Clustering analysis for classifying fake real estate listings

Data preparation

Acquisition of data. The online Durian Property listing in Malaysia provided the dataset utilized in this study. The dataset consists of 12,916 property records in October 2021 such as demographic images, geographical data, and text data of properties with 28 attributes.

Preprocessing of data. The main goal of this approach is to adapt the dataset before the data mining tool and the clustering algorithms can utilize it. Four pre-processing methods are shown in Fig. 2: Attribute generation, data transformation, data cleaning, and attribute selection. A statistical review of the data found some attributes with missing values such as ‘NA’ and −1. Attributes such as title, facing, land_D1, land_D2, postcode, and views are classified as attributes without value (contain −1 value) and were eliminated from the dataset. Whereas 84 data with missing values for almost all attributes were removed from the dataset. However, some records with missing values were replaced with values obtained from other attributes such as the Desc attribute. The Desc attribute contains text data that contains a lot of unstructured information. In order to extract the necessary information, knowledge exploration must be performed. To replace the missing values in the Car_Park attribute, the data for each housing type or Property_Type was analyzed to determine the most common Car_Park value. For example, number 2 was included as the Car_Park value for the Terrace House property because the frequency value of Car_Park is 2 for the Terrace House. The same method was applied to the Bathroom and Bedroom attributes. Three attributes were also generated: Longitude, Latitude, and Expert_Label based on the Address and Description attribute. There are only 14 attributes remaining out of the entire 28 attributes. Numerical input and output variables are often required for most machine learning algorithms (Adewole et al., 2020; Eren et al., 2020; Motaleb et al., 2021; Kiruthiga, Kola Sujatha & Kannan, 2014). This implies that, before being input into the clustering and classification model, all attributes, including categories or nominal variables, must be converted into numeric variables. All of this is addressed through the data transformation procedure. Table 2 displays the transformation of each attribute with its description.

Models of machine learning have the ability to translate input variables into output variables. However, each variable may have a distinct domain data distribution and scale. It is possible for input variables to have multiple scales since they can have distinct units. Variations in the input variables’ scale may make the modelled problem more challenging. A model that is trained with huge input values (such as a range of hundreds or thousands of units) may learn large weighting values. Large weight models are frequently unstable, which makes them perform badly during learning and make them sensitive to input values, which increases the generalization error. Therefore, the Z transform or Standard Scaler techniques were used in the property list datasets to conduct normalization. To enable comparison, the standard scaler ensures that each attribute’s value falls within the same range. Every value in a data set is normalized using the Z transformation. In this case, the standard deviation is equal to one and the mean value of all values is equal to zero (Li et al., 2021). The following formula can be used to normalize each value in a data set using the z-transform: Eq. (1), where σ is the sample data’s standard deviation, µ is the sample mean, and x j is the sample j’s input value.

(1) $${\mathrm{x}}_{\mathrm{j}}={\displaystyle \frac{x_j-x_{min}}{x_{max}-x_{min}}}$$

Descriptive analysis. After the property listing dataset is converted to numerical data, Table 3 displays the descriptive analysis of the dataset. The two attributes that have the biggest standard deviations are Price (5,098,460.11) and Built_Up_SF (64,153,663.9). Other than these two, there is an obvious gap in the other attributes.

Feature selection. For the purpose of feature selection, a variance threshold applied to the dataset. Variance, a metric measuring the dispersion of data within a dataset, becomes crucial in ensuring the development of an unbiased clustering model that is not skewed toward specific attributes. The selection of attributes with significant variance is essential before proceeding to build a machine learning model. High variance indicates unique attribute values or high cardinality, while low-variance attributes have relatively similar values. Attributes with zero variance exhibit identical values. Additionally, low-variance attributes, clustering close to the mean value provide minimal clustering information (Li et al., 2021). The variance thresholding technique, which solely evaluates the input attribute (x) without considering data from the dependent attribute, is particularly suitable for unsupervised modeling (y). Table 4 displays the variance of all attributes in property listings. Following the recommendation of Gaurav (2019), a variance threshold value of 0.3 was set for attribute selection in this study to eliminate redundant features with low variance.

Upon examining the variance values for each attribute in Table 4, it is observed that all 14 attributes have variance values exceeding 0.3, indicating high behavioral patterns. All attributes’ variance values fall between 0.9999 or 1.000. Consequently, all attributes such as Built_Up_SF, Price, Bathroom, Furnishing, Bedroom, Tenure, Car_Park, Negeri, Property_Type, Latitude, Longitude, Occupancy, Unit_Type, and label are selected for use in the subsequent phase.

Proposed clustering methodology

Clustering analysis proves to be a valuable method within the realm of fraud detection as it uncovers groups or patterns within a dataset that could potentially signify fraudulent activities (Mohamed Nafuri et al., 2022). By grouping similar data points together, it becomes possible to identify anomalies and outliers, which might be indicative of suspicious transactions. Moreover, clustering analysis can play a pivotal role in labelling or categorizing data points for fraud detection purposes. After clusters have been established, labels can be assigned to these clusters based on recognized fraud patterns or prior instances of fraud. This procedure is commonly known as cluster labelling or cluster characterization.

The K-means algorithm is a widely chosen clustering technique due to its simplicity and easily interpretable results. It groups adjacent objects into a specified number of centroids, denoted as ‘k’. The Elbow Method is a popular approach for determining the optimal number of clusters in K-means. It involves calculating the within-cluster variance (inertia) for different values of k, forming a variance curve. The optimal cluster count is often identified at the curve’s initial turning point. As an alternative, the Silhouette analysis provides another way to evaluate clustering quality. This technique computes coefficients for each data point, measuring its similarity within its cluster compared to others. The silhouette coefficient ranges from [1, −1], with higher values indicating better alignment with the respective cluster.

Clustering model evaluation

In the phase of clustering analysis, the accuracy and quality of clustering results play a crucial role in determining the algorithm’s performance with the study’s input data. Clustering evaluation is a distinct process, conducted after the final clustering output is generated, emphasizing its standalone nature (Mohamed Nafuri et al., 2022). Two methods are commonly employed to measure clustering quality: internal validation and external validation.

Internal validation involves assessing clustering in comparison to the clustering results themselves, focusing on the relationships within the formed clusters. This approach proves to be realistic and efficient, especially when dealing with real estate datasets characterized by increasing sizes and dimensions.

This particular study utilized three prevalent internal validation methods: the Davies-Bouldin index, Silhouette coefficient index, and Calinski-Harabasz index. Mathematical notations for grouping assessment measurements include D for the input data set, n for the number of data points in D, g for the midpoint of the entire D data set, P for the dimension number of D, NC for the number of groups, C_i for the i-th group, n_i for the number of data points in C_i, C_i for the midpoint of the Ci group, and d(x,y) for the distance between points x and y (Prasetyadi, Nugroho & Putra, 2022).

The Davies-Bouldin (DB) metric, a longstanding and commonly employed method in internal validation measurements, utilizes intragroup variance and inter-group midpoint distance to identify the least favourable group pairs. Consequently, a decrease in the DB index value indicates the optimal number of groups. Equation (2) (Gaurav, 2019) defines the mathematical formula for the DB metric, highlighting its significance in assessing clustering quality.

(2) $$\mathrm{D}\mathrm{B}={\displaystyle \frac{1}{NC}{\sum }_i\underset{j\ne i}{max}{\displaystyle \frac{{\displaystyle \frac{1}{n_i}{\sum }_{x\in c_i}d\left(x,c_i\right)+{\sum }_{x\in c_j}d\left(x,c_j\right)}}{d\left(c_i,c_j\right)}}}$$

Index of Silhouette Coefficients. The Silhouette Coefficient Index assesses the quality and cohesion of a group. A high Silhouette Coefficient value signifies a superior model, indicating that an object is well-matched within its cluster and distinctly differs from adjacent clusters. Equation (3) outlines the calculation for the Silhouette Coefficient of an individual sample:

(3) $$\mathrm{s}={\displaystyle \frac{1}{NC}{\sum }_i\left({\displaystyle \frac{1}{n_i}\sum _{x\in C_i}{\displaystyle \frac{b\left(x\right)-a\left(x\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left[b\left(x\right),a\left(x\right)\right]}}}\right)}$$where $a\left(x\right)={\displaystyle \frac{1}{n_i}{\sum }_{y\in C_i,y\ne x}d\left(x,y\right)}$, and $b\left(x\right)=mi{n}_{j\ne i}\left[{\displaystyle \frac{1}{n_j}\sum _{y\in C_j}d\left(x,y\right)}\right]$

S ignores c_i and g and calculates the density a(x) using pairwise distances between all objects in the clusters. At the same time, b(x) calculates separation, which is the average distance between objects and alternative groupings or the nearest second group. The silhouette coefficient values in Eq. (2) can range between −1 and 1. The stronger the positive value of the coefficient, the more likely it is to be classified in the correct cluster. Elements with negative coefficient values, on the other hand, are more likely to be placed in the incorrect cluster (Mohamed Nafuri et al., 2022; Kumar Hemwati Nandan et al., 2020).

The Calinski-Harabasz (CH) index concurrently assesses two criteria by considering the average power-added result between two groups and the average yield of two plus forces in the group. In the formula, the numerator signifies the degree of separation, representing the extent to which the midpoint of the group is dispersed. Conversely, the denominator reflects density, illustrating how closely objects in the group gather around the midpoint. Equation (4) defines the mathematical formula for CH:

(4) $$CH={\displaystyle \frac{{\sum }_i{d}^2\left(c_i,g\right)/\left(NC-1\right)}{{\sum }_i{\sum }_{x\in C_i}{d}^2\left(x,c_i\right)/\left(n-NC\right)}}$$

Distance measurement

K-Min uses a distance-based measure to calculate the similarity value of each data point to the centroid. The minimum distance between the data points and the centroid is the most optimal value. Therefore, distance calculation plays a very important role in the clustering process (Prasetyadi, Nugroho & Putra, 2022). This technique is needed to determine how the data are related to each other and how they are different or similar to each other (Kumar Hemwati Nandan et al., 2020). This study uses three techniques to calculate the distance: Overlapping similarity technique, Camberra distance and Jaccard distance.

Overlapping Similarity, often known as the Jaccard similarity coefficient, calculates the degree of similarity between two sets based on the size of their intersection to the size of their union. It is primarily used to compare collections that include category or binary attributes (Arshad, Riaz & Jiao, 2019). The mathematical formula is defined as Eq. (5):

(5) $$O\left(A,B\right)=\left|A\cap B\right|/\mathrm{m}\mathrm{i}\mathrm{n}\left(\left|A\right|,\left|B\right|\right)$$

Camberra distance is a measure of dissimilarity between two vectors or sets of numerical values. It calculates the normalized sum of the absolute differences between the corresponding elements of the vectors. Camberra distance is sensitive to small differences and is suitable for data with a wide range of magnitudes. It is commonly used in multidimensional scaling and clustering algorithms (Rahman et al., 2021). The mathematical formula is defined as Eq. (6):

(6) $$D\left(A,B\right)=\sum \left(a_i-b_i\right)/\left(a_i+b_i\right)$$

Jaccard distance is a measure of dissimilarity between two sets based on the ratio of their difference to their union size. It complements the Jaccard similarity coefficient by quantifying dissimilarity rather than similarity. To perform an accurate cluster analysis, the properties of each approach must be matched to the research data set (Bahmani et al., 2015). Equation (7) defines the mathematical formula:

(7) $$J\left(A,B\right)=\left|A\cap B\right|/\left|A\cup B\right|$$

Optimum cluster value

This section shows the clustering results produced by using the proposed approach. The following is a guide to choosing the best group value based on a specific group evaluation matrix such as: A low Davies Bouldin index value, a Silhoutte coefficient index with a high positive value, and a Calinski Harabasz index with a high value indicate the achievement of optimal grouping. Table 5 summarizes the index value for clusters 2 to 9 based on several cluster evaluation techniques. Based on the index value in the table, it was found that cluster 2 is best for the Silhoutte and Calinski-Harabasz methods. While cluster 7 is for Davies Bouldin technique. However, cluster 2 is preferred because it was found to be the majority best in two of the three techniques performed.

Silhouette plots are further analyzed to determine the optimal group number. As seen in Fig. 3, the plots in the image clearly show that all clusters are above the average value line of the Silhouette coefficient. The Silhouette coefficient index value for group 2 is 0.2621 (referring to the red dotted line in the figure). Furthermore, there is no fluctuation in the Silhouette plot for cluster 2, and all clusters have positive score values, indicating that almost all data have been divided into the right clusters. As opposed to other cluster values (clusters 3, 4, and 5), there is a fluctuation in the Silhouette plot. Based on the analysis of the findings, it was found that the value of cluster 2 is the best for this study.

Optimum distance

Distance calculation plays an important role in the clustering process. This technique is needed to identify how the data are interrelated, and how the data are different or similar to each other (Alijamaat, Khalilian & Mustapha, 2010). This study uses three distance calculation techniques, namely the overlapping similarity technique, Camberra distance and Jaccard distance. Table 6 is the distribution of data in groups for each technique. It was found that the Camberra Distance measurement technique criteria can provide accurate analysis based on non-linear real estate data conditions and is concerned with the selection of appropriate features.

Visualization of the clustering results

The principal component analysis (PCA) method was used to reduce the dimension into a two dimensional space for further investigation (Abdulkareem et al., 2021). In this research, a PCA diagram was produced to visually provide clustering findings. Figure 4 illustrates three PCA plots based on different distance measurement techniques: (a) Camberra distance, (b) Jaccard distance, and (c) overlapping similarity. Data plots are colored in different colors based on clusters.

The inter-cluster separation technique based on Camberra distance is the best because the clusters are well separated from each other based on the differentiated color, followed by Jaccard distance and Overlap Similarity. Camberra distance’s preference is based on its ability to handle datasets with varying attribute scales, outliers, and sparsity while promoting effective cluster separation. Its behavior aligns with the characteristics of such datasets, making it a valuable choice for clustering analysis. The Overlapping Equation is the weakest because it cannot separate the data points well, resulting in significant overlap. The presence of noise makes the cluster representation less accurate.

Features extraction

Based on the results of cluster analysis in Table 7, two data clusters were formed, namely Cluster 1 and Cluster 2. The significant difference between these two clusters is in terms of price and built-up area. It was found that the real estate price and built-up area of Cluster 1 are above average with a value of MYR 1,327,898.39 and a built-up area of 1,052,509.797 square feet. The property price of Cluster 2 is below the average value of MYR 1,052,509.80 and has a built-up area of 1,465,592.197 square feet. The main distribution of property locations for these two clusters is around Selangor and Kuala Lumpur, namely 41% for cluster 1 and 31.8% for cluster 2. The frequency of distribution for both clusters is the same for the number of bedrooms which is 4, 3 for bathrooms and two for parking spaces. Most property types in both clusters are condominiums, apartments, and service apartments, accounting for 23.1% in Cluster 1 and 18% in Cluster 2. The type of real estate unit is intermediate land, representing 47.9% in Cluster 1 and 36.6% in Cluster 2. Real estate ownership is also freehold, comprising 33.3% in Cluster 1 and 28.2% in Cluster 2. Properties in both clusters are not fully furnished, with rates of 28% for Cluster 1 and 24% for Cluster 2. Additionally, the properties in both clusters are either ready for occupancy or not yet occupied, with percentages of 46.3% in Cluster 1 and 35.4% in Cluster 2. Figures 5A–5C show a bar chart of property listings by clusters for each attribute.

Class label

Based on the analysis carried out, it can be concluded that clustering has created a balanced two class labels: cluster 1 (not false) with 7,276 data and cluster 2 (false) with 5,540 data. This represents a significant enhancement, given that a balanced class of data not only contributes to improved model performance but also addresses issues related to bias, ensuring fair and accurate predictions across different classes. Table 8 displays the number and percentage of property listing data that has been divided by cluster. Most of the properties in both clusters are located in the states of Selangor and Kuala Lumpur. Therefore, the comparison of the property clusters can be done based on the characteristics of other properties. Properties from Cluster 1 have a higher price than the average market value and a smaller built-up area than the average. Even with prices higher than this average, the main type of properties offered are condominiums/apartments/serviced residences. The main type of property is the intermediate property with ownership status, not yet furnished and not yet occupied.

Unlike the properties in Cluster 2, the value of the offered property is low because the owner is offered an additional bonus, namely a built-up area larger than the average value for properties in this location. The main properties in Cluster 2 are also condominiums, apartments and serviced apartments with ownership status in intermediate forms. The properties are unfurnished and unoccupied. Overall, the properties from Cluster 2 are more profitable as they offer lower prices and more spacious constructions. The real estate units are also freehold and still unoccupied. However, these particular characteristics are likely a tactic to trap buyers. In addition, the percentage of non-faults for properties in this group is much lower than that for properties in Group 2. It is impossible for the seller to sell a valued well unit below the market price because the property is located in a state with a high population density and a high demand for real estate. Therefore, properties in this group of Cluster 2 are considered likely to be Fake.

Classification model on fake property’s listing

After labelling the clusters, we proceeded to conduct further analysis by comparing the data labelled using the K-means method with the data labelled by experts. This comparison was carried out through the utilization of two distinct classification models (Random Forest and Decision Tree). This analysis aimed to ascertain the K-means model’s ability to effectively distinguish between fake and genuine properties in contrast to the labels provided by experts. The results presented in Table 9 offer a detailed analysis of the performance of two classification models, namely Random Forest and Decision Tree, in the context of data labelled by experts and clusters as either fake or not fake. Notably, when we consider the accuracy metric, we observe that the Random Forest model exhibits a higher accuracy rate of 0.9618 for data labelled by clusters, surpassing its accuracy of 0.9446 for expert-labelled data. Similarly, the Decision Tree model also displays superior accuracy for data labelled by clusters (0.9571) as compared to expert-labelled data (0.9064). However, the key point of interest lies in the statistical significance of these differences, which was assessed through paired t-tests. The remarkably low p-values (p = 0.0001) in both cases indicate that the disparities in accuracy between the models are indeed statistically significant, suggesting that these variations are not due to random chance.

Based on the table, it was found that the precision (0.0435), recall (0.0083), and F1 score (0.0139) of the expert labeling data were very low for both models. This is due to the unbalanced expert labeling data. It turns out that the expert designation data set has a very unbalanced distribution of data between the fake (579) and non-fake (12,237) classes. This leads to a bias of the model towards the majority class and thus poor performance in the minority class (Qi & Luo, 2022). Traditional metrics such as precision and recall are inherently sensitive to class imbalance. If the model misclassifies minority class data, precision and recall will be affected (Arshad, Riaz & Jiao, 2019). However, clustering overcame the problem and was found to significantly increase the value of precision (0.9611) and recall (0.9488) as compared to before. Overfitting is not a concern for this dataset, as the accuracy, precision, recall, and F1-score values show no significant difference between the training and test datasets.

Attribute ranking

The impact of attributes on the cluster and expert labels classification model was analyzed using summary plots SHapley Additive explanations (SHAP). This helps to understand the impact of different attributes on the model predictions.

From the SHAP plot for the cluster labels in Fig. 6, the most important attributes that influence the classification model are ‘Bathrooms’, ‘Price’, ‘Built_Up_SF’ and ‘Car_Park’. Expert label, tenancy, occupancy, and condition are attributes that have less influence. The tendency of the attributes to make false and non-false predictions can also be analyzed by this plot. The observation results show that the attributes ‘Price’, ‘Built_Up_SF’, ‘Car_Park’, ‘Unit_Type’ and ‘Occupancy’ tend to make false predictions. The attributes that tend to have no false predictions are ‘Tenure’ and ‘Expert_Label’. Otherwise, ‘Bathrooms’, ‘Latitude’, and ‘Longitude’ tend to be neutral.

In the SHAP diagram for the expert dataset in Fig. 7, the most important attributes that influence the classification model are ‘Longitude’, ‘Latitude’, ‘Price’, ‘Bathroom’ and ‘Bedroom’. Attributes that have less influence are ‘Tenure’, ‘Unit_Type’, ‘State’ and ‘Built_Up_SF’. This plot can also analyze the tendency of attributes to make false and non-false predictions. The observation results show that the attributes ‘Bathroom’, ‘Bedroom’, ‘Property_Type’, ‘Unit_Type’, ‘Tenure’ and ‘Occupancy’ tend to make false predictions. The attributes that tend not to make false predictions are ‘Price’, ‘Built_Up_SF’ and ‘Car_Park’. In addition, latitude and longitude tend to be neutral.