary computing in physics.

  • Clustering via machine learning applied to physics.

  • Vector quantization applied to physics.

Abstract

This paper presents an automatic method for data classification in nuclear physics experiments based on evolutionary computing and vector quantization. The major novelties of our approach are the fully automatic mechanism and the use of analytical models to provide physics constraints, yielding to a fast and physically reliable classification with nearly-zero human supervision. Our method is successfully validated using experimental data produced by stacks of semiconducting detectors. The resulting classification is highly satisfactory for all explored cases and is particularly robust to noise. The algorithm is suitable to be integrated in the online and offline analysis software of existing large complexity detection arrays for the study of nucleus–nucleus collisions at low and intermediate energies.

Introduction

Nuclear physics experiments significantly rely on data classification, i.e. the grouping of data into meaningful physics classes, to reconstruct nucleus–nucleus collision events and enable the exploration of the underlying physics. In studies that exploit the detection of charged particles, the classification problem is often that of identifying charge (Z) and mass (A) of detected ions. This process is usually indicated as particle identification. To this end, a number of detection systems capable to record information useful to the classification process have been developed in the last decades [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]. A quite common strategy consists in the use of detector arrays based on stacks of detection layers through which the particle penetrates before is completely stopped. In similar arrays, if organized in a 2D correlation plot, data recorded by pairs of independent layers assemble into bi-dimensional non-overlapping clusters, each representing a certain (Z, A) class. To this extent, the problem of nuclear physics data classification is equivalent to the extraction of clusters in a bi-dimensional space.

Numerous algorithms for Cluster Analysis (CA) or VectorQuantization (VQ) have been proposed in the literature so far, achieving a notable success in standard partitioning problems and being focused on obtaining clusters of nearly equal dispersion (see for example [11], [12], [13], [14]). However, the clusterization process in nuclear physics data is made more difficult by the large variability of size and dispersion of the clusters [15]. Because of these unique features, an optimal solution according to the CA/VQ approach, where a good equalization of the content of each cluster is obtained, might not be directly applicable to nuclear physics classification problems. An acceptable physical solution, instead, usually contains clusters with strongly unbalanced distortions. For this reason, only a reduced number of works have been previously carried out attempting to use CA/VQ methods in nuclear data classification problems. For example, fuzzy c-means algorithms have been successfully applied to the identification of particles in nucleus–nucleus collisions, but their use was restricted exclusively to cases characterized by the presence of few clusters with nearly equal distortion [16].

Several studies have been instead focused on the classification of nuclear physics data in more general cases. Among those, image processing techniques are widely applied. For example, unsupervised learning approaches exploiting contextual image segmentation methods [15], neural networks [17] or spatial density analysis [18] led to quite satisfactory classifications. However, these methods were conceived to classify only Z-values, thus being not particularly suitable for the vast majority of modern high-resolution experiments, where A-classification is often a crucial requirement [7]. In more recent times, another automatic classification method was proposed in Ref. [19]. This method allowed a good extraction of clusters, but the procedure does not comprise an explicit link between extracted clusters and physically meaningful classes. This task requires a significant human supervision, especially in the analysis of data produced by large detection arrays.

Because of the above discussed limitations, the vast majority of the approaches commonly used for the classification of data in nuclear physics experiments involve human-supervised techniques. In similar approaches, the operator manually extracts information by visually inspecting bi-dimensional distributions of data, which is then used as input for supervised learning procedures. In this respect, artificial neural networks have been proposed [20]. More frequently, error minimization procedures based on mathematical models [21], [22], which contain Z and A-values explicitly, are instead preferred. The latter allow to manually extract information only for a reduced number of clusters, while the resulting classification can be meaningfully extended to any possible (Z, A) ion by model extrapolation. An additional reduction in the required information can be finally obtained using the procedure suggested in Ref. [23].

However, despite the significant effort devoted to minimize human supervision, obtaining a physically meaningful data classification in nuclear physics experiments is still a quite repetitive and time consuming task for the operator. This represents a particularly important problem especially in the case of modern detection arrays, where the number of individual bi-dimensional plots to inspect ranges from few hundreds to thousands. As an example, depending on the number of bi-dimensional clusters to classify, the time required to an operator to perform a similar task ranges from days to months. In this framework, it is clear that new fully-automatic methods for data classification are highly required.

In this paper, we present an innovative approach to nuclear physics data classification that allows to reduce the task to a few minutes or hours of CPU-time with nearly-zero supervision by the operator. Our approach involves Evolutionary Computing (EC) and CA/VQ and is based on a two-level search for the optimal solution of the data clusterization problem. The upper level consists in a global search operated by an EC algorithm that treats each solution as an individual of a given population and applies some suitable evolutionary criteria. In our EC approach, an individual is encoded according to a given choice of functional parameters, which constrains a physically meaningful model for the description of bi-dimensional clusters1 and a number of (Z, A) physics classes. The lower level, used as a local hill-climbing operator for the EC process, performs a fast local search through a suitable VQ algorithm that exploits the resulting EC individual as the initial codebook. The major novelty with respect to previously published CA/VQ methods is that the codebook has a physical meaning and resulting solutions are immediately applicable to the data classification with nearly-zero effort required from the operator. In addition, our algorithm is fully automatic as no a priori information is required to the experimenter.

Since the proposed methodology is highly interdisciplinary, in order to effectively drive the reader through the paper, we provide an introduction of all individual research fields that cooperate in our algorithm. The paper is organized as follows: Section 2 gives a more quantitative description of the classification problem studied in this paper, Section 3 is concerned with a description of the programming techniques used in our study, i.e. EC and CA/VQ, Section 4 provides a detailed description of the algorithm, in Section 5 we test the performance of the algorithm in a typical experimental case, in Section 6 we compare our methodology with previously published approaches and, finally, Section 7 reports conclusions and possible future perspectives of our work.

Section snippets

Experimental context

Charged particles are among the most frequent products of a nucleus–nucleus collision. At low and intermediate incident energies (200 MeV/A) they consist almost exclusively of heavy ions (Z1). Their number in a typical collision event varies depending on the incident energy and the size of the nuclei involved in the collision and can range from a few units to more than 50. To meet the requirements of modern nuclear physics studies, state-of-the-art apparatus for the detection of charged

Description of the artificial intelligence techniques

The newly proposed methodology comprises two different artificial intelligence techniques that cooperate to obtain, in a fully automatic way, a solution to the proposed classification problem: EC and CA/VQ. In this section, we provide an introduction on the most salient concepts of both EC and CA/VQ.

Overview of the algorithm

C-EC is an algorithm for automatic data classification in nuclear physics experiments based on EC and VQ. It is conceived for the classification problem typical of experiments that involve the detection of charged particles produced in nucleus–nucleus collisions at low and intermediate energies through longitudinally stacked detectors. In previously published automatic approaches [15], [17], [18], [19] the link between extracted clusters and meaningful physics classes (Z, A) was a non-trivial

Test of the algorithm with experimental data

To probe the capabilities of the C-EC algorithm in the classification of nuclear physics data, we considered experimental data recorded by two longitudinally stacked layers of silicon. The experiment was performed at the TRIUMF laboratory of Vancouver (Canada). A 9Li accelerated beam was delivered on a LiF target at an energy of 65MeV. 9Li+6Li, 9Li+7Li and 9Li+19F collisions were investigated. They resulted in the production of several ions especially in the range 1Z5. Detection apparatus

Comparison with other approaches

Let us summarize the capabilities of the C-EC algorithm: (i) no a priori information is required, number of clusters to classify and relevant (Z, A) values are obtained through an individual improvement algorithm based on evolutionary criteria, (ii) after suitable codebook optimization, the solution of the clusterization problem is readily usable for data classification with explicit link to physically meaningful classes, (iii) the algorithm is robust to noise.

This section is dedicated to a

Conclusions and perspectives

The classification of data in nuclear physics experiments is key to extract the required physics information. Modern experiments have been largely focused on obtaining high-quality classification over a number of physically meaningful classes. In charged particles experiments at low and intermediate incident energies, the classification problem is to identify charge and mass of ions produced in nucleus–nucleus collision. This task is particularly repetitive and time consuming as it usually

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to thank the experimental nuclear physics group of the Ruđer Bošković Institute for making available the data used to probe the performance of the algorithm. The authors would also like to show their gratitude to Dr. Neven Soić and Dr. Nikola Vukman for useful discussions and to Dr. Dora Tot for carefully reviewing the manuscript.

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