*5.2. Classification*

Data obtained after the processing of the radar signal are treated as images. Since their original size cannot be easily handled, all matrices have been reshaped to the same dimension [195 × <sup>119</sup>]. In order to further reduce dimensionality and to extract features from images, Principal Component Analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm have been then applied separately to data.

In Figure 9a,b we show the classification accuracy resulting from exploiting a different number of principal components, by using a Nearest Neighbor (NN) classifier and a Support Vector Machine (SVM) algorithm. We choose to use a Gaussian kernel for the Support Vector Machine (SVM).The value of *k* for the k-Nearest Neighbor (NN) and the kernel used for Support Vector Machine (SVM) have been chosen by using a leave-one-out cross-validation algorithm, which aims at minimizing the validation error. Each sample of the dataset is alternatively selected as a validation set, whilst the remaining part represents the training set. In this way all samples are used only one time both for training, both for validation. Results obtained by the algorithm for odd values of *k* between 1 and 49 are shown in Figure 10, where *k* equal to 1 leads to an error of about 2.4%. The validation error obtained by different kernels in percentage is reported in Table 2, thus directing the choice to the use of linear kernel in our scenario.

**Table 2.** Results of the leave-one-out cross validation for support vector machine (SVM) with different kernels.


Sixty percent of the acquisitions are used for training, while the remainder is used for testing. Results have been averaged over 100 classification results obtained choosing training and test sets at random. We consider here only two classes, corresponding to the slow and fast walk. Interestingly, it is possible to observe that the number of principal components (or number of dimension in case of t-distributed Stochastic Neighbor Embedding (t-SNE) ) that here corresponds to the number of features, has a small impact on the classification performance. The application of Principal Component Analysis (PCA) or t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm to extract features from images leads to very similar results, although t-distributed Stochastic Neighbor Embedding (t-SNE) was originally designed to reduce data to two or three dimensions, and becomes very slow for higher values. In addition, we obtain the same results using both Range-Doppler and Doppler-Time maps.

**Figure 9.** Comparison of classification accuracy achieved by SVM and kNN considering 2 and 3 classes, applying (**a**) Principal Component Analysis (PCA) and (**b**) t-distributed stochastic neighbor embedding (t-SNE).

**Figure 10.** Results of the leave-one-out cross-validation for the k-Nearest Neighbor (kNN).

In Tables 3 and 4 we show the confusion matrices obtained by applying classification on two and three different classes. In the first table, measurements of slow walk and slow walk with hands in pockets have been incorporated into a single class, while in the second table they have been split into two separate classes. As predictable, distinguishing free hands from hands in pockets is a much more complicated task than identify different ways of walking. In the first case in fact the best accuracy obtained is about 72% and red boxes highlight the presence of a number of misclassified examples, although the fast walk is recognized from the other activities with a high precision (87.5%); SVM methods seem to achieve better performance than KNN algorithms. In the latter case we have instead an excellent accuracy of more than 93%. In both Tables 3 and 4 we highlighted a high presence of correct detections in green, while a high number of misclassified samples is marked in red.

**Table 3.** Confusion matrix obtained applying SVM and kNN (into parentheses) on two classes, considering 5 principal components, *acc* = 93.5%.


**Table 4.** Confusion matrix obtained applying SVM and kNN (into parentheses) on three different classes, considering 9 principal components, *acc*SVM = 72%, *acc*KNN = 66.7%.


In Table 5, we give an overview of the results obtained by other works focused on the classification of walking activities through radar measurements, showing the best accuracies achieved. [\*] denotes the present work. In Reference [45] 7 types of activities are considered, that is, walking backwards, limping, depressed, elderly, excited, holding the arm and walking in a zigzag, and the radar used is an Ultra-Wide Band; Reference [46] considers a Frequency Modulated Continuous Wave (FMCW) radar, and the examined activities are crawl, creep on hands and knees, walk, jog and run. Although the difference between walking slowly or quickly is less evident than the other activities, we prove that our system is able to achieve a better accuracy. Moreover, we consider a larger number of subjects that move differently from each other, thus confirming the validity of our method in a realistic context. The activity of holding the arm while walking [45], which is in some way comparable to our case of walking slowly with hands in pockets, could not be differentiated from the others at all, with a specific accuracy of 42.42% (see Reference [45], Table 2).

**Table 5.** Comparison of different radar based methods for human walking classification.


The subjectivity and the personal speed interpretation of the conducted tests represents the major error source for our classification model. A standardized time or number of steps during the experiment should probably improve the system performance, but this would not represent a realistic scenario and it is out of the scope of this work.

### **6. Conclusions and Future Works**

We have assessed the performance of an automotive radar to classify different types of movements, focusing our attention to the distinction of people's way of walking. The dataset was not built ad hoc, but we have collected acquisitions of subjects with different characteristics free to walk in a given indoor environment. We have considered the use of PCA and t-SNE techniques to reduce data dimensionality and to extract features, and then we have applied different classification algorithms. From the obtained results it is possible to state that movement classification of human targets is a much more complex task with respect to the discrimination of people from other objects. However, we have shown that, by exploiting the micro-Doppler components of the radar signal, we are able to identify with a high accuracy slow and fast walking. We have also characterized the presence or absence of movement of the arms with more than 72% of precision, which represents a good starting point for a future work. A possible future direction may also include the investigation of deep learning methods in our scenario in order to better distinguish small movements.

**Author Contributions:** G.C. designed the system, G.C. and L.S. performed the experimental tests and data processing, writing also the main part of the paper. A.D.S. and E.G. participated in data collection and processing. E.G. coordinated the project, the discussion of result, and the manuscript writing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
