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Physics
Prompt Description
A schematic diagram illustrating the principle and logic of the device, showing that the main body of the device can be divided into two parts: a detector and a processor. The detector is used to acquire the signals generated when spherical elements pass through the loading and unloading pipes, converting the ray intensity information of the spherical elements into current signals. The processor is used to determine the type of spherical element based on the signals, accurately distinguishing between fuel spheres and graphite spheres.
![The specific implementation process of PCA model training in PSF data processing is as follows:
1. **Data Matrix Construction:** Flatten the standardized PSF images into vectors to form a data matrix \(X_{\text{scaled}} \in \mathbb{R}^{N \times D}\).
2. **Singular Value Decomposition (SVD):** The implementation in the library uses SVD optimization instead of directly calculating the eigenvalue decomposition of the covariance matrix. Perform SVD decomposition on the flattened image matrix \(X_{\text{scaled}}\): \(X_{\text{scaled}} = U \Sigma V^\top\). Here, the column vectors of the right singular vector \(V \in \mathbb{R}^{D \times D}\) are the principal component directions, and the square of the singular value \(\sigma_k^2\) is proportional to the eigenvalue \(\lambda_k\).
3. **Principal Component Selection:** Sort the principal components according to the eigenvalue size and select the top \(K\) principal components. These principal components constitute the projection matrix \(V_K = [v_1, v_2, ..., v_K] \in \mathbb{R}^{D \times K}\), where \(v_1\) corresponds to the direction of maximum variance, \(v_2\) to the next, and so on.
4. **Dimensionality Reduction and Coefficient Extraction:** Project the centered data into a low-dimensional space: \(Z = X_{\text{centered}} V_K \in \mathbb{R}^{N \times K}\), where each row of \(Z\) is the coefficient (also called 'score') of the corresponding PSF in the principal component space.
Draw a schematic diagram of this process, requiring no shading or watermarks, and a color style that meets the requirements of SCI journal papers.](/_next/image?url=https%3A%2F%2Fpub-8c0ddfa5c0454d40822bc9944fe6f303.r2.dev%2Fai-drawings%2FVSt6TNY52kYACNod5QcmZwP8nP4PfcsA%2F284075ba-a796-4c71-9eeb-4dbea1d89ee4%2Fa852e641-9a39-4397-90cd-d4d710834d23.png&w=3840&q=75)
