Real-estate price prediction with deep neural network and principal component analysis

House price prediction based on existing real-estate data serves as fundamentals for property appraisal and real-estate market evaluation. The final sale price of a property is an important profitability determinant within an investment portfolio. Predicting the real-estate value allows individuals, companies and governments to effectively devise their financial plans. During the project feasibility stage, gauging the construction cost with the predicted sale price of a building directly influences the built/no built decision, which in turn determines the existence of a construction project. At the national level, the expected real-estate values have an impact on the associated contract, easements acquisition and pricing policies. An early estimate of the real-estate price value facilitates decision-making about its construction, purchase and/or regulation for real-estate owners, construction professionals and governments. Despite the importance of the topic for construction professionals and its stakeholders, it has not received adequate attention from the construction management field and it is mainly discussed by literature on real-estate price prediction within the real estate, finance, economy and business studies (Rafiei and Adeli 2016). While the real-estate price models within the literature have not been critically investigated (Li and Shi 2011), little attention has been paid to the price-prediction models that can be utilised over high-dimensional data-sets: data with several feature columns for explaining a limited number of records.

The real-estate price is influenced by a complex range of factors and thus a price predictor needs to incorporate this complexity in a computationally efficient manner (Khalafallah 2008; Park and Kwon Bae 2015; Chen et al. 2017; Hu et al. 2019; Ho et al. 2021). Thus, the existing literature implemented a variety of statistical and pattern recognition approaches over different real-estate pricing data with various features to simulate the influential factors that affect the final real-estate price value (Rafiei and Adeli 2016). Over the past decades, the machine learning (ML) approaches enhanced decision-making within different applications such as predicting identifying safe worker behaviour (Patel and Jha 2015), forecasting the variations in monthly material prices (Shiha et al. 2020) and predicting the house price values (Jiang and Shen 2019; Wang et al. 2019). The success of ML approaches within different fields encouraged the development of house price models that automatically extract the price information from different real-world datasets. To this end, artificial neural network (ANN), a widely used ML algorithm, is applied over a wide range of applications such as classification and language translation. However, a shortcoming of ANN is its difficulty in training the high-dimensional dataset (Awad and Khanna 2015).

A deep neural network (DNN) is a popular and strong extension of ANN that learns through a hierarchical procedure (Awad and Khanna 2015), and its performance is highly dependent on the quality and volume of the dataset. Even though the abundance of data improves the ML and subsequently DNN performance, still there are real-world cases where the dataset size is relatively small. Within this context, real-estate price valuation for developing cities restricts the study space to boundaries of that specific location and therefore limits the possible number of price-data records. These limited real-estate price records are often described within a high-dimensional feature space. Despite its wide application for price prediction, DNN adoption in real-estate applications is limited due to the mostly high-dimensionality and inaccessibility of big data. The high-dimensionality complicates the DNN training and decreases its price-prediction accuracy. In this respect, principal component analysis (PCA) is an unsupervised ML method that is used to reduce high-dimensionality within the dataset. The concept of PCA was invented by Pearson (1901) and further developed by Hotelling (1933). PCA projects the high-dimensional dataset into a lower subspace, where principal components are explained through a set of uncorrelated features (Ayesha et al. 2020). Accordingly, PCA extracts key features while retaining essential variance in the original feature attributes. This enables the identification and ranking of the influential features that improve the prediction accuracy of ML.

On the other hand, auto-encoders are projecting the dataset into the latent space for a better understanding of the dataset by the model. In this regard, PCA can also function similar to an auto-encoder for projecting the dataset into the lower-dimensional space (Reddy et al. 2020) and thence improves the DNN's understanding of a given high-dimensional dataset. Moreover, from applicational perspectives, both DNN and PCA are simple-to-implement algorithms, but despite this simplicity, their application over categorical construction and real-estate price data is not addressed by existing literature. This study demonstrates that the implementation of PCA after encoding enhances the model prediction ability. In other words, the PCA transformation of the high-dimensional real-estate dataset enhances the price-prediction accuracy of the DNN model. This study integrates PCA with DNN (PCA-DNN) to improve the prediction accuracy of real-estate sale prices. The PCA transforms the dataset into a new set of datasets with different feature columns, in which most of the variance is concentrated at the primary principal components.

This study's motivation for adopting PCA within a hybrid PCA-DNN model for real-estate price prediction is threefold: dimensionality reduction, feature selection and data transformation before processing in the DNN model. This study shows the efficiency of the PCA-DNN model over a hard-to-fit dataset, that is small-sized, high-dimensional and comprised of several categorical attributes. To this end, 1,244 real-world house price records were collected from the central area of Trabzon, Türkiye. The price records are described through categorical and numerical features, representing a general state of a data structure that can be found in a typical real-estate website in Türkiye.

To validate the developed model, its performance is benchmarked against a conventional DNN, and a stepwise regression analysis (SRA) combined with DNN (SRA-DNN) models. In addition, the number of trainable parameters associated with the number of layers and neurons is customised for each of the three models. Besides, these models were iterated for different loss optimisation and activation functions. Thus, the optimum network architecture (for each DNN, SRA-DNN and PCA-DNN models) was configured to enable comparison and evaluation amongst these models. Hence, the price-prediction performance of PCA-DNN model is compared with the benchmark models, using mean square error (MSE) (Pal 2017), mean absolute error (MAE) (Pal 2017) and mean absolute percentage error (MAPE) (Kim and Kim 2016) metrics. As a result, the PCA-DNN model developed in this study is useful for house price-prediction applications, where each real-estate unit price is described by a high-dimensional dataset.

The past research established the complexity of predicting the real-estate price value due to its influence from a wide range of influential determinates, such as inflation rate (Stukhart 1982; Poterba 1984; Qiao and Guo 2014), policy adjustment (Zheng and Yan 2017), environmental events (Yue et al. 2020), accessibility (Zhang et al. 2022) and urban (Zhang et al. 2022) and public transportation services (Wen et al. 2022). To date, several studies have explored artificial intelligence (AI) (Rafiei and Adeli 2016; Cao et al. 2018; Gondia et al. 2020) in a variety of construction and real-estate predictions applications. As a branch of AI, ML approaches were utilised over the real-estate dataset to evaluate the most influential house price determinates (Zhai et al. 2018; Zhang et al. 2020; Luo et al. 2021). In a recent study, the empirical house price data from China are operated with a Hedonic price model for the identification of influential price determinants (Luo et al. 2021). Furthermore, the real-estate price prediction was exercised by adopting different ML approaches such as multiple linear regression (Zhang 2021), ANNs (Khalafallah 2008; Claesen and De Moor 2015), multi-layer perceptron NN (MLP-NN) (Hu et al. 2019), Naive Bayes (NB) (Park and Kwon Bae 2015), decision trees (DTs) (Park and Kwon Bae 2015; Peng and Wang 2022), K-nearest neigh-bour (KNN) (Hu et al. 2019) and support vector machine (SVM) (Chen et al. 2017; Hu et al. 2019; Ho et al. 2021). The research has found that grouping the benefit of single ML approaches within a single predictor (ensemble model) facilitates the creation of a more robust predictor compared with the contributing single ML techniques. In this regard, real-estate price-prediction was experimented with mainly tree-based ensemble approaches such as random forest (RF) (Sanjar et al. 2020; Ho et al. 2021; Chen et al. 2022; Peng and Wang 2022), RF with extra trees (Hu et al. 2019), AdaBoosting (AB) (Park and Kwon Bae 2015), gradient boosting (GB) (Hu et al. 2019; Ho et al. 2021; Chen et al. 2022), and XGBoost (Abdul-Rahman et al. 2021).

With the increase in computational power, the ANN concept was extended to structure a stronger predictor known as DNN. Compared to ANN, DNN increases the number of hidden layers while using a backpropagation mechanism for hierarchically learning from the precedent layers (Awad and Khanna 2015). The adoption of DNN models for house price prediction has recently attracted researchers’ attention (Seya and Shiroi 2021), and applications of various DNN-based predictors were explored in the literature, such as convolutional neural network (CNN) (Piao et al. 2019) and long short-term memory (LSTM) (Kim et al. 2020). Seya and Shiroi (2021) showed that the prediction accuracy of DNN only improved when data size increased from order 4 (n = 10⁴) to order 5 (n = 10⁵), reaching a 90% MAPE value. However, their study is limited to medium-sized and large-sized datasets, and they have not investigated DNN application in the small-sized real-estate dataset. In this respect, this study challenges the use of a small-sized dataset with the order of 3 (n = 10³).

The small-sized real-estate price dataset can incorporate several price feature columns for explaining limited price records. While the increase in the number of price records enhances the prediction accuracy, the increase of influential feature columns reduces the price-prediction ability of the adopted ML approach. The addition of each price feature adds another dimension to the dataset, which complicates the learning of the machine (curse of dimensionality). The issue of high-dimensionality was addressed in literature by eliminating redundant and irrelevant features through various dimensionality reduction techniques (Ayesha et al. 2020): i.e., PCA, factor analysis, forward and backward stepwise regression and linear discriminant analysis (LDA). Reddy et al. (2020) identified PCA as a more effective dimensionality reduction method compared to LDA, when combined with the other ML algorithms, such as DT, SVM, NB and RF. In this regard, the existing studies in the broader literature exercised PCA for the identification and ranking of influential features as well as enhancing the prediction accuracy of ML (Wang and Zhang 2013; Zhan et al. 2021; Wen et al. 2022). However, in the context of real-estate and construction applications, there exists a comparatively small body of literature on AI methods incorporated with PCA. In this regard, the house price and construction dataset was processed using the PCA model combined with radial basis function network (RBFN) (Phan 2019; Xiao and Yan 2019), CNN (Piao et al. 2019), and RF (Piao et al. 2019). Furthermore, SVM and support vector regression (SVR) incorporated with PCA were effectively used within different fields of real-estate and construction applications. The improved performance achieved through the combination of PCA with SVM and SVR has also been well-established in the literature. Son et al., (2012) proposed a PCA-SVR model for cost prediction of commercial buildings, which enhances its performance, compared with the other four analysed data mining methods. All these works have acknowledged the vital role of PCA in dimensionality reduction and consequently the enhanced prediction accuracy of the accompanying algorithm. Despite its efficiency, the topic of the combined performance of PCA with ANN (PCA-ANN) on real-estate and construction was explored only in a few studies (Shi 2009; Xiao and Yan 2019). Shi (2009) used PCA to classify the price determinates for price prediction within the ANN structure. His results showed a good match between PCA-ANN prediction with price labels. Similarly, to predict house prices, Xiao and Yan (2019) combined PCA with RBFN, and their results showed high price-prediction accuracy. In this context, the prediction accuracy of DNN and dimensionality reduction of PCA on real-estate price data have not been addressed in the literature. Investigating the accuracy of the combined PCA-DNN model on the high-dimensional dataset still demands further research attention.

To fill in the gap aforementioned, this study purposes a PCA-DNN real-estate price-prediction model that can be utilised on high-dimensional real-estate datasets. Furthermore, the performance of the adopted PCA-DNN model is evaluated against the conventional DNN and SRA-DNN models, concerning both its dimensionality reduction ability and efficiency in handling the encoded categorical dataset. Thus, PCA is expected to improve the DNN model prediction by dimensionality reduction, dataset projection and transformation, and localisation of influential price features. This study includes five main stages: data collection using web scarping, pre-processing, feature engineering, network training and identification of the influential price features with the real-estate dataset (Figure 1).

Fig. 1

Fig. 2

At the network training stage (Figure 1), to structure the appropriate network architecture of each DNN, SRA-DNN and PCA-DNN models, they are iterated considering different combinations of neurons and layers along with various activation, loss and optimisation functions. This study evaluates both unsupervised and supervised learnings of the models.

Accurate real-estate price prediction is an important decision-making parameter for construction professionals. Despite the importance of the topic, the literature on construction management has not investigated the house price-prediction models for the use of construction professionals. One of the obstacles to using the existing house price predictors is the high-dimensionality of the real-world real-estate price dataset, which reduces the price-prediction accuracy of the adopted predictors. The existing literature on ML-based real-estate price prediction over the small-sized dataset has not reached a good prediction accuracy. This paper adopts PCA for dataset transformation, dimensionality reduction and localisation of the influential price features. The model performance is evaluated against benchmark DNN and SRA-DNN models. The PCA-DNN model significantly outperforms the DNN and SRA-DNN models, while exhibiting 90% accuracy with a good generalisation ability. The results suggest that the application of PCA not only reduces the high-dimensionality of the dataset but also enhances the quality of the encoded feature attributes. The observed improvement may be due to improved DNN learning through the utilisation of the transformed numerical and categorical price feature attributes in continuous numerical format.

The proposed PCA-DNN model proved to be efficient in managing the high-dimensional real-estate price dataset. Additionally, it was found that spatial features along with building age have the most influence in the determination of the total real-estate price. The adoption of the PCA-DNN model compensates for the reduced prediction accuracy due to the limited number of price records and the categorical nature of feature columns. The model is beneficial in real-estate and construction applications, where the absence of medium and big datasets decreases the price-prediction accuracy. Furthermore, the PCA utilised in this study works over the linear dataset, and the proposed study is yet to experiment with other real-estate datasets with different feature columns such as time-varying price and inflation features. Thus, it is recommended to conduct this study using the other variations of PCA, such as Kernel and robust PCA.