Principal component analysis

Principal component analysis (PCA) is one of the most widely used techniques in tabular, multivariate dataset analysis and is employed primarily for dimensionality reduction [Reference Kim and Rattakorn26, Reference Denimal and Camiz27]. Implementation wise, PCA can be easily implemented through singular value decomposition (SVD) [Reference Jolliffe and Cadima28]. Therefore, no implementation difficulties were encountered when processing the Electromagnetic (EM) data which is, inherently, complex-valued. Hence, when applying PCA to an MW tabular dataset, we directly used the complex-valued measurements of the scattering parameters.

In essence, PCA extracts a lower dimensional feature set that explains most of the variability of the original dataset. The k extracted features, or principal components, PC_is, are (each) a linear combination of the original features (X_j) scaled by a loading value (α_ij $ \in \mathbb{C}$). This process of combining original features is often also referred to as feature extraction. The loading values represent the importance that each original feature has in the formation of a PC. For example, α_ij indicates the degree of importance, or contribution, of the original jth feature in the ith PC. Mathematically, each ith PC is written as follows [Reference Song, Guo and Mei29]:

(1)\begin{equation}\begin{array}{*{20}{c}} {P{C_i} = {\alpha _{i1}}{X_1} + {\alpha _{i2}}{X_2} + \ldots + {\alpha _{ip}}{X_p}\,,} \end{array}\end{equation}

Each PC explains a proportion of the total variance of the dataset at hand. Since the PCs are calculated to preserve the maximum energy content of the data matrix, i.e., variance, the first PC always explains the most variance, the second PC always explains the second most variance, and so on. However, in the presence of a large number of original features, the consideration of only the first few PCs may be insufficient to account for most of the variability in the data. Thus, in this work, dimensionality is reduced to account for 95% of the total explained variance.

In the context of MW application, SVD is widely used as a powerful filter to block reflections from stronger scatterers [Reference Felício, Bioucas-Dias, Costa and Fernandes30]. With PCA, we obtain a multidimensional coordinate system that reveals the underlying linear energy trends of the data set. Following Parseval’s Relation, this means that we maintain capability of filtering the reflections of the higher energy scatterers from the interpretable time domain intensity function (see the “Physical-based detection metric” subsection further ahead) while having the interpretation possibility in the frequency domain through the loadings of each PC, i.e., a clear understanding of the contribution of an original variable to a certain PC.

From the relation of the extracted features with the original ones described above in Eq. (1), the absolute value of the loadings can statistically evaluate the contribution of the ith frequency component to the feature extraction result. The magnitude of this contribution represents the feature importance estimation associated to the dataset at hand [Reference Denimal and Camiz27]. Since each PC explains a proportion of the total variance, it is appropriate to weight each contribution by the respective proportion of explained variance, ${\pi_{i\,}}$ [Reference Kim and Rattakorn26]. This can be referred to as weighted PCA (WPCA) FS algorithm in which we can compute the importance ( $c$) of the jth feature as follows:

(2)\begin{equation}\begin{array}{*{20}{c}} {{c_j} = \mathop \sum \limits_{i = 1}^k \left| {{\alpha _{ij}}} \right|{\pi _i},k = 1,2, \ldots ,p\,\,\,\,,} \end{array}\end{equation}

where k is the total number of PCs retained and ${\pi_i}$ is the corresponding weight of the ith PC. Concatenating together the importances of all the features, we obtain the frequency importance vector of a certain MW dataset, ${c_{dataset}}$.

From Eq. (2), we can interpret that, in MW applications, by summing the contributions from consecutive frequencies within an arbitrary sub-band interval, we can determine its total importance, ${C_{sub - band}}$. Mathematically, for the measured ${N_f}$ frequencies within the chosen sub-band, its total importance is computed as in Eq. (3). To improve filtering and focus on the central frequency, we also apply a Hamming window (H) to the importance interval.

(3)\begin{equation}\begin{array}{*{20}{c}} {{C_{sub - band}} = \mathop \sum \limits_{f = 1}^{{N_F}} H\left( {{c_f}} \right)} \end{array}\end{equation}

Multilayer perceptron artificial neural networks

For classification model, we use a multilayer perceptron (MLP) [Reference Goodfellow, Bengio and Courville31]. The advantages are threefold: First, it has been shown in [Reference Gorishniy, Rubachev, Khrulkov and Babenko32] that, if well-tuned, its performance on tabular datasets is on par, accuracy-wise, with other ML algorithms commonly used to process tabular datasets (e.g., SVM, XGBoosts, and Gradient-Based Decision Trees). We verify that the use of the MLP model in the supervised learning workflow (see the “Supervised learning workflow” subsection further ahead) is superior to other tuned ML algorithms; Second, it serves as a baseline to develop more intricate neural network (NN) architectures for specific applications; Third, it is possible to implement this architecture in the complex domain (contrary to other ML algorithms) and directly process the complex-valued MW measurement data [Reference Hirose33].

In Fig. 1, we can observe an overview of the MLP architecture, with a neuron unit highlighted in blue (for visualization purposes), used to make a prediction on the magnitude of a 1D scattering parameter signal, ${S_{11}}$. At least three layers make up an MLP architecture: an input layer, an output layer, and one or more intermediate layers, commonly referred to as hidden layers (HLs), which define the depth of the NN [Reference Goodfellow, Bengio and Courville31]. The signal information flows from the input layer to the output layer.

Figure 1. Overview of the MLP architecture used to process a 1D signal consisting of the magnitude of a scattering parameter, ${S_{11}}$ (for visualization purposes). A neuron unit is highlight in blue.

The input layer neuron units directly take the values of the input features. Both the depth and number of neurons in each HL can be optimized as explained further ahead in the “Supervised learning workflow” subsection. For classification tasks, the output layer consists of ${n_c}$ neurons where ${n_c}$ is the number of classes. In binary classification specifically, we can use a single output neuron.

A neuron consists of a weighted sum of inputs from the previous layer and a bias parameter, to which is then applied a (nonlinear) activation function. Each neuron in the fully connected layers is connected to all neurons in the preceding layer. In a vectorized notation, an arbitrary output from the neurons of a fully connected layer, ${\boldsymbol{h}}_{}^{\boldsymbol{i}}$, in an MLP is computed as

(26)\begin{equation}\begin{array}{*{20}{c}} {{\boldsymbol{h}}_{}^{\boldsymbol{i}} = \sigma \left( {{W^i}{h^{i - 1}} + {b^i}} \right),} \end{array}\end{equation}

where ${W^i}$ is the weight matrix, ${b^i}$ is the bias vector, ${{\sigma }}$ is the activation function and ${h^{i - 1}}$ is the output from a previous layer.

It is the sequential application of the nonlinear activation function in the layer’s neurons, ${{\sigma }}$, that enable even shallow MLPs to learn complicate patterns of the data. The optimal activation function for the neurons in the HLs depends on the training (application) data and is typically determined empirically. For practically all test cases, the model selected from the fine-tuning process (see Appendix) uses ReLU [Reference Hirose33] as the activation function of the neurons in the HLs. Only in the output layer do we specifically required an activation function that outputs the probability distribution over the different classes. For this we used the softmax function [Reference Goodfellow, Bengio and Courville31].

The pattern recognition ability of MLPs is realized via supervised training. In this process, all the weights and bias parameters (denoted as ${W^i}$ and ${b^i}$, respectively) are continuously updated to ensure that the network output matches with the desired output based on the given labels of the training data. However, for each training input, there is still an error between the predicted output and the target one. This error evaluates the performance of our classifier and is quantified by a loss function, E. Since this is a classification task, we used the cross-entropy loss [Reference Goodfellow, Bengio and Courville31] as our loss function. The network parameters are trained by using stochastic gradient descent (SGD) and backpropagation. SGD is an optimization method that minimizes the cost of the error loss function by updating the network parameters with the error gradient from a small, randomly selected set of training inputs. Backpropagation is used to compute the error gradients of each pair of network parameters in the MLP, ∂E/∂W and ∂E/∂b, respectively. Accordingly, the update rule for both weights and biases follows W ← W − (∂E/∂W), where $\eta $ is the learning rate. The reader is referred to the works in papers [Reference Goodfellow, Bengio and Courville31] and [Reference Hirose33] for further details on the training algorithms.

The extension of the MLP model to the complex domain does not alter its architecture and employs the same formulation as described earlier. The main changes are in its capacity (e.g., the number of neurons) and the implementation of nonlinear functions to handle complex-valued data types [Reference Barrachina, Ren, Vieillard, Morisseau and Jp34]. However, the network’s output still needs to be mapped to a real-valued label, i.e., real domain. The mapping of complex to real ( $\mathbb{R} \to \mathbb{C}$), through magnitude, can be done either at the input or the output layer [Reference Hirose33]. This flexibility to compare the two types of architecture allows us to determine, empirically, the optimal placement of the mapping layer and selection of the optimal data type for our scattering parameter data during the fine-tuning process.

Acquisition

The most common types of plastic that end up as marine litter are single-use items, containers and wrappers, like bottles, styrofoams, etc. [Reference Lebreton, Slat, Ferrari, Sainte-Rose, Aitken, Marthouse, Hajbane, Cunsolo, Schwarz, Levivier and Noble23]. As previously referred, these low mass, single-use plastic items are typically found scattered in deep-sea. These items are made of low permittivity polymers such as polypropylene (PP), polyethylene terephthalate (PET), and polystyrene (PS) [35]. In Fig. 2, we show the single-use plastic items used in the measurement campaign. From left to right: PET plastic bottle ( ${\varepsilon _r}$ ≈ 3.4); PP plastic straw ( ${\varepsilon _r}$ ≈ 2.1); PS cylinder foam ( ${\varepsilon _r}$ ≈ 1.6); and PP plastic lid ( ${\varepsilon _r}$ ≈ 2.2).

Figure 2. Low permittivity plastic litter targets measured. From left to right: plastic bottle ( ${\varepsilon _r}$ ≈ 3.4), plastic straw ( ${\varepsilon _r}$ ≈ 2.1), cylinder foam ( ${\varepsilon _r}$ ≈ 1.6), and plastic lid ( ${\varepsilon _r}$ ≈ 2.2). Dimensions in millimeters.

A measurement campaign was conducted at the 75 × 8.5 m water basin, inside a closed pavilion, at DELTARES facilities [24]. This facility replicates water surfaces in near-deep-sea conditions. The waves are generated by computer-controlled wave paddles that produce a moving water surface according to a JONSWAP spectrum defined a priori [Reference Hasselmann and Olbers36]. This wave spectrum can be generated according to two parameters that characterize the water surface system: significant wave height ${H_s}$; and peak wave period ${T_p}$. For the purpose of this study, we considered an identical wave spectrum with ${H_s}\, = \,${9;17} cm and ${T_p}\, = $ 1.2 s across all test cases. An illustrative example corresponding to the 9 cm case is presented in Fig. 3(a).

Figure 3. Indoor controllable scenario: (a) JONSWAP wave spectrum measured at several wave gauges (WHM) that ensured a water surface with ${H_s}$ = 9 cm and ${T_p}\, = \,$ 1.2 s throughout the basin; (b) measurement setup surveying middle of the basin.

The measurement setup is represented in Fig. 3(b). It consisted of a monostatic setup with a single V-pol reflector antenna mounted 9 m above the water level on an existing wooden walkway, to approach a typical satellite look angle. Vertical polarization to transmit and receive the MW signal (VV) was selected to maximize the plastic target’s response at MW frequencies. The antenna was pointing at a common point on the water surface, approximately 7.64 m away from the antenna, with a 38° incidence angle ( ${{\theta }}$). It was operating in pure backscatter mode whilst connected to the first port of an Agilent E5071C Vector Network Analyzer that measures the frequency response ( ${S_{11}}$) between 2.5 and 11.5 GHz with 1601 equally spaced points. Each frequency sweep had a time duration of approximately 1 s. The water waves travel along the antenna’s cross-range direction, the Z-axis in the aforementioned figure.

Measurements always started without any objects in the water (reference measurements) and continued while and after plastic litter was added. The plastic targets drifted within the footprint (target measurements) following the water wave’s direction of propagation, Z. For each test case, we attempted to keep a constant concentration of 10 $g/{m^2}$. However, since the items are dropped at the beginning of the basin, near the wave paddles, they sometimes accumulated and created intermittent litter patches across the antenna’s footprint. This varies the backscatter intensity level in the sequential target measurements.

The experimental data is arranged as a tabular dataset where each input is one of the sequential measurements, i.e., a discretized backscattering ${S_{11}}$ frequency sweep, and its features correspond to the MW response sampled at the subsequent frequency points ( ${f_i}$) within the measured spectrum. Considering that we have video footage of every test case, we filter and divide each MW measurement dataset into two identical tabular datasets composed of n units and p features for reference and target measurements, Reference and Target, respectively. In every test case, both the Reference and Target datasets had, roughly, around 400 measurements with 1601 frequency points between 2.5 and 11.5 GHz. Lastly, we label each Reference signal as class “0” and each Target signal as class “1.”

Analysis and detection

Next, we describe the signal preprocessing routine, and the subsequent unsupervised and supervised learning workflows to characterize the experimental frequency dependency scattering behavior in the presence of the spread out plastic targets and identify the optimal MW frequencies for detection, respectively.

Signal preprocessing

To obtain an accurate measured backscatter response, we apply a background subtraction calibration method. This operation also removes all responses from undesired stationary scatterers (e.g., basin walls). Since the water surface is a stochastic process, this is computed by subtracting the mean response of the reference measurements [Reference Felício, Costa, Vala, Leonor, Costa, Marques and de Maagt10]. In a real deployment, there would be practically no stationary targets in the open sea, so the signal could be directly processed from the MW sensing instrument.

To ensure that we consider the frequency response of just the water surface within the antenna’s footprint, we apply distance gating to every S-parameter signal to remove any clutter leftover from the mean reference subtraction. Figure 4 summarizes the steps of this preprocess and subsequent calculation of the time domain EnR metric (see the “Physical-based detection metric” subsection further ahead). For every reference and target measurement, we compute its inverse Fast Fourier Transform (IFFT) to obtain the time-domain (radar) response, ${I_{ij}}$; gate the radial distances outside the basin limits of the field of view; and then re-apply an FFT to obtain the corresponding, footprint frequency MW response. We use the interval between [10;15] m as radial distances.

Figure 4. Preprocessing signal routine to remove clutter leftover from the mean reference subtraction and subsequent derivation of EnR metric (see the “Physical-based detection metric” subsection).

Unsupervised learning workflow

Following the previous data preprocessing routine, we first describe the unsupervised learning workflow from our preliminary work [Reference Da Costa, Felício, Vala, Leonor, Costa, Marques and De Maagt25], summarized in Fig. 5(a). The goal of this workflow is to characterize, experimentally, the difference in importance of each MW frequency across the measured spectrum when considering the presence of the floating macroplastic targets. First, we compute and concatenate the feature importance at each frequency point for the Target and Reference datasets using the WPCA algorithm described in Eq. (2) to obtain ${c_{Target}}$ and ${c_{Reference}}\,$(or, for short, ${c_{Tg}}$ and ${c_{Ref}}$), respectively (step 1). We then subtract ${c_{Ref}}$ to ${c_{Tg}}$ to obtain the difference in feature importance between the two datasets, ${{{\delta }}_c} = \,{c_{Tg}}$— ${c_{Ref}}$, to gauge the difference in importance variation across the measured BW when considering the presence of the floating plastic targets (step 2). Next, we define two sub-bands intervals, with 1 and 2 GHz of bandwidth, to slide over the importance variation from the previous step, ${{{\delta }}_c}$ (step 3). At each iteration of the sliding 1 and 2 GHz window, we compute the total importance from ${{{\delta }}_c}$ using Eq. (3), using the ${N_f}$ frequency points within the window, to obtain ${{\text{C}}_{1GHz}}$ and ${{\text{C}}_{2GHz}}$ (step 4).

Figure 5. Machine learning workflows: (a) unsupervised; (b) supervised.

Physical-based detection metric

Lastly, we intend to compare the proposed (supervised) ML approach with an alternative detection metric for floating macroplastics, the EnR [Reference Felício, Costa, Vala, Leonor, Costa, Marques and de Maagt10], that closely relates to the physical scattering process. Similarly to accuracy, this metric summarizes the detection performance in a single number but based on the time-varying comparison of the scattering intensity response (i.e., time-domain response, ${I_{ij}}$) of the water surface with floating macroplastics and without.

Since we already performed distance gating in the signal preprocessing, we can easily obtain the EnR associated with the corresponding dataset from the one-sided IFFT of the input signals (see Fig. 4). EnR provides interpretability of the backscatter response, i.e., logic behind the MW measurements, that complements well the ML analysis. Thus, the comparison is justified. Following [Reference Felício, Costa, Vala, Leonor, Costa, Marques and de Maagt10], we define in Table 1 the EnR detection thresholds for the 9 and 17 cm wave datasets ( $EnR_9^{th}$and $EnR_{17}^{th}$, respectively) considering S-, C-, and X-bands. These thresholds are based on the uncertainty of the reference measurement datasets over time.

Table 1. EnR detection thresholds of 9 and 17 cm waves for S-, C-, and x-bands

The two main drawbacks with EnR are identified as bandwidth and threshold definition. EnR requires large bandwidths, at least in the order of 2 GHz within the C- and X-bands, as it loses interpretability when using smaller bandwidths, e.g., 1 GHz or below. However, narrower bandwidths are required to comply with the available bands for Earth Exploration Satellite Services (EESS) in active remote sensing. In Table 2, we show existing EESS frequency intervals in S-, C-, and X-bands for active remote sensing applications [38]. EnR also requires sequential reference measurements of a certain water state to establish the threshold detection level. This can restrict its application to continuous real-time monitoring, especially considering higher velocity platforms.

Table 2. Regulated EESS frequency intervals used in this study [38]

Simulation analysis

To demonstrate the frequency selective behavior of the backscatter produced by the floating plastic items, we consider a 1 × 1 m patch of static water. Floating on the flat surface, we consider the plastic bottle target (see Fig. 2) with thin walls. This object creates a cylindrical indentation on the water surface, with a depth d that is a function of its weight. We carry out full-wave finite difference time-domain (FDTD) simulations for different indentation depths in CST Microwave Studio [39]. In the simulations, we consider an incident plane wave with linear vertical polarization and an incident angle of 37° measured with respect to the horizontal plan.

Figure 6 shows the backscattered electric field across the measured MW spectrum for different d values. The results demonstrate a frequency selectivity effect, in which the optimal frequency for the maximum intensity of the backscattered signal varies according to the indentation depth. We also evaluated the field distribution near the indentations. For deeper indentations, the backscatter signal is caused by the resonances due to by “trapped” fields at the edges of the indentation [Reference Bethe40]. The results demonstrate a preference for higher MW frequencies, i.e., X-band. This is a consequence of the electrical lengths of the indentations. These interpretations can only be obtained by simulation; however, the total response follows the one obtained experimentally for the same target [Reference Felício, Costa, Vala, Leonor, Costa, Marques and de Maagt10]. Hence, we can conclude that the backscattering signal coming from the low permittivity target depends on the interplay between the indentation depth and the surrounding water surface.

Figure 6. Backscattered electric field of plastic bottle vs frequency with different sinking depths d = {5, 15, 25, 35, 45, 55, 65, 75} mm.

In dynamic water scenarios, the backscatter field produced by the scattered plastic items is mixed with scattering from the surrounding rough surface. Furthermore, the MW backscattering is dependent on several parameters, for instance quantity, individual object geometry, weight, orientation w.r.t incident wave, water surface level, etc. [Reference Felício, Costa, Vala, Leonor, Costa, Marques and de Maagt10]. Some of these can change significantly between consecutive measurements. Hence, in a dynamic scenario, we require multiple measurements to study the frequency selective behavior of the backscattering. The size in terms of wavelength, of a statically presentative sample of this surface demands an unaffordable amount of computational resources for FDTD simulations; therefore, CST’s asymptotic numerical solver is used instead.

We simulate the time evolving water surface generated from a JONSWAP spectrum with an ${H_s}$ of 9 and 17 cm, representing the experimental scenario. The targets are 250-mm plastic bottles represented by their water indentation. The backscatter is calculated across S-, C-, and X-bands multiple times, considering sequentially different locations and orientations of the drifting indentation targets. We calculate Reference and Target datasets in each band (see the frequency interval limits in Table 1). Each simulated backscatter signal is preprocessed with the subtraction of the mean of references (see the “Signal preprocessing” subsection).

As an initial exploratory analysis, we apply PCA, see Eq. (1), to the simulated datasets across S-, C-, and X-bands to observe the data separability. In Fig. 7(a) and 7(b), we represent the clusters of the simulated Reference and Target datasets, for the first two PCs. For each sub-band, we indicate in the figure insets the Euclidean distance between the centroids of the two classes of data. The distance between the centroids of the Reference and Target classes is larger in the lower water wave height case. The smaller distances between clusters in higher water wave height suggests a deterioration of the detection performance when $Hs$ increases. In fact, we observe in the simulations that the increase in water wave height leads to a higher number of ray bounces (multipath). Hence, in every Target surface, there is an additional backscattering contribution from the higher order reflections that is mixed with the bottles’ response. Notably, for this shallow indentation, the backscattered field is described by a specular reflection. Across both water wave height cases, we observe that the increase in MW frequency also increases the distance between clusters, an indication of improved detection performance.

Figure 7. Clusters of simulated Reference and Target datasets for the plastic bottles test case across S-, C-, and X-bands for an emulated time evolving water surface generated from a JONSWAP spectrum with an ${H_s}$ of (a) 9 cm; (b) 17 cm. For each sub-band, we show in the insets the Euclidean distance between the centroids of the two classes of data.

In the next subsection, we will use our unsupervised ML workflow to characterize the experimental frequency dependent scattering behavior across the measured MW spectrum in the presence of the floating macroplastics.

Frequency importance analysis

In our preliminary analysis (see Fig. 3 from paper [Reference Da Costa, Felício, Vala, Leonor, Costa, Marques and De Maagt25]), we had already analyzed the individual frequency importances of both Target and Reference datasets ( ${c_{Tg}}$ and ${c_{Ref}}$, respectively) for all measured cases in 9 cm waves, i.e., output of step 1 of the unsupervised workflow, see Fig. 5(a). For the same test cases in 17 cm waves, the behavior of the ${c_{Ref}}$ and ${c_{Tg}}$ curves were identical.

Figures 8 and 9 show the normalized difference in feature importance curves between Target and Reference datasets, ${{{\delta }}_c}$, and the corresponding areas of total importance for the sliding windows of 1 and 2 GHz, ${C_{1GHz}}$ and ${C_{2GHz}}$, for the test cases with an ${H_s}\,$ of 9 and 17 cm waves, respectively. This corresponds to the outputs of steps 2 and 4 of the unsupervised workflow. The ${{{\delta }}_c}$ curves summarize the prior analysis for the setup at hand, showing that the presence of the floating macroplastic litter leads to an increase of the importance (with ${\delta _c} \gt 0$) of upper C- and X-band frequencies (> 6 GHz). For the higher X-band frequencies (around 10 GHz), even though there is a decrease in difference importance, it is still relevant due to the very low importance of ${c_{Ref}}$ curves. From Eqs (1) and (2), we observe that importance coefficients are scaled by the corresponding PC variance. This means that the principal contributors to the variance of the first PCs, i.e., main scatterers of the surface in each scenario, sway the importance curve. Consequently, the optimal frequencies to denote the presence of the floating plastic targets are on the positive part of the difference curve ( ${{{\delta }}_c} \gt 0$).

Figure 8. The line shows the normalized difference in frequency importance between the Target and Reference datasets, ${{{\delta }}_c}$, and the areas represent to the total importances of the sliding 1 and 2 GHz sub-band intervals, ${C_{1GHz}}$ and ${C_{2GHz}}$, for the test cases measured with a water surface height of ${H_s} = \,$9 cm. (a) Plastic bottles; (b) plastic straws; (c) cylinder foams; (d) plastic lids. The inset shows the plastic target’s dimensions in millimeters.

Figure 9. The line shows the normalized difference in frequency importance between the Target and Reference datasets, ${{{\delta }}_c}$, and the areas represent the total importances of the sliding 1 and 2 GHz sub-band intervals, ${C_{1GHz}}$ and ${C_{2GHz}}$, for the test cases measured with a water surface height of ${H_s} = \,$17 cm. (a) Plastic bottles; (b) plastic straws; (c) cylinder foams; (d) plastic lids. The inset shows the plastic target’s dimensions in millimeters.

Regarding the areas of total importance for the 1 and 2 GHz bandwidth, we observe that using the wider 2 GHz sub-band computes, for the most part, higher total importance. Even with the use of the Hamming window to compute the total importance, this is expected as the ${C_{2GHz}}$ interval considers more frequencies in the sum. Since 2 GHz is an unrealistic bandwidth to use in real-world applications due to regulatory constraints, we focus on the positive area parts where the ${C_{1GHz}} \geqslant $ ${C_{2GHz}}$. For the 9 and 17 cm wave cases, this mainly happens around 8, 9 and 10.5 GHz. Considering the previous simulation results, this further accentuates that X-band frequencies are more relevant for the detection of floating macroplastics.

In the next subsection, we will employ the supervised learning workflow to confirm if this relationship across the wideband spectrum also points to higher MW frequencies for best detection.

Detection analysis

We apply the supervised ML workflow to the four test cases measured in the two water wave states. In Fig. 10, we can observe the accuracy output of the binary classification considering 9 (left) and 17 (right) cm wave heights, respectively. Starting with the 9 cm cases, all four test cases lead to a confident detection (above 90%) with upper C- and X-band frequencies. For the plastic bottles, straws, lids, and cylinder foams, the maximum accuracy obtained is 99.05%, 99.45%, 96.51%, and 95.68% at 8, 9, 9.8, and 10.4 GHz, respectively. For the 17 cm wave cases, the maximum accuracy obtained for the same cases is 83.82%, 93.81%, 85.43%, and 88.29% at 8.9, 10.2, 9.3, and 10.4 GHz, respectively. These results show that the frequencies with positive difference in feature importance are in C- and X-bands, which is consistent with the previous unsupervised analysis. Our tuned MLP model learnt the backscatter intensity pattern denoting the presence of floating macroplastic. It successfully discriminated reference measurements from target measurements (and vice-versa), independently of the type of plastic target, through upper C- and X-band frequencies. Thus, we can in fact confirm that the classification of each signal is mainly associated with the strength of targets’ backscatter response. Noteworthy, for the worse 17 cm water waves scenario, only with X-band frequencies around 9 and 10 GHz does the accuracy remain above 80% for all test cases. The previous numerical analysis also justifies this result considering that the frequency selective scattering behavior from each individual plastic item contributes with higher backscatter responses at X-band frequencies.

Figure 10. Accuracy output for supervised learning workflow using 1 GHz sub-bands for the test cases with an ${H_s}$ of (a) 9 cm and (b) 17 cm.

Finally, even though the plastic straws case shows the highest accuracy output along the X-band (especially in the 17 cm water waves), this only means that the target measurements from this class have a more consistent backscatter intensity level at these frequencies. This can be attributed to the much higher number of plastic straws on top of the water surface in contrast to the other heavier plastic items to makeup the continuous concentration of 10 $g/{m^2}$. This leads to fewer misclassifications when separating from the lower intensity reference measurements.

Comparison with physical-based detection metric

Next, we compare the detection performance of the supervised ML model using the standard EESS frequency intervals (see Table 2) and of the alternative physical-based EnR metric, which requires larger bandwidths. First, we investigate detection using the EnR metric, quantifying the difference in backscatter intensity produced by the scatterers in the antenna footprint for the Reference and Target datasets (see the “Physical-based detection metric” subsection for details). Besides the physical interpretability, we can also estimate the impact of higher waves and different MW frequencies in the detection sensitivity. The first three columns in Table 3 presents the EnR values for all four test cases with 9 and 17 cm wave height, considering the S-, C-, and X-bands of Table 1. Recall that the EnR detection threshold for ${H_s} = 9\,cm\,$ is slightly below 1.4 and for ${H_s} = 17\,cm\,$ it is slightly below 1.5 (Table 1). While the EnR is only slightly above the threshold at S-band, it is much above it for C- and X-band at ${H_s} = 9\,cm$ and for the X-band at ${H_s} = 17\,cm$.

Table 3. Detection values of 9 and 17 cm waves for all four target types across S-, C-, and X-bands using EnR and supervised ML to EESS intervals

Notably, the water surface wave height impacts the detection sensitivity at all MW frequencies. In fact, Table 3 shows that the EnR metric decreases across the measured MW spectrum when the water wave height increases. Conversely, when the water wave height is fixed, the metric increases with frequency. This holds true for both the test cases and thresholds. This means that the increase in water waves height and MW frequencies lead to higher backscatter intensity signals. The presence of the scattered, floating macroplastics items further contributes towards the increase in backscattered intensity. This verifies the previous simulation analysis behavior and corroborates the previous ML results using a wider 1 GHz.

Next, we analyze the performance of the MLP considering the narrower EESS intervals. Columns 4–8 of Table 3 show the detection accuracy obtained using only steps 3 and 4 of the supervised learning workflow. For both 9 and 17 cm test cases, the performance using ML accompanies the EnR metric, increasing with MW frequency and worsening with the increase in water wave heights. Albeit slightly lower, these accuracy results agree with the supervised workflow results discussed previously in the “Detection analysis” subsection that use a wider 1 GHz. As we narrow the frequency interval, we limit the number of features considered by the ML model and, consequently, possibly exclude MW frequencies with a resonant scattering response for the detection. Still, the accuracy results maintain the relationship with water wave height and MW frequency, i.e., decrease and increase, respectively. Additionally, except for the 9-cm plastic bottles and lids cases, the last column of Table 3 shows that the consideration of the noncontiguous EESS frequency intervals can lead to better detection results. Accordingly, this improvement is justified because the detection performance benefits from adding more (optimal) X-band frequency information as features of the model.

This analysis shows that the EnR metric and the MLP model obtain compatible results. On one hand, EnR provides physical interpretability in terms of the excess scattered energy in the presence of plastic, but at the cost of bandwidth, need for an unpractical reference measurement and need of sequential measurements of the same scenario to capture targets drift (although the latter can be obtained with spotlight mode [Reference Belcher and Baker41]). On the other hand, ML automation can consider standard EESS bands and shuffled input signals when training the model. This leads to a more robust detection performance that can be adapted for fast-changing deep-sea scenarios, suitable for real-time monitoring.

Multiclass analysis

Thus far, the analysis considered the datasets of each type of target at a time (either bottles, or straws, or lids, or foam). In this subsection, we evaluate if can use supervised ML to differentiate between the different plastic targets.

We apply the supervised ML workflow to merged datasets of the four types of targets (see the “Supervised learning workflow” subsection) and perform multiclass classification to distinguish between them. We test cases for 9 and 17 cm water wave heights. We show in Fig. 11(a) the accuracy output of this multiclass scenario. In neither the 9 nor 17 cm water wave height cases, did the maximum accuracy reach a high enough value for detection. Still, similarly to binary classification, we observe an identical trend in accuracy with respect to MW frequency and water wave height: accuracy increases with MW frequency but decrease with water wave height. To further investigate the low accuracy results, we present in Fig. 11(b) and 11(c) the confusion matrices for the optimal detection case (maximum accuracy) for 9 and 17 cm water wave height cases, respectively.

Figure 11. (a) Multiclass classification accuracy output for supervised learning workflow using 1 GHz sub-bands for the test cases with an ${H_s}$ of 9 and 17 cm; (b) confusion matrix for highest accuracy output of the 9 cm case; (c) confusion matrix for highest accuracy output of the 17 cm case.

First, let us consider the 9 cm test cases. While the reference measurements are mostly correctly classified, most of the four types of target measurements are incorrectly classified. This means that the MLP model easily separates reference measurements from target ones (seen already with the previous detection analysis), but it struggles to confidently discriminate between the different target measurements. This explains the low accuracy output when predicting on the unseen data.

For the 17 cm wave case, we observe an increase in misclassified references and target measurements, particularly for the plastic bottles and straws classes. As the water wave height increases, the MLP model struggles to define multiple decision boundaries, making it difficult to differentiate between targets. The scattering intensity across the MW spectrum from the target measurements is already very similar in the lower wave height case, and the increase in wave height further reduces this distinction. This is because the scattering intensity from the water surface increases, which deteriorates the detection sensitivity for the different types of plastic items. Hence, the results indicate that even with the use of the optimal X-band frequencies, multiclass classification is reduced to a binary one.