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We estimated the abundance of desert bighorn sheep in a captive facility located within the Chihuahuan Desert of New Mexico (Fig. 1). The area is arid, mountainous, with steep cliffs punctuated by ravines. The entire facility is enclosed by a high fence, preventing desert bighorn sheep ingress or egress. These animals are wild, unconditioned to humans, and used by The New Mexico Game and Fish Department (NMDGF) to establish and bolster other desert bighorn sheep populations within New Mexico16.
NMDGF leads an annual spring census to enumerate desert bighorn sheep numbers within the facility. Methodologically, the census uses a ground crew of spaced individuals walking in a line perpendicular to pen fencing, within the facility (i.e., drive count or census). Each individual keeps track of neighboring individuals to space the line, and to count any desert bighorn sheep breaking past them. Most desert bighorn sheep are herded ahead of the line. Other biologists at high topographical sites use spotting-scopes and binoculars to count and age class the moving sheep. Census counts are classified by animal ages and sex. We consider young sheep any animal ≤ 1.5 years old. Adult rams and ewes consist of males and females aged  > 1.5 years old, respectively. The group “adult” includes all sheep  > 1.5 years old.
We established 11 motion activated camera traps (Bushnell Trophy Cam) at the centers of an 800-m grid with a random geographical start. Cameras were secured to T-posts or existing vegetation when rocky areas thwarted post establishment. Most cameras were oriented north, to minimize sun exposure in the imagery. When vegetation or rock blocked the camera view, the camera orientation was rotated eastward until a clear view was obtained. Camera heights were 0.9–1.2 m with declination perpendicular to the ground. Cameras were checked at 6 month intervals and the retrieved SD cards were never full. Cameras were motion activated and set at the shortest delay possible (10 s; meaning that the camera waits at least 10 s after recording a picture before it will record another). In practice, the fastest trigger speed that cameras recorded imagery was a mean of 14.92 s (N = 6 cameras; SD = 0.94), a value we rounded to 15 s and employed in our analyses. Cameras recorded one image per trigger. We deployed cameras by 15 May 2017 and retrieved cameras no earlier than 30 April 2018. Our analyses period began on 1 October 2017 and ended on 1 May 2018. We employed a 5 month acclimation period to avoid the cameras serving as a novel attractant for desert bighorn sheep, which would violate distance sampling assumptions. Further, we experienced 1 camera failure during this acclimation period, and relocated 2 misplaced cameras. Lastly, some desert bighorn sheep gathered in shady locations near cameras during hot months (June–September) which created extreme variation in the encounter rate. The 1 October 2017–1 May 2018 period lacked all of these issues.
Imagery of desert bighorn sheep were identified and then classified by sex and age class: rams, ewes, young, adults (an adult-sized animal with sex undiscernible), and unknown [undiscernible (e.g. picture of a hoof, or animals blocking a clear view another animal)17]. To quantify distances, an individual stood at each camera and used the printed images of desert bighorn sheep to position another person at the exact locations that an animal was imaged. Distances between individuals were measured with a laser rangefinder and metric tape (Fig. 2; the authors confirm that informed consent was obtained to publish the identifying information/images in an online open-access publication). We supplemented these measurements by recording distances between the camera and several recognizable objects in the images (e.g. rocks, plants), to ensure accurate distance delineations for the imaged sheep.
The sensitivity of a trail camera’s passive infrared sensor (PIR) will decline as radial distance from the camera increases. Other factors, like vegetation and topography, also cause animal detections to decline with distance. This situation makes distance sampling an appealing approach, as its’ foundational premise is that the probability of detecting an animal declines with distance from the observation point15. The technique relies on measured distances between animals and the observation point. Therefore, we used the distance measures of desert bighorn sheep to the respective trail camera imaging them, to estimate sheep abundances using the ‘distance’ package (version 0.9.812) in program R. We analyzed data using a fall period (1 October 2017–31 January 2018) and a spring period (1 March 2018–1 May 2018). Dates for these periods were selected by season while ensuring sufficient sample sizes.
The camera trap operates like a point count sample. The sampling angle for each camera’s field of view was 50°18. Therefore, we multiplied sampling effort by this fraction (50/360) to correctly represent the amount of sampling area.
When analyzing data within a distance sampling approach, obtaining unbiased density estimates relies on correspondence between the sampling period and the period describing when the target species are active and therefore available for detection10,15. In our situation, this means aligning the sampling period of distance measurements with the period of time that desert bighorn sheep were active and able to trigger the trail camera10. In our study, we acquired very few nocturnal images of desert bighorn sheep (Fig. 4). Therefore, we censored study effort and distance data to the period defined by 1 h before sunrise through 2 h after sunset for each month, on a daily basis. Doing so removed  More

A comprehensive description of the methodological aspects used during the field surveys and image analysis have been published in González-Rivero et al.23,25,35. Therefore, here we include a synopsis of how this dataset was generated and made available to the wider community.
Our approach involved the rapid acquisition of high-resolution imagery over large extent of reefs and efficient image analysis to provide key information about the state of coral reef benthic habitat across multiple spatial scales23. The data generation and processing involved three main components: (1) photographic surveys, (2) post-processing of images and (3) image analysis, which are described and summarised below in Fig. 1.
Fig. 1

The workflow for generating the global dataset of coral reef imagery and associated data. The 860 photographic surveys from the Western Atlantic Ocean, Southeast Asia, Central Pacific Ocean, Central Indian Ocean, and Eastern Australia, were conducted between 2012 and 2018. Reef locations are represented by points colour-coded according to the survey region. Surveys images were post-processed in order to transform raw fish-eye images into 1 × 1 m quadrats for manual and automated annotation (inset originally published in González-Rivero et al.23 as Figure S1). For the image analysis, nine networks were trained. For each network, images were divided in two groups: Training and Testing images. Both sets were manually annotated to create a training dataset and verification dataset. The training dataset was used to train and fine-tune the network. The fully trained network was then used to classify the test images, and contrast the outcomes (Machine) against the human annotations (Observer) in the test dataset during the validation process. Finally, the non-annotated images (photo-quadrats) were automatically annotated using the validated network. The automated classifications were processed to originate the benthic covers that constitute this dataset. QGIS software was used to generate the map using the layer “Countries WGS84” downloaded from ArcGIS Hub (http://hub.arcgis.com/datasets/UIA::countries-wgs84).

Full size image

Photographic surveys
An underwater propulsion vehicle customised with a camera system (“SVII”, Supplementary Fig. 1), consisting of three synchronised DSLR (Digital Single-Lens Reflex) cameras (Cannon 5D-MkII cameras and Nikon Fisheye Nikkor lens with 10.5 mm focal length), was used to survey the fore-reef (reef slope) habitats from five major coral reef regions: Central Pacific Ocean, Western Atlantic Ocean, Central Indian Ocean, Southeast Asia and Eastern Australia in 23 countries or territories (Table 1, Supplementary Fig. 2). Within each region, multiple reef locations were surveyed aiming to capture the variability and status of fore-reefs environments across regions and within each region. Sampling design varied according to particular environmental and socioeconomic factors potentially influencing the distribution and structure of coral reef assemblages at each region and/or country. Overall, prior to field expeditions, reef localities were selected considering factors such as wave exposure, reef zones (i.e. fore-reefs), local anthropogenic stressors (e.g. coastal development), fishing pressures, levels of management (e.g. marine park, protected areas), and presence of monitoring sites.
Table 1 Summary of the photographic surveys conducted between 2012 and 2018.
Full size table

Underwater images were collected in each reef location once every three seconds, approximately every 2 m apart, following a transect along the seascape at a standard depth of 10 m (±2 m). Although overlap between consecutive images is possible, the process for extracting standardised photo-quadrats from an image ensures that the photo-quadrats are non-overlapping between and within images (see further details next section). Each transect averaged 1.8 km in length, hereafter referred to as a “survey”. See Supplementary Fig. 3 for an explanation of the hierarchical structure of the photographic surveys. No artificial illumination was used during image capture, but light exposure was manually adjusted by modifying the ISO during the dive, using an on-board tablet computer encased in an underwater housing (Supplementary Fig. 1). This computer enabled the diver to control camera settings (exposure and shutter speed) according to light conditions. Images were geo-referenced using a surface GPS unit tethered to the diver (Supplementary Fig. 1). Altitude and depth of the camera relative to the reef substrate and surface were logged at half-second intervals using a Micron Tritech transponder (altitude, Supplementary Fig. 1) and pressure sensor (depth) in order to select the imagery within a particular depth and to scale and crop the images during the post-processing stage. Further details about the photographic surveys are provided in González-Rivero et al.25,35.
Post-processing of images for manual and automated annotation
The post-processing pipeline produced images with features required for manual and automated annotation in terms of size and appearance. The process involved several steps that transformed the raw images from the downward facing camera into photo-quadrats of 1 m2, hereafter referred to as a “quadrat” (Fig. 1). As imagery was collected without artificial light using a fisheye lens, each image was processed prior to annotation in order to balance colour and to correct the non-linear distortion introduced by the fisheye lens23 (Fig. 1). Initially, colour balance and lens distortion correction were manually applied on the raw images using Photoshop (Adobe Systems, California, USA). Later, in order to optimise the manual post-processing time of thousands of images, an automatic batch processing was conducted on compressed images23 (jpeg format) using Photoshop and ImageMagick, the latter an open-source software for image processing (https://imagemagick.org/index.php). In addition, using the geometry of the lens and altitude values, images were cropped to a standardised area of approximately 1 m2 of substrate23,35 (Fig. 1). Thus, the number of nonoverlapping quadrats extracted from one single raw image varied depending on the distance between the camera and the reef surface. Figure 1 illustrates a situation where the altitude of the camera allowed for the extraction of two quadrats from one raw image. Further details about colour balance and lens distortion correction and cropping are provided in González-Rivero et al.23,35.
Image analysis: manual and automated annotation for estimating covers of benthic categories
Manual annotation of the benthic components by a human expert took at least 10 minutes per quadrat, creating a bottleneck between image post-processing and the required data-product. To address this issue, we developed an automated image analysis to identify and estimate the relative abundance of benthic components such as particular types of corals, algae, and other organisms as well as non-living components. To do this, automated image annotation based on deep learning methods (Deep Learning Convolutional Neural Networks)23 were applied to automatically identify benthic categories from images based on training using human annotators (manual annotation). The process for implementing a Convolutional Neural Network (hereafter “network”) and classify coral reef images implied three main stages: (i) label-set (benthic categories) definition, (ii) training and fine-tuning of the network, and (iii) automated image annotation and data processing.
Label-set definition
As a part of the manual and automated annotation processes to extract benthic cover estimates, label-sets of benthic categories were established based on their functional relevance to coral reef ecosystems and their features to be reliably identified from images by human annotators25. The labels were derived, modified and/or simplified from existing classification schemes40,41, and were grouped according to the main benthic groups of coral reefs including hard coral, soft coral, other invertebrates, algae, and other. Since coral reef assemblages vary in species composition at global and regional scales, and surveys were conducted at different times between 2012 and 2018 across the regions, nine label-sets accounted for such biogeographical and temporal disparity. In general, a label-set was developed after each main survey expedition to a specific region. The label-sets varied in complexity (from 23 to 61 labels), considering the differential capacity to visually recognise (in photographs) corals to the lowest possible taxon between the regions. While label-sets for the Atlantic and Central Pacific (Hawaii) included categories with coral genus and species, for the Indian Ocean (Maldives, Chagos Archipelago), Southeast Asia (Indonesia, Philippines, Timor-Leste, Solomon Islands, and Taiwan), and Eastern Australia, corals comprised labels based on a combination of taxonomy (e.g., family and genus) and colony morphology (e.g., branching, massive, encrusting, foliose, tabular).
The other main benthic groups were generally characterised by labels reflecting morphology and/or functional groups across the regions. “Soft Corals” were classified into three groups: 1) Alcyoniidae (soft corals), the dominant genera; 2) Sea fans and plumes from the family Gorgoniidae; and 3) Other soft corals. “Algae” groups were categorised according to their functional relevance: 1) Crustose coralline algae; 2) Macroalgae; and 3) Epilithic Algal Matrix. The latter is a multi-specific algal assemblage smothering the reef surface of up to 1 cm in height (dominated by algal turfs). “Other Invertebrates” consisted of labels to classify sessile invertebrates different to soft corals (e.g., Millepora, bryozoans, clams, tunicates, soft hexacorrallia, hydroids) and some mobile invertebrates observed in the images (mostly echinoderms). The remaining group, “Other”, consisted of sand, sediments, and occasional organisms or objects detected in the images such as fish, human debris (e.g., plastic, rope, etc.), and transect hardware. The exception within these main groups were the “Sponges”, which were classified and represented by multiple labels only in the Atlantic (given their abundance and diversity in the Caribbean), including categories with sponge genus and species, and major growth forms (rope, tube, encrusting, massive).
Training and fine-tuning of the network
The deep learning approach used relies on a convolutional neural network architecture named VGG-D 1642. Details on the initialisation and utilisation of this network are provided in González-Rivero et al.23. A total of nine networks were used, one for each country within the regions, except for the Western Atlantic Ocean, where the network was trained using data from several countries, and the Philippines and Indonesia, where the network was trained using data from those two countries. (Table 2). The first step in implementing a network was to randomly select a subset of images from the whole regional set to be classified, which were then divided into training and testing sets (Fig. 1). Human experts manually annotated both sets using the corresponding label-set under CoralNet43, an online platform designed for image analysis of coral reef related materials (https://coralnet.ucsd.edu/). The number of images and points manually annotated per network is presented in Table 2 (generally 100 points per image for training sets and 40 or 50 points per image for testing sets).
Table 2 Summary of the images, manual point annotations, and test transects used during the train and test processes of each network.
Full size table

Each training and testing data set were exported from CoralNet43 and used along with the associated quadrats to support an independent training and fine-tuning process aimed to find the network configuration that produced the best outcomes. Initially, each quadrat used from the training and testing sets was converted to a set of patches cropped out around each annotation point location. The patch area to crop around each annotation point was set to 224 × 224 pixels to align with the pre-defined image input size of the VGG-D architecture. The fine-tuning exercise ran in general for 40 K iterations to establish the best combination of model parameters or weights that minimised the cross-entropy loss while the overall accuracy increased. An independent 20% subset from the original set of quadrats was used to assess the performance of the final classification (% of accuracy). In addition, parameters of learning rate and image scale were independently optimised for each network by running an experiment using different values for such parameters in order to select the values that derived the smallest errors per label. Further details of the model parametrisation for each network are provided in González-Rivero et al.23 (see Supplementary Material).
Automated image annotation and data processing
Once optimised, a network was used to automatically annotate the corresponding set of non-annotated quadrats. The quadrats were processed through the network, where for each quadrat, 50 points (input patches) were classified using the associated labels. Upon completion of automated image annotation for a specific region/country, the annotation outputs containing locations of 50 pixels (i.e., their x and y coordinates) with their associated labels per quadrat (a csv file per quadrat) were incorporated and collated into a MySQL database along with information about the field surveys. In addition to the manual and automated annotations tables (raw data), we provide two levels of aggregation for the benthic data. First, the relative abundance (cover) for each of the benthic labels per quadrat, which was calculated as the ratio between the numbers of points classified for a given label by the total number of points evaluated in a quadrat. Second, the relative abundance for each of the main benthic groups (hard coral, soft coral, other invertebrates, algae, and other) per survey, which involved three calculations: 1) summarise the quadrat covers by image averaging all the quadrats from one single image per label, 2) summarise image covers by survey averaging all the images across one survey per label, and 3) merge survey data by main benthic groups summing the covers of all labels belonging to the same group across one survey. More

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DeepHL system architecture
The DeepHL system consists of three server computers. The first one is a web server that receives a trajectory data file from a user and provides analysis results to the user (Intel Xeon E5-2620 v4, 16 cores, 32 GB RAM, Ubuntu 14.04). The second one is a storage server that stores data files and analysis results. The third one is a GPU server that analyzes data provided by the user (Intel Xeon E5-2620 v4, 32 cores, 512 GB RAM, four NVIDIA Quadro P6000, Ubuntu 14.04). Supplementary Information, Algorithm, provides a complete description of the DeepHL method. DeepHL is accessible on the Internet through http://www-mmde.ist.osaka-u.ac.jp/maekawa/deephl/. Supplementary Information, User guide to DeepHL, provides a user guide to DeepHL. In addition, Supplementary Information, Usage of Python-based Software, and Supplementary Software 1 present the Python code of DeepHL.
Preprocessing
An input trajectory is a series of timestamps and X/Y coordinates associated with a class label. To perform position- and rotation-independent analysis, we convert the series into time series of speed and relative angular speed and then standardize them (Supplementary Information, Algorithm). Note that the absolute coordinates of wild animals, which can relate to the distance from a nest or feeding location, for example, are important in understanding behavior of the animals. Hence, DeepHL allows the original coordinates to be input to DeepHL-Net along with the speed and relative angular speed. In addition, other biological time-series sensor data measured by the user can be fed into DeepHL-Net when these time-series data are included in a data file uploaded by the user. For example, a time series of the heading direction of animals obtained from digital compasses can be useful for behavior understanding. Moreover, primitive features usually used in trajectory analysis can be easily fed into DeepHL-Net. DeepHL automatically computes the travel distance from the initial position, the straight-line distance from the initial position, and the angle from the initial position (Supplementary Table 1) as primitive features. Using the web interface of DeepHL, the user can easily select primitive features and other sensor data to be fed into DeepHL-Net (Supplementary Information, User guide to DeepHL). See Supplementary Information, Effect of input features, for effects of input features on classification accuracy. Normally, the inputs of DeepHL-Net are two-dimensional time series, that is, speed and relative angular speed. When we input an additional time series (such as the original coordinates) into DeepHL-Net, the additional time series are added as additional dimensions of the inputs.
Multi-scale layer-wise attention model (DeepHL-Net)
Here, we explain DeepHL-Net shown in Fig. 2f in detail. The input of the model is a time series of primitive features, that is, an lMAX × Nf matrix, where lMAX is the maximum length of the input trajectories and Nf is the dimensionality of the time series, that is, the number of the primitive features. Because the lengths of observed trajectories are not identical to each other in many cases, we fill in missing elements in the matrix with  −1.0 and mask them when we train DeepHL-Net. In each 1D convolutional layer of the convolutional stacks, we extract features by convolving input features through the time dimension using a filter with a width (kernel size) of Ft. We use different filter widths in the four convolutional stacks (3%, 6%, 9%, and 12% of lMAX) to extract features at different levels of scale. We use a stride (step size) of one sample in terms of the time axis. We also use padding to allow the outputs of a layer to have the same length as the layer inputs. In addition, to reduce an overfitting, we employ a dropout, which is a simple regularization technique in which randomly selected neurons are dropped during training44. The dropout rate used in this study is 0.5.
In each LSTM layer of the LSTM stacks, we extract features considering the long-term dependencies of the input features. LSTM is a recurrent neural network architecture with memory cells, and it permits us to learn temporal relationships over a long time scale. LSTM learns long-term dependencies by employing memory cells that hold past information, updating the cell state using write, read, and reset operations with input, output, and forget gates (see Supplementary Information, Algorithm). In addition, we employ dropout to reduce overfitting. The attention information of each layer is computed by using Eq. (1), and then it is multiplied by the layer output. Here, the softmax and tanh functions in Eq. (1) are defined as follows:

$$,{text{softmax}},({x}_{j})=frac{exp ({x}_{j})}{{sum }_{i}exp ({x}_{i})},$$
(2)

$$tanh ({x}_{j})=frac{exp ({x}_{j})-exp (-{x}_{j})}{exp ({x}_{j})+exp (-{x}_{j})}.$$
(3)

Note that parameters in Eq. (1) for each layer, that is, Wa and ba, as well as parameters in the convolutional and LSTM layers are estimated during the network training phase. Here, we introduced the tanh activation function into Eq. (1) to smooth out the output attention values. When an outlying large value is included in WaZT + ba at time t, attention values other than time t become extremely small without using the tanh function. When we visualize a trajectory using such attention values, only a single data point is colored in red, making it difficult for a user to identify important segments.
Training and testing of DeepHL-Net
The DeepHL user can select the parameters of DeepHL-Net used in the analysis, that is, the number of convolutional/LSTM layers and the number of neurons in each layer (default: four layers with 16 neurons). Then, DeepHL-Net is trained on 80% of randomly selected trajectories to minimize the binary classification error of the training data, employing backpropagation based on Adam45 (Supplementary Information, Algorithm). (Note that each trajectory has a class label for binary classification.) Then, the trained DeepHL-Net is tested using the remaining 20% of trajectories to compute the classification accuracy, providing an indication of the degree of difference between the two classes.
Computing the score of each layer
To screen the layers in DeepHL-Net, we compute a score for each layer according to Eq. (4)

$$s({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})={s}_{mathrm{fc}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})+{s}_{mathrm{it}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}}).$$
(4)

Here, ({A}_{i,{C}_{mathrm{A}}}) is a set of attention vectors calculated from trajectories belonging to class A using the ith layer. In addition, ({A}_{i,{C}_{mathrm{B}}}) is a set of attention vectors calculated from trajectories belonging to class B using the ith layer. As mentioned in the main text, an attention vector from a discriminator layer should have large values within limited segments. Therefore, ({s}_{mathrm{fc}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})) in Eq. (4) calculates the averaged variance of the attention values normalized by the average length of the trajectories, as described in Eq. (5). When the layer focuses on a part of a trajectory, the variance increases

$${s}_{mathrm{fc}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})=sqrt{frac{1}{| {A}_{i,{C}_{mathrm{A}}}cup {A}_{i,{C}_{mathrm{B}}}| cdot l({A}_{i,{C}_{mathrm{A}}}cup {A}_{i,{C}_{mathrm{B}}})}sum _{{bf{a}}in {A}_{i,{C}_{mathrm{A}}}cup {A}_{i,{C}_{mathrm{B}}}}V({bf{a}})}.$$
(5)

Note that V(⋅) calculates the variance and l(⋅) calculates the average length of the trajectories. We take the square root of the average variance to derive the average standard deviation. Using (l({A}_{i,{C}_{mathrm{A}}}cup {A}_{i,{C}_{mathrm{B}}})), which calculates the average length of ({A}_{i,{C}_{mathrm{A}}}cup {A}_{i,{C}_{mathrm{B}}}), we normalize the computed variance. Because the softmax function in Eq. (1) ensures that all values sum to 1, resulting in a larger variance for longer trajectories, we normalize the average variance using the average length.
In addition, as mentioned in the main text, the distribution of attention values by the layer for one class should be different from that for another class. Therefore, ({s}_{mathrm{it}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})) calculates the difference between the distributions of the attention values of classes A and B as follows:

$${s}_{mathrm{it}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})=(1-,{mathrm{Intersect}},(h(A_{{i,{C}}_{mathrm{A}}}),h({{A}}_{{i,{C}}_{mathrm{B}}}))).$$
(6)

Here, h(⋅) calculates a normalized histogram of attention with 200 bins, and Intersect(⋅ , ⋅) calculates the area overlap between two histograms, and is described as follows:

$${mathrm{Intersect}},(H_{1},H_{2})=mathop{sum}limits_{i}min (H_{1}(i),H_{2}(i)),$$
(7)

where H1(i) shows the normalized frequency of the ith bin of histogram H1. As described in Eq. (4), the final score is calculated as the sum of the two scores of ({s}_{mathrm{fc}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})) and ({s}_{mathrm{it}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})).
Here, ({s}_{mathrm{fc}}({A}_{i,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}})) in Eq. (4) is used to find a layer that focuses only on a portion of a trajectory. Owing to the term, only a small important portion of trajectories is highlighted in many cases, as shown in Figs. 3, 5, and 6, especially for the trajectories of beetles. However, substantial portions of several trajectories of the normal mice are highlighted, as shown in Fig. 4d. Because the characteristics of the normal mouse trajectories are the distance from the initial position, the segments in the trajectories far from the initial position are highlighted.
Computing the correlation between attention values and handcrafted features
To help the user understand the meaning of the highlights, DeepHL automatically computes the Pearson correlation coefficients between the attention values of each layer and handcrafted features computed by DeepHL, as shown in Supplementary Table 1. In addition, the correlation coefficients with sensor data and handcrafted features included in a trajectory data file are automatically computed. Computing the correlation with environmental sensor data can reveal the relationship between a behavior and environmental conditions. If a specific behavior is exhibited only when the temperature is high, for example, we can infer that the behavior relates to the high temperature condition. Furthermore, DeepHL automatically computes the moving average, moving variance, and derivative of each of the above features/sensor data, and then computes the correlation coefficients with the attention values, which are presented to the user (Supplementary Fig. 1).
Computing the difference between distributions of each handcrafted feature for the two classes within highlighted segments
To help the user understand the meaning of the highlights, DeepHL automatically computes the difference between distributions of each handcrafted feature for two classes within highlighted segments. The difference is computed as follows:

$${mathrm{diff}}({A}_{i,{C}_{mathrm{A}}},{F}_{j,{C}_{mathrm{A}}},{A}_{i,{C}_{mathrm{B}}},{F}_{j,{C}_{mathrm{B}}})=1-,{mathrm{Intersect}},(h(m({{A}}_{{i,{C}}_{mathrm{A}}},{{F}}_{{j,{C}}_{mathrm{A}}})),h(m({{A}}_{{i,{C}}_{mathrm{B}}},{{F}}_{{j,{C}}_{mathrm{B}}}))).$$
(8)

Here, ({F}_{j,{C}_{mathrm{A}}}) is a set of time series of the jth handcrafted feature calculated from trajectories belonging to class A. In addition, m(⋅ , ⋅) is a masking function that extracts feature values within highlighted segments. Because the softmax function in each attention layer ensures that all attention values in a sum of 1, we consider an attention value larger than c/(# time slices) as a potential attended value (c = 1.2 in our implementation).
Data acquisition of worms
Data acquisition was performed according to Yamazoe-Umemoto et al.22. In brief, several worms were placed in the center of an agar plate in a 9-cm Petri dish, 30% 2-nonanone (v/v, EtOH) was spotted on the left side of the plate, which was covered by a lid and placed on the bench upside down. Then, the images of the plate were captured with a high-resolution USB camera for 12 min at 1 Hz. Because the worms do not exhibit odor avoidance behavior during the first 2 min because of the rapid increase in odor concentration46, the data for the following 10 min (i.e., 600 s) was used. From the images, individual worms were identified and the position of the centroid was recorded by an image processing software Move-tr/2D (v. 8.31; Library Inc., Japan). The number of recorded trajectories is 325 (Supplementary Table 2). The comparison was between the naive worms (control class) and the worms after preexposure to the odor (preexposed class).
DeepHL analysis of worms
A multivariate time series of movement speed, relative angular speed, distances from the initial position, and angle from the initial position extracted from the time series of trajectories was fed into DeepHL-Net, yielding a binary classification accuracy of 93.9%, where 20% of the data are used as test data. The discriminator layer used in this investigation has the highest score of all layers. As shown in Fig. 3d, which was calculated from the moving variance of the speed within highlighted segments, we can state that the changes in the speed of preexposed worms is larger than those of control worms. Figure 3e shows spectrograms of the speed calculated from entire trajectories (Fig. 3c) with a 128-s wide sliding window shifted in 1-sample intervals. In addition, Fig. 3f shows histograms of the dominant frequency of speed calculated from entire trajectories using the 128-s wide sliding window shifted in 1-sample intervals. These results also indicate the difference in the frequency of speed between the preexposed and control worms. Our investigation revealed that the dominant frequency of speed significantly differs between the preexposed and control worms using GLMM with Gaussian distributions (t = −6.60; d.f. = 322.8; p = 1.68 × 10−10, effect size(r2) = 0.232). The p value is two sided. Individual factors were treated as random effects. The number of data points for the control class is n = 76, 784 and that for the preexposed class is n = 75, 750. We used GLMM with Gaussian distributions because the objective variable has a continuous value and we used the lmerTest package (v. 2.0–36) of R (v. 3.4.3) for the analysis.
Data acquisition of mice
We collected 52 trajectories of normal mice and unilateral 6-hydroxydopamine (OHDA) lesion mouse models of PD while they freely moved for 10 min in an open field (60 × 55 cm2, wall height = 20 cm; normal: 22, PD: 30). The trajectories were detected by the animal’s head position, which was captured by an overhead digital video camera (60 fps). Two sets of small red and green light-emitting diodes were mounted above the animal’s head so that it could be located in each frame. Custom softwares based on Matlab (R2018b, Mathworks, MA, USA) and LabVIEW (Labview 2018, National Instruments, TX, USA) were used for tracking. We then created 30-s segments by splitting each trajectory because training a DNN requires a number of trajectories. We used 966 segments in total (normal: 374, PD: 592) collected from nine C57BL/6J mice (normal: 5, PD: 4). Note that we excluded 30-s segments that contain no movements of a mouse.
DeepHL analysis of mice
Movement speed, relative angular speed, travel distances, straight-line and travel distances from the initial position, and angle from the initial position were fed into our model. The accuracy for the binary classification of normal and 6-OHDA model mice was 74.7%, where 20% of the data are used as test data. The score of the discriminator layer was the highest of all LSTM layers and the sixth highest of all layers. Our investigation revealed that the behavior of visiting locations far away from the initial position can be characteristic of normal mice.
To evaluate PD symptoms from animal behaviors, previous studies have exclusively focused on the movement speed of animals in the open-field tests (frequency and bout duration of ambulation as well as immobility or fine movement) because typical symptoms in the animal model of PD are thought to be slowness of movement and a paucity of spontaneous movements. As shown in Fig. 4e–g, we found significant differences in average movement speed during ambulation periods, average movement speed during fine movement periods, and average maximum distance within a ±60-s window in a session. These differences were derived from the findings of DeepHL using the two-sided Wilcoxon rank-sum test (W = 544, p = 3.486 × 10−5, effect size (Cliff’s delta) = −0.648; W = 511, p = 5.869 × 10−4, effect size (Cliff’s delta) = −0.548; W = 521, p = 2.666 × 10−4, effect size (Cliff’s delta) = −0.579). The 95% confidence intervals are [1.222, 3.481], [0.139, 0.468], and [13.726, 43.175], respectively. We used the exactRankTests package (v. 0.8–29) of R (v. 3.2.3). Note that these behavioral features are extracted from original 10-min trajectories.
The maximum distance, which was derived from a finding of DeepHL, is more useful for evaluating the PD symptoms than conventional measures based on the movement speed. Note that the new feature is designed based on an insight drawn from an analysis by deep learning. These results suggest that DeepHL helps find a novel measure not directly linked to the movement speed, that is, a straight-line distance within a certain time window. When the aim of an animal is to visit all locations in an area, the travel distance over a short duration commonly becomes longer. Besides, it is well known that rodents, including mice and rats, spontaneously prefer to explore an environment, particularly in novel places. Thus, DeepHL may capture the fact that the abnormal behavior of the 6-OHDA lesion model of PD hinders such spontaneous behavioral traits of normal mice. Indeed, the 6-OHDA lesion mouse model appears to remain in the same place. Although this hypothesis should be verified based on the causality between behavioral traits and neural activity patterns underlying PD symptoms using neuronal recording together with its optogenetic manipulation in the basal ganglia and motor cortex23, it is beyond the scope of this study.
Behavioral features of mice
According to Kravitz et al.23, ambulation was defined as periods when the velocity of the animal’s center point averaged >2 cm/s for at least 0.5 s. Immobility was defined as continuous periods of time during which the average change of the trajectory was More