Segmentation of E-Commerce Users on Cart Abandonment and Product Recommendation Using Double Transformer Residual Super-Resolution Networ

Initially,the e-commerce data gathered from a multicategory store [22]. Then, the data are provided to the pre-processing phase.

The pre-processing stage involves the application of FACF [23] to provide personalized items or content to users based on their preferences and behavior. Fair user embedding’s reached by attaching classifier f₁ to infer sensitive from user embedding’s. Likewise, item classifier f₂ to forecasts sensitive information hidden in items’ embedding. Assuming each items sensitive labels d, present FACF. Filter module is put in to user-items’ embedding utilizing classical CF method N. The filtered embedding space, forecasts that rating m^ol{{\hat m}_{ol}} of the user u for item l is intended in filtered embedding space n Equation(1) 1m^ol=HoRHl+qo+ql+α.{{\hat m}_{ol}} = H_o^R{H_l} + {q_o} + {q_l} + \alpha . where H_l denotes item l’s filtered item and predicted rating m^ol{{\hat m}_{ol}}of user o for item l intended in filtered embedding space. Dual adversarial modules are implemented to remove the sensitive information from user, items’ embedding. Choose filtered embedding input, user classifier efforts to forecast users’ sensitive labels, item classifier efforts to forecast pseudo sensitive labels of items. Describe overall loss function in Equation (2) 2Call=Cδ(HO,SL)−γCF1(HO,A)−βCF2(HL,D),{C_{all}} = {C_\delta }\left( {{H_O},{S_L}} \right) - \gamma {C_{F1}}\left( {{H_O},A} \right) - \beta {C_{F2}}\left( {{H_L},D} \right), where the first phrase is accuracy loss, and next phrase is users’ sensitive categorization outcomes, and the third term is outcomes from pseudo item labels. Here, the γ, β denotes balancing parameters control outcomes. While β equals zero, outcomes is disappear. Here, the optimization of the overall function using minimal value is given in Equation (3) 3minδ,JmaxF1,F2Cδ(HO,HL)−γCF1(HO,A)−βCF2(HO,D),\mathop {\min }\limits_{\delta ,J} \;\mathop {\max }\limits_{F1,F2} {C_\delta }\left( {{H_O},{H_L}} \right) - \gamma {C_{F1}}\left( {{H_O},A} \right) - \beta {C_{F2}}\left( {{H_O},D} \right), where C_F1(H_o, A) is optimizes classifiers and C_δ(H_o, H_L) denotes employed to develop recommendation accurateness is given in Equation (4) 4Cδ(HO,HL)=1G∑ (mol−m^ol)2.{C_\delta }\left( {{H_O},{H_L}} \right) = {1 \over G}\sum {{{\left( {{m_{ol}} - {{\hat m}_{ol}}} \right)}^2}} .

Pseudo item labels are allocated, deliberate design of loss function C_F2(H_o, D). The FACF identifies and groups users based on their preferences and behaviours. This step helps in creating user segments that can be utilized in subsequent stages of the methodology.

The GIFCMC extends traditional Fuzzy c-means [24] clustering by introducing conception of an intuitionistic fuzzy set. Intuitionistic fuzzy sets accommodate not only degree of membership but also the degree of non-membership, a hesitation degree for each data point, offering a more comprehensive representation of uncertainty in the data. The pre-processed data undergo segmentation utilizing GIFCMC to create target-based customer groups. First, the numerical value is transformed into discrete values, then the values are calculated in Equation (5). 5Bd=c+mi−(mMin)d(mMax)d−(mMax)d(f−c){B_d} = c + {{{m_i} - {{\left( {{m_{Min{\rm{ }}}}} \right)}^d}} \over {{{\left( {{m_{Max{\rm{ }}}}} \right)}^d} - {{\left( {{m_{Max{\rm{ }}}}} \right)}^d}}}(f - c) where (m_Min)^b denotes the dataset B_d minimal value of the dataset in the b^th volume, and (m_Max)^b denotes its highest value. f is a user data and c denotes the item data; b^th is the volume of the dataset m_i. This starts the intuitionistic fuzzification process. The distance between each data-item is calculated once the dataset has been normalized to [0, 1]. The distance matrix for the dataset that has been normalized is shown in Equation (6) 6R={ RI=DIJ*Bkm,1≤I,J≤R }R = \left\{ {{R_I} = {D_{IJ}}*{B_{km}},1 \le I,J \le R} \right\} here, the distance of each data B is calculated. The normalized dataset’s distance matrix is called D_IJ. The cluster matrix’s reciprocation is provided in Equation (7).7V=1RecV = {1 \over {Rec}} where, the cluster value matrix for each dataset z_i is provided by the matrix V, and reciprocation of matrix is denoted by record dataset. Consider the record as a candidate rule if the frequency of the record exceeds the AU. The clustering criterion comes next in Equation (8).8Ka=∑L=1b∑J=1hXLJ(mJ,cJ){K_a} = \sum\limits_{L = 1}^b {\sum\limits_{J = 1}^h {{X_{LJ}}} } \left( {{m_J},{c_J}} \right) where, m_J = (μ_i, ν_i, π_i) is the cluster method representation of the J^th data-point, which has XD features, with each feature having cluster re-presentation. These candidate criteria are used to create positive and negative clusters; any record that does not ?it the candidate guidelines will be regarded as an outlier record and it is shown in Equation (9) 9∑I=1BviL>0,1≤L≤d\sum\limits_{I = 1}^B {{v_{iL}}} > 0,1 \le L \le d where v_iL membership matrix of order L, and ∑I=1B\sum\nolimits_{I = 1}^B {} is the set of cancroids of these d clusters. Lagrange’s state of unknown multipliers G-IFCM is utilized in order to group the heart disease patients record using the formula given below Equation (10) 10μL=∑I=1BvILnμzI∑I=1BvILn{\mu _L} = {{\sum\nolimits_{I = 1}^B {v_{IL}^n} {\mu _{zI}}} \over {\sum\nolimits_{I = 1}^B {v_{IL}^n} }} where vILnv_{IL}^n is the number of groups in Cluster μ_zI that have the leading class label, μ_L denotes total number of clusters, B and signifies the number of examples in cluster.

The final output is a set of clusters, each containing data points assigned to it based on their membership degrees. In the context of the SEC-CAPR-DTRSRN methodology, GIFCMC is applied to segment the preprocessed e-commerce data into customer groups, helping to identify patterns and preferences that can be used for targeted product recommendations using the subsequent DTRSN.

The DTRSN [25] is employed to enhance cart transactions by recommending products. Cart abandonment may stem from discrepancies between consumer perceptions and digital site experiences, leading to frustration and cart abandonment. The DTRSN takes as input the segmented and pre-processed e-commerce data, which includes information about user behaviors, preferences, and historical interactions with the platform. The input data is passed through an embedding layer to convert categorical variables and user_item interactions into a continuous vector representation suitable for deep learning. The core of the DTRSN lies in its Double Transformer architecture. The Transformer model is a powerful Neural Network (NN) architecture originally intended for Natural Language Processing (NLP) but adaptable to various sequence-based tasks. Remaining connections are engaged to solve vanishing gradient issue, aid training of deep networks. Such connections permit method to learn remaining mappings, making it easier to optimize and improve the flow of information through the network. The DTRSN is trained using a suitable loss function that calculates the dissimilarity among the predicted recommendations and the actual user behavior (e.g., purchase history). The optimization algorithm is employed to optimize the model’s parameters during training. The mathematical representation is as follows;

The module can extract concealed weight information in the spatial area. Recombine spatial features create feature vectors through spatial similarity in accordance with the correlation of the features. Thus, it is given by the Equation (11) 11xi=[ αr(yi),βr(smi) ]+[ αr(yi),βr(sai) ]{x_i} = \left[ {{\alpha _r}\left( {{y_i}} \right),{\beta _r}\left( {{s_{mi}}} \right)} \right] + \left[ {{\alpha _r}\left( {{y_i}} \right),{\beta _r}\left( {{s_{ai}}} \right)} \right] where, α and β indicates embedded purposes of feature then global association. S_mi and S_ai represents the relationship between y_i, thus the pixel is given by the Equation (12) 12ZSR(x,y)=k(KLR(x′,y′),Q(x,y)){Z_{SR}}(x,y) = k\left( {{K_{LR}}\left( {{x^\prime },{y^\prime }} \right),Q(x,y)} \right) Z_SR(x, y) Indicates the pixel value of super-perseverance, k is the feature mapping function, Q(x, y) denotes weight calculation segment of pixel, K_LR is the feature vector on corresponding pixels. Projection conversion function M is expressed using Equation (13) 13(x′,y′)=M(x,y)\left( {{x^\prime },{y^\prime }} \right) = M(x,y) where, M denotes Projection conversion function, and x, y denotes weight estimation. Each body region’s final features are obtained, and then we feed them into the layer, which consists of two entirely associated connection layers which are given by the Equation (14) 14Did=−∑l=1L∑f=1Fxf·log(x^l){D_{id}} = - \sum\limits_{l = 1}^L {\sum\limits_{f = 1}^F {{x_f}} } \cdot\log \left( {{{\hat x}_l}} \right) where, F and L denote the total number of recognized samples and samples sets, x_f represents the dual label of the sample, x^l{{\hat x}_l} and indicates the probability prediction.

The utilization of DTRSN in this context aims to provide a sophisticated and personalized approach to product recommendations, with the ultimate goal of reducing cart abandonment and enhancing overall user satisfaction during e-commerce transactions.

The PCBESA [26] is an optimization method for fine-tuning the parameters of the DTRSN to enhance its effectiveness in making precise product recommendations. PCBESA method is used to enhance weights parameters [α and β] of proposed DTRSN. Below is a general description of the PCBESA and its steps:

• Step 1:

  Initialization

  The initial population of PCBESA is, initially generated by randomness. Then, the initialization is derived as Equation (15) 15ρ={ ρ1,1ρ1,2…ρ1,uρ2,qρ2,2…ρ2,uρn,1ρn,2…ρn,u }\rho = \left\{ {\matrix{ {{\rho _{1,1}}} \hfill & {{\rho _{1,2}}} \hfill & \ldots \hfill & {{\rho _{1,u}}} \hfill \cr {{\rho _{2,q}}} \hfill & {{\rho _{2,2}}} \hfill & \ldots \hfill & {{\rho _{2,u}}} \hfill \cr {{\rho _{n,1}}} \hfill & {{\rho _{n,2}}} \hfill & \ldots \hfill & {{\rho _{n,u}}} \hfill \cr } } \right\} where, ρ is the poplar’s diameter of the jth initialization position.

• Step 2:

  Random generation

  The input weight parameter [α and β] is produced at random using PCBESA metho.

• Step 3:

  Fitness function

  It creates a random solution from initialized assestments. It is assesssed utilizing the optimizing parameter. This is calculated using Equation (16): 16Fitness Function = optimizing [α and β]{\rm{Fitness Function }} = {\rm{ optimizing }}[\alpha {\rm{ and }}\beta ]

• Step 4:

  Exploration Phase:

  In the initialization phase, the PBES algorithm must also regulate the border, and each individual can be dispersed throughout the entire search space. Thus, the polar angle F has a value range of (0, 2π). In addition, boundaries must be defined for the polar diameter in order to prevent the PBES algorithm from exceeding them during the optimization process. Then the exploration is given as Equations (17), (18), and (19): 17ρj,New=ρj+W1*(ρj−ρMean)+N1*(ρj−ρj+1){\rho _{j,New}} = {\rho _j} + {W_1}*\left( {{\rho _j} - {\rho _{Mean}}} \right) + {N_1}*\left( {{\rho _j} - {\rho _{j + 1}}} \right) where, ρ_Best denotes the area that was found to be the greatest choice for the bald eagles to choose during the prior search; ρ_j indicates where the bald eagles are located; ρ_j,New is where the bald eagles have relocated; ρ_Mean denotes position of bald eagles’ average distribution following previous exploration; n₁ and w₁ symbolize arithmetic normalization of η, and ρ_j+1 is the jth bald eagles’ most recent revised position.18n1=η1max(| η1 |){n_1} = {{{\eta _1}} \over {\max \left( {\left| {{\eta _1}} \right|} \right)}} where, n₁ symbolize the arithmetic normalization of η; η₁ denoted as every bald eagles location is updated.19η2= rand *cos(θ){\eta _2} = {\rm{ rand }}*\cos (\theta ). where, θ by renewing, the specific position is update; η₂ denoted as every bald eagles location is updated and Rand is a random integer between 0 and 1.

• Step 5:

  Exploitation phase for optimizing [α and β]:

  Retention and replacement are the two scenarios that exist. Proceed with the first operation if novel fitness value is determined to be better than present fitness value; if not, proceed with the second operation. Instead of using the Cartesian coordinate system, the PBES updates individual positions in the polar coordinate system. The location of person is derived through updates. Individuals’ update speeds will increase significantly as a result, and convergence efficiency will rise by Equations (20), (21), and (22): 20ρj,new=rand*ρbest+w2*(ρj−z1*ρmean )+n2*(ρj−z2*ρbest ){\rho _{j,{\rm{ }}new{\rm{ }}}} = {\mathop{\rm rand}\nolimits} *{\rho _{best{\rm{ }}}} + {w_2}*\left( {{\rho _j} - {z_1}*{\rho _{mean }}} \right) + {n_2}*\left( {{\rho _j} - {z_2}*{\rho _{best }}} \right) where, ρ_j,new is where the bald eagles have relocated; ρ_mean denotes position of bald eagles’ average distribution following previous exploration; ρ_best denotes area that was found to be the greatest choice for the bald eagles to choose during the prior search; pj indicates where the bald eagles are located; rand is a random integer between 0 and 1; n₂ and n₂ needs to be compared to one another’s bald eagle and z₁ and z₂ are the enhancement coefficient, which is taken by all of them to be 2.21n2=η2max(| η2 |){n_2} = {{{\eta _2}} \over {\max \left( {\left| {{\eta _2}} \right|} \right)}} where, n₂ needs to be compared to one another’s bald eagle and η₂ is denoted as every bald eagles, location is updated.22η2=r1*cosg(θ)η2{\eta _2} = {r_1}*\cos g(\theta ){\eta _2} where, r₁ is a random integer between AU 0; η₂ is denoted as every bald eagles’ location is updated and Cosg is denoted by renewing, the specific position is updated. Then the specific position is updated is given as Equation (23): 23θj+1=β*θj±2*cos−1(2*rand−1){\theta _{j + 1}} = \beta *{\theta _j} \pm 2*{\cos ^{ - 1}}(2*rand - 1) here,β denotes coefficient of disturbance, with values among 0, 2; Rand is a random integer between 0; θ_j+1 the new role for each individual is established and θ_j needs to be compared to one another.

The PCBESA aims to efficiently explore the solution space and find optimal parameters for the DTRSN, enhancing its performance in the specific task of product recommendation in e-commerce. The algorithm draws inspiration from the bald eagles’ hunting behavior and their ability to navigate and search effectively in their environment.