## 3 The Proposed Model
### Feature Extraction and Embedding
#### 3.1.1 Image Feature Extraction and Embedding  
In this study, the goal is to transform apparel images into a format that can efficiently support continuous learning models for predicting apparel characteristics. To achieve this, we applied a transfer learning strategy, utilizing the ResNet50 model pre-trained on the ImageNet dataset to extract visual features. The ResNet50, based on the residual neural network architecture (ResNet), offers strong performance and the ability to capture both low-level and high-level features in the images [25]. To standardize the data, we first performed a pre-processing operation on the apparel images. We rescaled the original image \(I_{orig}\in\mathbb{R}^{H\times W\times C}\), where \(H\) is the height of the image, \(W\) is the width, and \(C\) represents the color channels [26]. To meet the input requirements of ResNet50, we resized the image to \(224\times 224\) pixels, and stored the RGB channels, representing the input \(I_{input}\in\mathbb{R}^{224\times 224\times 3}\), where the RGB channels are mapped to the values in the range [0, 255]. The image processing is as follows:  
For efficient neural network training and speed, the pixel values of the image are first normalized from the range [0, 255] to [0, 1], with the original pixel value \(I_{input}(i,j,k)\) being transformed to:  
\[I_{norm}(i,j,k)=\frac{I_{input}(i,j,k)}{255}\]  
For the image values to be more consistent, the images were standardized using ImageNet data. The mean values for the ImageNet dataset are [0.485, 0.456, 0.406], and the standard deviations for the ImageNet dataset are [0.229, 0.224, 0.225]. Thus, the normalization process was performed as follows:  
\[I_{std}(i,j,k)=\frac{I_{norm}(i,j,k)-\mu_{k}}{\sigma_{k}}\]  
Next, we used ResNet50 for feature extraction. ResNet50 performed convolution operations to extract high-level features from the input images and produced a feature vector \(F_{resnet}\in\mathbb{R}^{H^{\prime}\times W^{\prime}\times D}\), where \(D\) is the depth of the convolution (i.e., the number of channels) [26]. The feature extraction process can be expressed as:  
\[F_{resnet}=\text{Conv2D}(I_{std},W_{conv},b_{conv})\]  
where \(W_{conv}\) and \(b_{conv}\) are the weights and biases of the convolution layers. In this layer, ResNet50 extracts both low-level features such as garment textures and high-level features such as clothing styles and color patterns. The extracted feature map was subsequently passed through a fully connected layer, which utilized the GELU activation function to introduce non-linearity and enhance the model's ability to capture complex relationships. The flattening operation was applied to reduce the high-dimensional feature map into a one-dimensional vector:  
\[F_{1}=\text{GELU}(W_{1}\cdot\text{Flatten}(F_{resnet})+b_{1})\]  
where \(W_{1}\in\mathbb{R}^{dm1\times D}\) is the weight matrix and \(b_{1}\in\mathbb{R}^{dm1}\) is the bias vector, the GELU function serves as the activation function [2], and Flatten denotes the operation of flattening the feature map into a one-dimensional vector. To mitigate overfitting, a dropout layer is incorporated after the fully connected layer [27], with a dropout rate set to \(p\). During each training iteration, a random proportion \(p\) of neurons are discarded. Subsequently, the resulting \(F_{1}\in\mathbb{R}^{dm1}\) is compressed into the final visual feature vector through a second fully connected layer, with an output dimensionality of \(dm2=300\). The second fully connected layer is defined as:  
\[E_{1}=W_{2}\cdot F_{1}+b_{2}\]  
where \(W_{2}\in\mathbb{R}^{dm2\times dm1}\) is the weight matrix and \(b_{2}\in\mathbb{R}^{dm2}\) is the bias term. The resulting feature vector \(E_{1}\in\mathbb{R}^{300}\) serves as the visual feature representation of the clothing image and is passed to the subsequent recommendation algorithm model. This image feature vector encapsulates both low-level features of the clothing image, such as edges and textures, and high-level semantic features, such as shape, category, and color.