How Many Animals Are Euthanized Every Year

• Research article
• Open up Access
• Published: 05 February 2021

Increasing adoption rates at animal shelters: a two-phase approach to predict length of stay and optimal shelter allocation

BMC Veterinary Research volume 17, Commodity number:70 (2021) Cite this article

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Abstract

Background

Among the vi–viii million animals that enter the rescue shelters every twelvemonth, nearly iii–4 1000000 (i.e., l% of the incoming animals) are euthanized, and 10–25% of them are put to decease specifically because of shelter overcrowding each yr. The overall goal of this report is to increase the adoption rates at animal shelters. This involves predicting the length of stay of each animal at shelters considering central features such as animate being type (dog, cat, etc.), historic period, gender, breed, animal size, and shelter location.

Results

Logistic regression, artificial neural network, slope boosting, and the random forest algorithms were used to develop models to predict the length of stay. The performance of these models was adamant using three performance metrics: precision, think, and F1 score. The results demonstrated that the slope boosting algorithm performed the best overall, with the highest precision, recall, and F1 score. Upon further observation of the results, it was institute that age for dogs (puppy, super senior), multicolor, and large and pocket-size size were of import predictor variables.

Conclusion

The findings from this study tin be utilized to predict and minimize the animal length of stay in a shelter and euthanization. Hereafter studies involve determining which shelter location volition most likely lead to the adoption of that animal. The proposed two-phased tool can be used past rescue shelters to reach the best compromise solution by making a tradeoff between the adoption speed and relocation toll.

Background

As the problem of overpopulation of domestic animals continues to rise, animal shelters across the nation are faced with the claiming of finding solutions to increase the adoption rates. In the United states, about 6–8 million dogs and cats enter animal shelters every year, and 3–4 million of those animals are euthanized [one]. In other words, near 50% of the total canines and felines that enter animal shelters are put to expiry annually. Moreover, ten–25% of the total euthanized population in the Usa is explicitly euthanized because of shelter overcrowding each year [two]. Though animal shelters provide incentives such as reduced adoption fees and sterilizing animals before adoption, only a quarter of full animals living in the shelter are adopted.

Animal adoption from shelters and rescues

There are various places to adopt an animate being, and each potential possessor must complete the adoption process and paperwork to take their new animal dwelling [iii]. Public and private fauna shelters include animal command, city and county animal shelters, and law and wellness departments. Staff and volunteers run these facilities. Animals may besides exist adopted from a rescue organization, where pets are fostered in a home or a private boarding facility. These organizations are normally run by volunteers, and animals are viewed during local adoption events that are held at dissimilar locations, such as a pet store [3].

There could exist several reasons for the euthanization of animals in a shelter, such every bit overcrowding, medical issues (ex. sick, disabled), or behavioral issues (ex. too aggressive). The causes for the overpopulation of animals include failure to spay or neuter animals leading to reckless breeding habits and abandonment or surrender of offspring, animal abandonment from owners who are no longer able to take care of or practice not want the animal, and individuals even so ownership from pet stores [4]. With the finite room capacity for animals that are abased or surrendered, overpopulation becomes a key challenge [five]. Though medical and behavioral issues are harder to solve, the overpopulation of good for you adoptable animals in shelters is a trouble that can be addressed through machine learning and predictive analytics.

Literature review

In this section, we describe the enquiry conducted on animal shelters evaluating euthanasia and factors associated with animal adoption. The articles provide insights into factors that influence the length of stay and what characteristics influence adoption.

Studies have been conducted investigating the positive influence of pre-adoption neutering of animals on the probability of pet adoption [2]. The author investigated the impact of the cooperation of veterinary medical schools in increasing pet adoption past offer free sterilization. Results demonstrated that the collaboration betwixt veterinary hospitals and local beast shelters decreased the euthanization of adoptable pets.

Hennessy et al. [vi] conducted a study to determine the human relationship betwixt the behavior and cortisol levels of dogs in animal shelters and examined its outcome in predicting behavioral issues after adoption. Shore et al. [7] analyzed the reasons for returning adopted animals by owners and obtained insights for these failed adoptions to accomplish more successful futurity approvals. The researchers constitute that prior failed adoption had led to longer-lasting future acceptances. They hypothesized that the failed adoptions might lead owners to notice their canis familiaris preferences past assessing their living situation and the blazon of creature that would meet that requirement.

Morris et al. [8] evaluated the trends in income and upshot data for shelters from 1989 to 2010 in a large U.S. metropolitan expanse. The results showed a decrease in euthanasia, adoption, and intake for dogs. For cats, a reduction in intake was observed until 1998, a decrease in euthanasia was observed until 2000, and the adoption of cats remained the same. Fantuzzi et al. [9] explored the factors that are significant for the adoption of cats in the animate being shelter. The report investigated the effects of toy allocation, cage location, and cat characteristics (such every bit age, gender, color, and action level). Results demonstrated that the more active cats that possessed toys and were viewed at heart level were more likely to impress the potential adopter and exist adopted. Chocolate-brown et al. [10] conducted a study evaluating the influence of historic period, breed, color, and coat pattern on the length of stay for cats in a no-kill shelter. The authors concluded that while color did not influence the length of stay for kittens, whereas gender, glaze patterning, and breed were significant predictors for both cats and kittens.

Machine learning

Machine learning is one possible tool that tin exist used to identify risk factors for creature adoption and predict the length of stay for animals in shelters. Auto learning is the ability to program computers to learn and improve all by itself using training experience [11]. The goal of motorcar learning is to develop a system to analyze big data, quickly deliver accurate and repeatable results, and to adapt to new information independently. A organization can be trained to make accurate predictions by learning from examples of desired input-output information. More specifically, machine learning algorithms are utilized to detect classification and prediction patterns from big data and to develop models to predict future outcomes [12]. These patterns evidence the human relationship between the aspect variables (input) and target variables (output) [thirteen].

Widely used information mining tasks include supervised learning, unsupervised learning, and reinforcement learning [14]. Unsupervised learning involves the use of unlabeled datasets to railroad train a system for finding hidden patterns inside the data [15]. Clustering is an example of unsupervised learning. Reinforcement learning is where a system is trained through direct interaction with the environs by trial and mistake [fifteen]. Supervised learning encompasses classification and prediction using labeled datasets [fifteen]. These classification and regression algorithms are used to classify the output variable with a discrete label or predict the outcome as a continuous or numerical value. Traditional algorithms such as neural networks, determination trees, and logistic regression typically utilise supervised learning. Effigy 1 provides a pictorial of the steps for developing and testing a predictive model.

Fig. ane

Pictorial Representation of Developing a Predictive Model

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Contributions to the literature

Although prior studies have investigated the touch on of several factors, such as age and gender, on the length of stay, they focus on a single shelter, rather than multiple organizations, as in this study. The goal of this study is to investigate the length of stay of animals at shelters and the factors influencing the charge per unit of animal adoption. The overall goal is to increment adoption rates of pets in creature shelters by utilizing several factors to predict the length of stay. Machine learning algorithms are used to predict the length of stay of each animal based on numerous factors (such as breed, size, and color). We address several objectives in this study that are listed below.

1. i.

   Place take a chance factors associated with adoption rate and length of stay

2. 2.

   Utilize the identified risk factors from collected data to develop predictive models

3. three.

   Compare statistical models to decide the best model for length of stay prediction

Results

Exploratory Data results

From Fig. 2, it is evident that the return of dogs is the highest result type at 43.3%, while Fig. 3 shows that the adoption of cats is the highest effect blazon at 46.i%. Both figures illustrate that the euthanization of both cats and dogs is still prevalent (~ twenty%). The results from Table 1 demonstrate that the longest time spent in the shelter is at 355 days by a male person cat that is adopted and a female dog that is euthanized. Observing the results, adoption has the lowest variance among all fauna types compared to the other outcome types. Adopted male cats have the everyman variance for days spent in the shelter, followed by female person dogs. Female cats that are returned have the highest variance for days spent in the shelter.

Fig. two

Distribution of Outcome Types for Dogs

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Fig. 3

Distribution of Result Types for Cats

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Tabular array ane Data Summary

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Figure iv shows a comparison of cats and dogs for the iii different outcome types. It is observed from the data that there are more dogs returned than cats. From Fig. 5, it is observed that the number of days a dog stays in the shelter decreases as the age increases. This is non expected, as it is predicted that the number of days in a shelter would be lower for younger dogs and puppies. This ascertainment could exist due to having more information points for younger dogs.

Fig. 4

Comparison of Outcome Types for Cats and Dogs

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Fig. 5

Historic period vs. Days in Shelter for Cats and Dogs

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Auto learning results

Examining Table 2, it is clear that the about proficient predictive model is developed past the gradient boosting algorithm for this dataset, followed by the random forest algorithm. The logistic regression algorithm appears to perform the worst with depression precision, recall, and F1 score performance metrics for all categories of length of stay. For the prediction of depression length of stay in a shelter, the random forest algorithm is the best performing model in comparing to the others at around 64–70% performance for precision, recall, and F1 score. The ANN algorithm is found to be the best when evaluating the precision and F1 score for medium length of stay, while the random forest algorithm is amend for assessing recall. However, the performance of these models in predicting the medium length of stay for the given dataset is depression for all iii-performance metrics. The gradient boosting algorithm performs the best when predicting the high length of stay. Finally, the gradient boosting and random wood algorithms perform well when predicting the very high length of stay at effectually 70–80%.

Tabular array 2 Consolidated Results

Full size table

Results from Table 2 besides demonstrate that the model adult from the slope boosting algorithm has a higher performance when predicting the high length of stay that leads to adoption, and when the result is euthanization. Evaluating the average of all three-performance metrics for all algorithms, the gradient boosting is the most proficient model at about 60%, while logistic regression appears to be the worst. Table two as well provides the computational time for each motorcar learning algorithm. For the given dataset, logistic regression runs the fastest at nine.41 southward, followed by slope boosting, bogus neural network, and finally, random forest running the longest. The gap in the performance measure (pm) is calculated by \( \frac{p{chiliad}_{all-time}-p{m}_{worst}}{p{m}_{all-time}} \), and is nearly 34, 39, and 32% for precision, retrieve, and F1 score, respectively.

Table 3 provides information on the elevation features or factors from each machine learning algorithm. Observing the tabular array, we notice that age (senior, super senior, and puppy), size (large and pocket-size), and color (multicolor) has a significant impact or influence on the length of stay. Specifically, we detect that older-aged animals (senior and/or super senior) appear equally a significant factor for every algorithm. For the artificial neural network, older age is the #2 and #iii predictor, and super senior is the #2 predictor for the gradient boosting algorithm. Large and small-sized animals are also observed to be important features, as both are shown as the #1 predictor in the gradient boosting and ANN algorithms. The results also demonstrate that gender, animal type, other colors besides multicolor, middle age, and medium-sized animals did not significantly bear on the length of stay.

Table three Top Three Features using Different Machine Learning Algorithms

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Discussion

Results from our study provided information on what factors are meaning in influencing length of stay. Brown et al. [10] conducted research that found that historic period, brood designation, coat color, and coat pattern influenced the length of stay for cats in animate being shelters. Similar to these studies, observations from our study also advise that age and color accept a significant impact or influence on the length of stay.

Determining which algorithm will develop the best model for the given set of information is critical to predict the length of stay and minimize the chances of euthanization. The goal of predictive analytics is to develop a model that best approximates the true mapping function for the human relationship betwixt the input and output variables. To approximate this function, parametric or non-parametric algorithms tin can be used. Parametric algorithms simplify the unknown function to a known form. Non-parametric algorithms exercise not make assumptions about the construction of the mapping function, allowing gratuitous learning of whatever functional grade. In this study, we utilize both parametric (logistic regression and artificial neural network) and non-parametric (random wood and gradient boosting) algorithms on the given information. Observing the results from Tabular array 2, the gradient boosting and random forest (non-parametric algorithms) perform the best on the dataset. It is observed from the results that using a not-parametric arroyo leads to a better approximation of the truthful mapping function for the given records. These results also support prior studies on parametric versus non-parametric methods. Neely et al. [16] detailed the theoretical superiority of not-parametric algorithms for detecting pharmacokinetic and pharmacodynamic subgroups in a written report population. The author suggests this superiority comes from the lack of assumptions made well-nigh the distribution of parameter values in a dataset. Bissantz et al. [17] discussed a resampling algorithm that evaluates the deviations between parametric and non-parametric methods to exist noise or systematic by comparing parametric models to a non-parametric "supermodel". Results demonstrate the non-parametric model to be significantly better. The use of algorithms that do not approximate the truthful function of the relationship betwixt input and output provides better performance results for this application equally well.

Current literature also supports the employ of ensemble methods to increase prediction accuracy and operation. Dietterich [xviii] discussed the ongoing inquiry into developing good ensemble methods as well as the discovery that ensemble algorithms are often more authentic than individual algorithms that are used to create them. Pandey, and Due south, T [xix]. conducted a study to compare the accuracy of ensemble methodology on predicting pupil academic operation every bit research has demonstrated better results for blended models over a single model. This study applied ensemble techniques on learning algorithms (AdaBoost, Random Forest, Rotation Forest, and Bagging). For our study with the given records, the results support this merits. Both the gradient boosting and random forest algorithms are ensemble algorithms and performed the best on the animal shelter data.

Results from Table two demonstrate the best operation of the gradient boosting and random forest algorithm when the length of stay was classified as very high or the brute was euthanized. This is beneficial as the models can predict long stays where the result is euthanasia. This tin lead to shelters identifying at-take chances animals and implementing methods and solutions to ensure their adoption. These potential methods are the second phase of this research study, which volition involve relocating animals to shelters where they volition more likely exist adopted. This phase is discussed in the future directions section.

Studies have been conducted evaluating euthanasia-related stress on workers (e.m., [1]). In other words, overpopulation not merely leads to euthanasia but tin can, in turn, cause mental and emotional bug for the workers. For example, Reeve et al. [20] evaluated the strain related to euthanasia among animal workers. Results demonstrated that euthanasia related strain was prevalent, and an increment in substance abuse, job stress, work causing family disharmonize, complaints, and low chore satisfaction was observed. Predicting the length of stay for animals will aid in them being more than probable to be adopted and will pb to fewer animals being euthanized, adding value not only to animals finding a dwelling house but also less stress on the workers.

The arroyo developed in this newspaper could exist beneficial non simply to reduce euthanasia only too to reduce overcrowding in shelters operated in countries where euthanasia of healthy animals is illegal, and all animals must be housed in shelters until adoption (or natural decease). It is essential to develop an information organization for a collaborative animal shelter network in which the entities tin can coordinate with each other, exchanging data about the animate being inventory. Another benefit of this written report is that it investigates applying machine learning to the animal care domain. Previous studies have looked into what factors influence the length of stay; however, this study utilizes these factors in addition to classification algorithms to predict how long an creature will stay in the shelter. Moreover, the use of a prescriptive analytics approach is discussed in this newspaper, where the predictions fabricated by the car learning algorithms will be used forth with a goal programming model to determine in what shelter is an animal almost likely to be adopted.

Limitations of this study include lack of behavioral data, limited sample size, and the use of simple algorithms. The outset limitation, lack of behavioral data of the animal during intake and result, would be beneficial to develop a more comprehensive model. Though behavioral bug are harder to solve, having data would provide insight into how long these animals with behavioral problems are staying in shelters and what the outcome is. Studies accept shown that behavioral issues play a pregnant role in preventing bonding betwixt owners and their animals and one of the most common reasons cited for animate being surrender [21, 22]. These behavioral problems tin include poor manners, too much energy, aggression, and devastation of the household. Dogs surrendered to shelters because of behavioral bug have also been shown to be less likely to be adopted or rehomed, and the ones that are adopted are more probable to be returned [21]. Studies take besides been conducted to evaluate the consequence of the length of time on the behavior of dogs in rescue shelters [23,24,25]. Most of them ended that ecology factors led to changes in the behavior of dogs and that a prolonged period in a shelter may lead to unattractive beliefs of dogs to potential owners. Acquiring data on behavioral problems gives more than data for the algorithm to larn when developing the predictive model. This allows more in-depth predictions to be made on how long an animal will stay in a shelter, which could also assistance in adoption. This approach can be used to shorten the length of stay, which makes sure that healthy animals are not developing behavioral issues in the shelters. It is not only crucial for the creature to be adopted, but also that the adoption is a practiced fit between possessor and pet. Shortening the length of stay would also lessen the chance that the animal will be returned past the adopter because of behavior. Having this information volition also allow shelters to observe other shelters close by where animals with behavioral issues are more likely to be adopted. To overcome this limitation of the lack of data on behavioral bug, behavioral problems volition exist used equally a factor and will be specifically asked for when acquiring data from shelters.

Another limitation includes collecting more data from animal shelters across the U.s.a., allowing for more than representative data to exist collected and inputted into these algorithms. However, this presents a challenge due to most shelters beingness underfunded and low on staff. Though we reached out to shelters, most replied that they lacked the resources and staff to provide the information needed. Future work would include applying for funding to provide a stipend to staff for their assistance in gathering the data from respective shelters. With more than data, the algorithm has more information to learn on, which could improve the performance metrics of the predictive models developed. There may likewise exist other factors that testify to be significant as more than data is collected.

Finally, the final limitation is the apply of simpler algorithms. This study considers bones ML algorithms. However, in recent years, there has been development in the ML field of more complex networks. For example, Zhong et al. [26] proposed a novel reinforcement learning method to select neural blocks and develop deep learning networks. Results demonstrated loftier efficiency in comparison to most of the previous deep network search approaches. Though only iv algorithms were considered, future piece of work would investigate deep learning networks, besides as bagging algorithms. Using more complex algorithms could ensure that if intricate patterns in the data are present, the algorithm can learn them.

Future direction

Phase 2: goal programming approach for making relocation decisions

Using the information gathered in this study, nosotros can predict the type of animals that are beingness adopted the most in each region and during each flavor of the year. To achieve this, we utilize a two-stage arroyo. The first phase was leveraging the machine learning algorithms to predict the length of stay of each animal based on numerous factors (such as breed, size, and color). Phase-2 involves determining the best shelter to ship adoptable animals to increase the adoption rates, based on several conflicting criteria. This benchmark includes predicted length of stay from phase-i, the distance between where the animal is currently housed and the potential animal shelters, transportation costs, and transportation fourth dimension. Therefore, our goal is to increase adoption rates of pets in animal shelters by utilizing several factors to predict the length of stay, as well as determine the optimal animal shelter location where the animate being will take the least amount stay in a shelter and near likely exist adopted.

After predicting the length of stay of an incoming brute that is currently housed in the shelter l ^′ using the motorcar learning algorithms, the next stage is to evaluate the potential relocation options for that animal. This strategic decision is specifically essential if the length of stay of the brute at its current location is high/very loftier. Nonetheless, while making this relocation conclusion, information technology is also necessary to consider the cost of transporting the creature between the shelters. For example, if a dog is brought into a shelter in Houston, Texas, and is estimated to have a high/very high length of stay. Suppose if the dog is predicted to have a low length of stay at New York City and a medium length of stay at Oklahoma City, then a tradeoff has to be fabricated between the relocation toll and the adoption speed. The objectives, length of stay, and relocation costs are conflicting and have to be minimized. Phase-2 attempts to yield a compromise solution that establishes a trade-off between these two criteria.

Goal programming (GP) is a widely used arroyo to solve problems involving multiple alien criteria. Under this method, each objective function is assigned every bit a goal, and a target value is specified for the individual benchmark [27]. These target numbers tin can be fulfilled past the model with certain deviations, while the objective of the GP model is to minimize these deviations. Pertaining to this report, the desired values for the length of stay and relocation price is pre-specified in the model and can be fulfilled with deviations. The GP model attempts to minimize these deviations. Thus, this technique attempts to produce a solution that is as close every bit possible to the targets, and the model solutions are referred to as the "most preferred solution" by prior studies (due east.thou., [28, 29]).

Equally mentioned earlier, the primary task to be completed using this phase-two goal programming approach is the relocation decisions considering the adoption speed and the cost of transporting the animal from the current location.

Model notations

Sets and Indices:
l∈50	Set up of shelter locations
Parameters:
l ′	Index for shelter location that is currently hosting the incoming animal
s	Size of the brute (minor, medium, and large)
y	Type of beast (domestic dog, cat, etc.)
e l	Length of stay of the animate being at shelter l. e l is categorical and is obtained from the output of Stage-i.
\( {r}_{fifty^{\prime number },l} \)	Relocation cost if the animal is transported betwixt shelters fifty ′ (that is currently hosting the animal) and l
t l, y, s	Remaining housing units available for animal blazon y of size s at shelter l. Typically shelters are designed such that in that location is a fixed number of rooms for each animal's size and type.
u LS	Upper bound on the length of stay
u RC	Upper spring on the relocation cost
Goal Parameters:
p s	Desired value for the preferred length of stay
p r	Desired value for the preferred relocation price
Variables:
X 50	if the incoming animal is assigned to shelter l
	0 otherwise
\( {d}_g^{-} \)	Negative divergence variable for goal g
\( {d}_g^{+} \)	Positive divergence variable for goal g

Goal programming model formulation

Goal constraints

Objective 1: Minimize the overall length of stay of the animal under consideration (Eq. 1).

$$ \operatorname{Minimize}\kern0.50em {LS}^O={\sum}_{50=1}^Fifty{e}_l{X}_l $$

(1)

Goal constraint for objective 1: The respective goal constraint of objective ii is given using Equation [30].

$$ {\sum}_{50=one}^L{due east}_l{X}_l+{d}_1^{-}-{d}_1^{+}={p}^s $$

(2)

Objective two: Minimize the overall relocation cost for transporting the animal nether consideration (Eq. iii).

$$ \operatorname{Minimize}\ {\mathrm{RC}}^O={\sum}_{\begin{array}{l}l=1\\ {}fifty\ne l\hbox{'}\end{array}}^L{r}_{50\hbox{'},l}{Ten}_l $$

(3)

Goal constraint for objective 2: The respective goal constraint of objective two is given using Equation [eighteen].

$$ {\sum}_{\begin{array}{c}l=1\\ {}l\ne {50}^{\prime}\end{array}}^L{r}_{l^{\prime },l}{X}_l+{d}_2^{-}-{d}_2^{+}={p}^r $$

(iv)

Hard constraints

Equation [9] ensures that the animal tin can exist assigned to merely 1 shelter.

$$ {\sum}_{l=1}^L{X}_l=1 $$

(5)

The animal can exist accommodated in shelter l only if there are a shelter capacity and type for that detail creature size category, and this is guaranteed using constraint [31]. It is important to notation that both y and south are input parameters, whereas fifty is the set of shelters.

$$ {X}_l\le {t}_{l,y,due south}\kern2.4em \forall fifty $$

(6)

Equation [21] sets an upper limit on the length of stay category if the shelter l is assigned as the destination location. This prevents relocating animals to a shelter that might potentially have a high or very loftier length of stay.

$$ {e}_l\times {Ten}_l\le {u}^{LS}\kern2.52em \forall l $$

(7)

Similarly, Equation [32] sets an upper limit on the relocation cost, if the shelter l is assigned as the destination location. This prevents relocating animals to a very far location. The current shelter location, l ^′, that is hosting the brute is an input parameter.

$$ {r}_{l\hbox{'}l}\times {X}_l\le {u}^{RC}\kern2.4em \forall l $$

(8)

Objective function

Since the current problem focuses on minimizing the expected length of stay and relocation price, the objective part of the goal programming approach is to reduce the sum of the weighted positive deviations given in Equations ([xviii, 30], as shown in Equation [6].

$$ \operatorname{Minimize}\ \mathrm{Z}={\mathrm{w}}_1{d_1}^{+}+{w}_2{d_2}^{+} $$

(9)

where w _chiliad is the weight assigned for each goal g.

It is necessary to scale the deviation (since the objectives accept different magnitudes too as units) to avert a biased solution.

If the scaling factors are represented by f _g for goal g, then the scaled objective function is given in Equation [14].

$$ \operatorname{Minimize}\ \mathrm{Z}=\frac{w_1\times {d}_1^{+}}{f_1}+\frac{w_2\times {d}_2^{+}}{f_2} $$

(10)

Using this goal programming approach, the potential relocation options are evaluated considering the length of stay from phase-ane. This phase-two goal programming approach is useful, specially if the length of stay of the beast at its current location is loftier/very high, and a merchandise-off has to be fabricated between relocation cost and length of stay. Phase-2 acts as a recommendation tool for assisting administrators with relocation decisions.

Determination

Most 3–iv million animals are euthanized out of the half dozen–8 million animals that enter shelters annually. The overall objective of this study is to increment the adoption rates of animals entering shelters past using key factors plant in the literature to predict the length of stay. The second phase determines the all-time shelter location to transport animals using the goal programming arroyo to make relocation decisions. To achieve this objective, first, the information is acquired from online sources as well as from numerous shelters beyond the United States. Once the data is caused and cleaned, predictive models are developed using logistic regression, bogus neural network, gradient boosting, and random forest. The operation of these models is adamant using three operation metrics: precision, call back, and F1 score.

The results demonstrate that the gradient boosting algorithm performed the best overall, with the highest precision, remember, and F1 score. Followed closely in 2d is the random forest algorithm, then the artificial neural network, and then finally, the logistic regression algorithm is the worst performer. Nosotros also observed from the data that the gradient boosting performed better when predicting the high or very loftier length of stay. Further observing the results, it is found that historic period for dogs (e.chiliad., puppy, super senior), multicolor, and big and small size are important predictor variables.

The findings from this study can be utilized to predict how long an fauna will stay in a shelter, likewise as minimize their length of stay and run a risk of euthanization by determining which shelter location will near likely lead to the adoption of that fauna. For future studies, nosotros will implement phase 2, which will determine the best shelter location to transport animals using the goal programming arroyo to brand relocation decisions.

Methods

Information description

A literature review is conducted to determine the factors that might potentially influence the length of stay for animals in shelters. These factors include gender, breed, age, and several other variables that are listed in Table 4. These features volition be treated as input variables for the machine learning algorithms. Overall, there are eight input or predictor variables and one output variable, which is the length of stay.

Table 4 Factor Description

Full size table

Animal shelter intake and outcome data are publicly made available by several land/city governments on their website (e.g., [33, 34]), specifically in several southern and south-western states. These online sources provide datasets for beast shelters from Kentucky (150,843 data rows), California (334,016), Texas (155,115), and Indiana (4132). Since in that location is no nationwide database for animal shelters, information is also collected through individual animal shelters that conduct euthanization of animals. We contacted over 100 fauna shelters across the United states of america and inquired for data on the factors mentioned in Table 4. Nosotros received responses from xx of the animal shelters that were contacted. Almost responses received stated there was non enough staff or resource to be able to provide this information. From the responses that were received back, just four shelters were able to provide any information. Of those four, only 2 of the datasets contained the factors and information needed, which are Colorado (8488 data rows) and Arizona (four, 667 data rows).

The data that is collected from the database and creature shelters included data such equally animal type, intake and outcome date, gender, color, breed, and intake and outcome status (behavior of animate being entering the shelter and beliefs of animal at outcome blazon). These records as well included information on several types of animals, such as dogs, cats, birds, rabbits, and lizards. For this study, the focus is on dogs and cats. Afterward filtering through these records, we found that merely California, Kentucky, Colorado, Arizona, and Indiana had all of the factors needed for the report. Upon downloading data from the database and receiving data from the animal shelters, the acquired data underwent data integration, information transformation, and data cleaning (as detailed in Fig. 1). Later data pre-processing, there are over 113,000 animal records.

Data cleaning methods

Next, data cleaning methods are utilized to notice discrepancies in the data, such as missing values, erroneous data, and inconsistencies. Information cleaning is an essential stride for obtaining unbiased results [35, 36]. In other words, identifying and cleaning erroneous information must be performed before inputting the data into the algorithm every bit it can significantly touch on the output results.

The following is a list of commonly used data cleaning techniques in the literature [11]:

• Exchange with Median: Missing or incorrect information are replaced with the median value for that predictor variable.

• Substitution with a Unique Value: Erroneous data are replaced with a value that does not autumn within the range that the input variables can have (e.g., a negative number)

• Discard Variable and Substitute with a Median: When an input variable has a significant number of missing values, these values are removed from the dataset, and the features that remain with missing or erroneous values are replaced with the median.

• Discard Variable and Substitute with a Unique Value: Input variables with a significant number of missing values are removed from the dataset, and the features that remain with missing or erroneous values are coded equally − 1.

• Remove Incomplete Rows Entirely: Incomplete Rows are removed from the dataset.

Data preprocessing

Some animate being breeds are listed in multiple formats and are inverse to maintain uniformity. An case of this is a Russian Blue cat, which is formatted in several ways such as "Russian", "Russian Blueish", and "RUSSIAN Bluish". Animals with multiple breeds such as "Shih Tzu/mix" or "Shih Tzu/Yorkshire Terr" are classified as the outset breed listed. Other uncommon breeds are classified equally "other" for simplicity. Finally, all animate being breeds are summarized into three categories (small, medium, or big) using the American Kennel Clubs' brood size classification [37]. Role of the data cleansing procedure also includes categorizing multiple colors establish throughout the sample size into five singled-out color categories (brown, black, blueish, white, and multicolor). We classified age into five categories for dogs and cats (puppy or kitten, boyish, adult, senior, super senior). The puppy or kitten category includes data points 0–one yr, adolescence includes information points 2–3 years one-time, adulthood includes animals 4–7 years of age, and senior animals are 8–10 years of age. Whatsoever animate being that is older than 10 years are categorized as a super senior, based on the recommendations provided in Wapiti Labs [38].

As mentioned previously, the output variable is the length of stay and is classified as depression, medium, high, and very high/euthanization. The length of stay is calculated by taking the difference between the intake date and issue engagement. To remove erroneous information entries and special cases, the number of days in the animal shelter is also capped at a yr. The "low" category represents animals that are returned (in which case, they are assigned the days in the shelter as 0) or spent less than 8 days before getting adopted. It is important to go on these animals at the shelter and then that the owner may notice them or they are transferred to their new homes. Animals that stayed in a shelter for 9–42 days and are adopted are categorized as "medium" length of stay. The "high" category is given to animals that stayed in the shelter for 43–365 days. Finally, animals that are euthanized are categorized as "very high".

After integrating all data points from each animal shelter, the sample size includes 119,691 records. Afterwards the evaluation of these information points, 5436 samples are found to have miscellaneous (such every bit a negative length of stay) or missing values. After applying data cleaning techniques, the final cleaned dataset includes 114,256 data points, with 50,466 cat- and 63,790 dog-records.

Auto learning algorithms to predict the length of stay

The preprocessed records are and then separated into grooming and testing datasets based on the type of classification algorithm used. Studies accept demonstrated the need for testing and comparing car learning algorithms, as the performance of the models depends on the awarding. While an algorithm may develop a predictive model that performs well in 1 application, it may non exist the best performing model for another. A comparing between the statistical models is conducted to determine the overall best performing model. In this department, we provide a description equally well as the advantages of each classification algorithm that is utilized in this written report.

Logistic regression

Logistic regression (LR) is a machine learning algorithm that is used to empathize the probability of the occurrence of an effect [39]. It is typically used when the model output variable is binary or categorical (see Fig. 6), unlike linear regression, where the dependent variable is numeric [xl]. Logistic regression involves the use of a logistic function, referred to as a "sigmoid function" that takes a existent-valued number and maps it into a value between 0 and i [41]. The probability that the length of stay of the animal at a specific location will be low, medium, high, or very high, is computed using the input features discussed in Table 4.

Fig. six

Pictorial Representation of the Logistic Regression Algorithm

Total size prototype

The linear predictor function to predict the probability that the creature in tape i has a low, medium, high, and very loftier length of stay categories is given by Equations (eleven) –[3], respectively.

$$ f\left( depression,i\right)={\beta}_{0,\mathrm{depression}}+{\beta}_{\mathrm{type},\mathrm{low}}{x}_{\mathrm{type},\mathrm{i}}+{\beta}_{\mathrm{breed},\mathrm{low}}{ten}_{\mathrm{breed},\mathrm{i}}+\dots $$

(11)

$$ f\left( med,i\right)={\beta}_{0,\mathrm{med}}+{\beta}_{\mathrm{type},\mathrm{med}}{10}_{\mathrm{type},\mathrm{i}}+{\beta}_{\mathrm{breed},\mathrm{med}}{10}_{\mathrm{breed},\mathrm{i}}+\dots $$

(12)

$$ f\left( high,i\right)={\beta}_{0,\mathrm{high}}+{\beta}_{\mathrm{type},\mathrm{high}}{x}_{\mathrm{blazon},\mathrm{i}}+{\beta}_{\mathrm{breed},\mathrm{high}}{x}_{\mathrm{breed},\mathrm{i}}+\dots $$

(13)

$$ f\left(5. high,i\right)={\beta}_{0,\mathrm{v}.\mathrm{high}}+{\beta}_{\mathrm{type},\mathrm{5}.\mathrm{high}}{ten}_{\mathrm{type},\mathrm{i}}+{\beta}_{\mathrm{breed},\mathrm{v}.\mathrm{high}}{x}_{\mathrm{breed},\mathrm{i}}+\dots $$

(xiv)

Where β _{v, fifty} is a set of multinomial logistic regression coefficients for variable v of the length of stay category fifty, and x _{v, i} is the input feature v corresponding to data observation i.

Artificial neural network

Bogus Neural Network (ANN) algorithms were inspired by the brain'south neuron, which transmits signals to other nerve cells [40, 42]. ANN's were designed to replicate the way humans learn and were developed to imitate the operational sequence in which the body sends signals in the nervous system [43]. In an ANN, in that location exists a network structure with directional links connecting multiple nodes or "artificial neurons". These neurons are information-processing units, and the ties that connect them represent the relationship between each of the connected neurons. Each ANN consists of three layers - the input layer, subconscious layer, and the output layer [32, 44]. The input layer is where each of the input variables is fed into the artificial neuron. The neuron volition commencement summate the sum of multiple inputs from the independent variables. Each of the connecting links (synapses) from these inputs has a characterized weight or strength that has a negative or positive value [32]. When new information is received, the synaptic weight changes, and learning will occur. The hidden layer learns the human relationship between the input and output variables, and a threshold value determines whether the artificial neuron will fire or pass the learned information to the output layer, every bit shown in Fig. 7. Finally, the output layer is where labels are given to the output value, and backpropagation is used to correct whatsoever errors.

Fig. vii

Pictorial Representation of the Artificial Neural Networks

Total size epitome

Random Forest

The Random Woods (RF) algorithm is a type of ensemble methodology that combines the results of multiple decision trees to create a new predictive model that is less likely to misclassify new information [30, 45]. Decision Copse accept a root node at the elevation of the tree that consists of the attribute that best classifies the training data. The aspect with the highest data gain (given in Eq. sixteen) is used to determine the best attribute at each level/node. The root node volition be split into more subnodes, which are categorized as a decision node or leaf node. A decision node can be divided into further subnodes, while a leaf node cannot be split further and volition provide the final classification or discrete label. RF algorithm uses mtree and ntry as the two main parameters in developing the multiple parallel conclusion trees. Mtree specifies how many trees to train in parallel, while ntry defines the number of independent variables or attributes to cull to split each node [30].. The majority voting from all parallel trees gives the final prediction, as given in Fig. eight.

$$ \mathrm{Entropy}=\sum \limits_i-{p}_i{\log}_2{p}_i $$

(15)

$$ \mathrm{Information}\ \mathrm{Gain}=\mathrm{Entropy}\ \left(\mathrm{parent}\correct)-\mathrm{Weighted}\ \mathrm{Boilerplate}\ \left[\mathrm{Entropy}\ \left(\mathrm{children}\right)\right] $$

(xvi)

Fig. 8

Pictorial Representation of the Random Woods Algorithm

Full size prototype

Slope boosting

Boosting is another type of ensemble method that combines the results from multiple predictive algorithms to develop a new model. While the RF approach is built solely on decision trees, boosting algorithms can utilize diverse algorithms such as conclusion trees, logistic regression, and neural networks. The primary goal of boosting algorithms is to convert weak learners into stronger ones by leveraging weighted averages to identify "weak classifiers" [31]. Samples are assigned an initial uniformed weight, and when incorrectly labeled by the algorithm, a penalization of an increment in weight is given [46]. On the other hand, samples that are correctly classified by the algorithm will decrease in weight. This procedure of re-weighing is washed until a weighted vote of weak classifiers is combined into a robust classifier that determines the final labels or nomenclature [46]. For our report, gradient boosting (GB) will exist used on decision trees for the given dataset, as illustrated in Fig. 9.

Fig. 9

Pictorial Representation of Boosting Algorithm

Full size image

Machine learning model parameters

The clean animal shelter data is split into ii datasets: preparation and testing data. These records are randomly placed in the two groups to train the algorithms and to exam the model adult by the algorithm. 80% of the data is used to railroad train the algorithm, while the other twenty% is used to exam the predictive model. To avoid overfitting, a tenfold cross-validation procedure is used on the training data. There are no parameters associated with the machine learning of logistic regression algorithms. However, a grid search method is used to tune the parameters of the random forest, gradient boosting, and artificial neural network algorithms. This allows the all-time parameter in a specific set up to be chosen by running an in-depth search by the user during the preparation menstruation.

The number of copse in the random forest and gradient boosting algorithms is changed from 100 to k in increments of 100. A learning rate of 0.01, 0.05, and 0.10 is used based on the recommendations of previous studies [47]. The minimum observations for the trees' terminal node are prepare to vary from two to 10 in increments of one, while the splitting of copse varies from 2 to ten in increments of two. A feed-forrad method is used to develop the predictive model using the artificial neural network algorithm. The feed-forward algorithm consists of 3 layers (input, hidden, output) as well every bit backpropagation learning. The independent and dependent variables represent the input and output layers. Since the input and output layers are already known, an optimal betoken is reached for the number of nodes when between 1 and the number of predictors. This means that for our written report, the nodes of the subconscious layer vary from 1 to 8. The learning rate values used to train the ANN are 0.01, 0.05, and 0.10.

To find the optimal setting for each machine learning algorithm, a thorough search of their corresponding parameter infinite is performed.

Functioning measures

In this report, nosotros use three performance measures to evaluate the ability of car learning algorithms in developing the best predictive model for the intended application. The measures considered are precision, F1 score, and sensitivity/recall to decide the best model given the inputted information samples. Table 5 provides a defoliation matrix to define the terms used for all possible outcomes.

Table v Defoliation Matrix

Total size tabular array

Precision evaluates the number of correct, true positive predictions by the algorithm while all the same considering the incorrectly predicted positive when it should have been negative (Eq. 17). By having high precision, this means that in that location is a low rate of false positives or type I error. Sensitivity or recall evaluates the number of true positives that are correctly predicted by the algorithm while considering the incorrectly predicted negative when it should have been positive (Eq. eighteen). Recall is a skillful tool to use when the focus is on minimizing faux negatives (type II error). F1 score (shown in Eq. 19) evaluates both blazon I and type Two errors and assesses the ability of the model to resist false positives and false negatives. This performance metric evaluates the robustness (low number of missed classifications), every bit well as the number of data points that are classified correctly by the model.

$$ Precision=\frac{True\ Positive}{True\ Positive+ Simulated\ Positive\ } $$

(17)

$$ Sensitivity/ Recall=\frac{True\ Positive}{True\ Positive+ Simulated\ Negative\ } $$

(18)

$$ F1\ Score=\frac{2\left( True\ Positive\correct)}{2\left( True\ Positive\right)+ False\ Positive+ False\ Negative\ } $$

(xix)

Availability of information and materials

Most of the datasets used and/or analyzed during the current study were publicly available online equally open source data. The data were available in the website details given below:

https://information.bloomington.in.gov/dataset

https://data.louisvilleky.gov/dataset

https://data.sonomacounty.ca.gov/Government

We too obtained data from Sun Cities four Paws Rescue, Inc., and the Rifle Animal Shelter. No administrative permission was required to access the raw data from these shelters.

Abbreviations

LR:

Logistic Regression

ANN:

Artificial Neural Network

RF:

Random Forest

GB:

Slope Boosting

GP:

Goal Programming

CV:

Coefficient of Variation

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Acknowledgments

We would like to thank the Sunday Cities 4 Paws Rescue, Inc., and the Rifle Fauna Shelter for providing the length of stay reports in order to complete this study.

Funding

This research was not funded by whatsoever agency/grant.

Author information

Authors and Affiliations

1. Section of Bioengineering, Academy of Missouri Columbia, Columbia, MO, 65211, USA

   Janae Bradley

2. Department of Industrial and Manufacturing Systems Technology, University of Missouri Columbia, Columbia, MO, 65211, U.s.a.

   Suchithra Rajendran

3. Department of Marketing, University of Missouri Columbia, Columbia, MO, 65211, U.s.a.

   Suchithra Rajendran

Contributions

JB performed data mining, data cleaning and analyses of the animal shelter data and machine learning algorithms. JB was too a major contributor in writing the manuscript. SR performed data mining, cleaning, and analyses of the machine learning algorithms, also as the goal programming. All authors have read and canonical the final manuscript.

Corresponding writer

Correspondence to Suchithra Rajendran.

Ethics declarations

Ethics approving and consent to participate

Nearly of the datasets used in this study are open source and are publicly bachelor. The remaining data was collected from creature shelters with their consent to utilise the data for research purposes.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

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Bradley, J., Rajendran, S. Increasing adoption rates at animate being shelters: a two-phase arroyo to predict length of stay and optimal shelter allocation. BMC Vet Res 17, lxx (2021). https://doi.org/10.1186/s12917-020-02728-ii

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• Received: 07 January 2020

• Accepted: 22 December 2020

• Published: 05 February 2021

• DOI : https://doi.org/10.1186/s12917-020-02728-2

Keywords

• Brute shelter
• High euthanization rates
• Machine learning algorithms
• Prediction models
• Goal programming approach
• Determination support tool

Source: https://bmcvetres.biomedcentral.com/articles/10.1186/s12917-020-02728-2

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