Star-like body light variation curve fitting and clustering analysis method based on Gaussian process and self-supervised learning

Abstract

The invention relates to a gaussian process and self-supervised learning-based star-like body optical variation curve fitting and clustering analysis method, and aims to improve the analysis accuracy of star-like body optical variation data. Star-like coordinates are obtained through an SDSS DR16 data set and are subjected to cross matching with a ZTF star catalogue to extract optical variation data, and a local abnormal factor algorithm and a statistics-based algorithm are adopted to perform data cleaning. And performing curve fitting on the denoised data by using a Gaussian process regression model, and extracting features through a self-supervised learning model (BYOL). After features are extracted, clustering analysis is carried out on the features by using K-means and hierarchical clustering algorithms, and a clustering result is optimized through multiple evaluation indexes. And finally, establishing a relation between the clustering result and the physical characteristics of the star-like body. According to the method, an effective tool is provided for star-like body research, and the physical characteristics and the evolution process of the star-like body can be deeply understood.

Description

Technical Field

[0001] The present invention relates to the field of astronomical data processing, and is mainly aimed at an analysis method for quasar light variation data, in particular, light variation curve fitting and feature clustering performed by combining Gaussian process and self-supervised learning technology. Background Art

[0002] With the advancement of astronomical observation technology, the ZTF (Zwicky Transient Facility) star catalog provides a large amount of quasar light variation data. These data record the brightness of celestial bodies over time and can provide important information for scientists. However, quasars are celestial bodies very far away from the earth, and their raw data are often affected by noise and outliers. Therefore, developing an efficient and accurate analysis method has important scientific value.

[0003] To solve this problem, we used the Gaussian process (GP) method to fit the quasar light variation data and successfully reconstructed the light curve. This method can effectively capture the changing trend of the data and provide uncertainty estimates. After obtaining the light curve, we used the self-supervised learning framework, especially the BYOL (Bootstrap Your OwnLatent) model, to train the extracted features. This process not only improves the expressiveness of the features, but also enhances the generalization performance of the model.

[0004] Finally, the K-means clustering algorithm was used to perform cluster analysis on the features obtained through training. Through this analysis, we were able to identify the significant features of quasars, thus laying the foundation for subsequent scientific research and data mining. This series of methods provides new ideas for the processing of quasar light variation data and promotes the development of astronomical data analysis. Summary of the invention

[0005] The present invention relates to a quasar analysis method based on light variation data, specifically, by combining multiple advanced machine learning techniques with astronomical data processing methods to model, extract features and cluster analysis of quasar light variation curves. This method aims to improve the accuracy and effectiveness of quasar light variation feature analysis and provide a deeper understanding for astronomical research.

[0006] S1 data acquisition and preprocessing: First, by accessing the SDSS DR16 (Sloan Digital Sky Survey) data set, the celestial coordinates of the quasar, including right ascension (ra) and declination (dec), are systematically retrieved. Then, the obtained ra and dec coordinates are used to cross-match the ZTF (Zwicky Transient Facility) star catalog to extract relevant light variation data. These data include brightness observations of quasars at different times, which constitute an important basis for studying the behavior of quasars. After the light variation data is obtained, the local outlier factor (LOF) algorithm and the statistical-based anomaly detection method are used for data cleaning. The LOF algorithm effectively removes noise and improves data quality by identifying outliers that are significantly different from the surrounding data. This denoising step is crucial for the subsequent light variation curve fitting, ensuring that the data more accurately reflects the true light variation characteristics of the quasar.

[0007] S2 curve fitting: A Gaussian process regression model is used to fit the denoised light variation data. The non-parametric nature of the Gaussian process enables it to flexibly cope with various forms of data while generating a smooth light variation curve. With this method, we can not only capture the overall trend of the light variation data, but also quantify the uncertainty of the prediction, providing a robust foundation for subsequent feature extraction.

[0008] S3 feature extraction: After the light curve fitting is completed, the self-supervised learning model (BYOL) with the Transformer layer added is used for feature extraction. This model can automatically identify the deep features of the data through unlabeled learning, improving the richness and accuracy of feature extraction. The introduction of the Transformer layer enhances the processing ability of time series data, making the extracted features more representative and effectively capturing the subtle differences in quasar light variation.

[0009] S4 Clustering Analysis: After extracting features, the K-means algorithm and hierarchical clustering algorithm are used to cluster the light curves. The K-means algorithm quickly identifies the similarities between light curves by dividing the data points into multiple clusters. Hierarchical clustering provides an intuitive hierarchical structure to help us understand the relationship between quasars more deeply. This dual clustering analysis method ensures that we can comprehensively and accurately identify different patterns of quasar light variation.

[0010] S5 Clustering evaluation: Based on the clustering analysis results, multiple clustering evaluation indicators (Silhouette coefficient, Davies-Bouldin index and Calinski-Harabasz index) are used to select the best clustering method and number of clusters. This evaluation process not only verifies the reliability of the clustering results, but also optimizes the analysis scheme so that the final clustering results can best represent the true characteristics of quasars.

[0011] S6 result display: The present invention successfully discovered the similarity between the clustering results and the physical characteristics, which proves that the technical solution of the present invention can effectively improve the processing efficiency of light-variable data and the accuracy of clustering analysis, provide astronomical researchers with more effective quasar research tools, and help to deeply understand the evolution process of quasars and their physical properties, and has broad application prospects.

[0012] Beneficial effects: Compared with the prior art, the present invention is the first to use Gaussian process to fit the light curve of quasar light variation data. Gaussian process can flexibly process complex data, generate smooth curves, quantify uncertainty, and enhance the reliability of fitting. The present invention introduces the BYOL model BYOL-t with a Transformer layer to extract features from the light curve of quasars. The model's ability to understand light variation data is improved, and richer and deeper features can be extracted. The present invention provides a new methodology for quasar light variation data analysis, which can effectively extract and analyze complex light variation features on large-scale data sets, and has broad application prospects and important scientific research value. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a basic flow chart of the present invention;

[0014] Figure 2 is a scatter plot of light-varying data before fitting in the present invention;

[0015] Figure 3 is a light curve diagram after fitting by the present invention;

[0016] Figure 4 This is the BYOL-t structure diagram of the feature extraction network proposed in the present invention;

[0017] Figure 5 It is a quasar light variation anomaly diagram fitted by the present invention in combination with common physical characteristics of quasars;

[0018] Figure 6 This is the first type of representative quasar light curve diagram clustered by the present invention;

[0019] Figure 7 This is the second type of representative quasar light curve diagram clustered by the present invention;

[0020] Figure 8 This is the third type of representative quasar light curve diagram clustered by the present invention;

[0021] Fig. 9 This is the fourth type of representative quasar light curve clustered by the present invention. DETAILED DESCRIPTION

[0022] The content of the present invention is further described below in conjunction with the accompanying drawings.

[0023] like Figure 1 Shown is a basic flow chart of the present invention, comprising the following steps:

[0024] S1: We used the SDSS (Sloan Digital Sky Survey) DR16 data set to systematically search for quasars and extract the right ascension (ra) and declination (dec) of each quasar. These coordinates not only provide the basis for subsequent data intersection, but also ensure that we can accurately locate the position of the target quasar in astronomical observations.

[0025] S2: Next, we use the ra and dec coordinates retrieved from SDSS to cross-match on the ZTF (Zwicky Transient Facility) star catalog. This process involves comparing the quasar coordinates obtained in SDSS with the observational data in the ZTF star catalog to identify relevant light variation data. A total of 13,703 quasar light variation data with more than 600 observations were downloaded. These light variation data contain the brightness changes of quasars at different time points, providing a basis for in-depth analysis of their light variation characteristics. We only selected 10,884 quasars with a light variation amplitude of less than 1.5 magnitude for in-depth study. The light variation data are shown in Table 1:

[0026] Table 1 Distribution statistics of quasar observation times in the present invention

[0027] Number of observations 600-799 800-999 1000-1199 1200-1399 1400 and above Number of quasars 4293 2772 1650 972 1197

[0028] S3: After obtaining the light curve data, we used the local outlier factor (LOF) algorithm and statistical methods to detect and denoise outliers. The LOF algorithm identifies outliers that are significantly different from the surrounding data by evaluating the local density of data points. We identified points with anomaly scores less than -3 and points that deviated from the mean by three standard deviations as outliers. A total of 8735 outlier observation points were eliminated. This process not only improved the quality of the data, but also ensured the accuracy of subsequent analysis, making the light curve more reliable.

[0029] S4: We use the Gaussian process regression model to fit the denoised light curve data. The Gaussian process is a powerful non-parametric Bayesian method that can generate smooth light curves and provide quantification of prediction uncertainty. This process not only captures the main trends of the data, but also can further effectively deal with the noise and uncertainty in the data. In this work, we also compared multiple network combinations of GP, DNN, Transformer, GP+DNN, GP+Transformer, DNN+Transformer, and GP+DN+Transformer on the test set. According to the comparison of three evaluation indicators (mean square error MSE, mean absolute error MAE, root mean square error RMSE), the results show that the three indicators of GP Gaussian process are the best. Finally, it is determined that the Gaussian process GP has the best fitting effect. The experimental data are shown in Table 2:

[0030] Table 2 Comparison of experimental results of the present invention and other classification neural network algorithms

[0031] MSE MAE RMSE GP 0.429183638 0.470879918 0.645025718 DNN 1.418240714 0.936920846 1.189231221 Transformer 0.481245684 0.503173333 0.684626426 GP+DNN 0.683004701 0.635939097 0.82503425 GP+Transformer 0.442867571 0.47948066 0.65586116 DNN+Transformer 0.687708223 0.634761536 0.827813296 GP+DN+Transformer 0.547294664 0.554756933 0.735364617

[0032] S5: After obtaining the light curve, we use the BYOL (Bootstrap Your Own Latent) model with a Transformer layer to extract features. Through this advanced self-supervised learning technology, the model can learn the implicit features of the data without labels. The introduction of the Transformer layer improves the model's ability to process time series data, making the extracted features richer and more representative.

[0033] S6: After feature extraction, we applied both K-means and hierarchical clustering algorithms to cluster the light curves. K-means can quickly identify the similarities between light curves by dividing data points into multiple clusters, while hierarchical clustering provides more intuitive clustering results by constructing a hierarchical tree structure. This comprehensive analysis method enables us to have a more comprehensive understanding of the light variation characteristics and group behavior of quasars.

[0034] S7: After cluster analysis, we used multiple clustering evaluation indicators (Silhouette coefficient, Davies-Bouldin index, and Calinski-Harabasz index) to determine the best clustering method and number of clusters. This process not only ensures the reliability and effectiveness of the clustering results, but also enables us to select the clustering scheme that best represents the data characteristics, thereby optimizing the clustering effect and maximizing the scientific value of the analysis. Finally, combining the three evaluation indicators, we determined that the K-means algorithm clustered into 4 categories was the best. The evaluation results are shown in Table 3:

[0035] Table 3 Clustering evaluation results

[0036] Clustering methods Number of clusters Silhouette coefficient Davies-Bouldin Index Calinski-Harabasz Index Hierarchical clustering 2 0.35148093 1.0161942004923497 7743.032419313056 K-means clustering 2 0.40174717 0.9332868190529268 10591.089275523465 Hierarchical clustering 3 0.24454314 1.20973888041636 7181.615836512352 K-means clustering 3 0.36742098 1.1526302697469998 9840.519661695319 Hierarchical clustering 4 0.28612398 1.0977338639888023 7742.820686656211 K-means clustering 4 0.4564136 0.9274139398785642 10590.51815417371 Hierarchical clustering 5 0.15968329 1.41252331073608 5133.28322212933 K-means clustering 5 0.20185648 1.417923752917676 5883.690810623747 Hierarchical clustering 6 0.13941649 1.6637648530849996 4584.695979974151 K-means clustering 6 0.17495292 1.5474659973071365 5129.559751535557 Hierarchical clustering 7 0.113729514 1.7703504755736645 4115.924233873699 K-means clustering 7 0.17249341 1.582099371250946 4580.58036240915 Hierarchical clustering 8 0.116110735 1.7162526154313642 3773.6631725819943 K-means clustering 8 0.14485377 1.6781787895117963 4181.08219083554 Hierarchical clustering 9 0.10971862 1.8475967572310803 3429.5992247760787 K-means clustering 9 0.1247979 1.8157483341027014 3811.6295003027535

[0037] S8, S9: Finally, through the above steps, we obtained clustering results with obvious characteristics, and compared them with the light curve formed by special physical phenomena:

[0038] We found that the light curves of most quasars in the first category are straight lines. By observing the scatter plot and studying the light variation data, we found that the light variation amplitude of this type of quasars is almost less than 0.5 magnitude in the observation period of 2,200 days and more than 600 times, with no obvious fluctuations and a relatively uniform distribution. This category contains 2,875 quasars.

[0039] We found that most of the quasar light curves in the second category showed obvious periodicity. Most of their light curves were sinusoidal. In the observations lasting 2,200 days and more than 600 times, they almost showed 1-3 light variation periods. This type of light variation is similar to the Baryon Acoustic Oscillation (BAO) phenomenon. It is a residual effect of density fluctuations in the early universe and may appear as periodic fluctuations in the light variation of quasars. It is a long-term effect on the time scale, usually appearing within a few years to decades. Its magnitude change is usually small, about 0.1 magnitude. It is characterized by slow and periodic small fluctuations. The behavior of this type of celestial body is very similar to the Baryon Acoustic Oscillation phenomenon. This category contains 691 quasars.

[0040] We found that the light curves of most quasars in the third category gradually increase or decrease, and gradually return after maintaining the peak for a period of time. This type of light variation is similar to the microlensing effect. The lensing effect is the bending of light caused by foreground stars (such as stars or black holes), which causes the brightness of background light sources (such as quasars) to change. When the microlensing effect occurs, the brightness of the quasar may suddenly increase or decrease, forming a short-term light variation, which is usually sudden. Time scale: several months to several years. The magnitude change is usually 0.1 to 1.0 magnitude, and in extreme cases it can reach 2.0 magnitude. This category contains 2062 quasars.

[0041] We found that most of the quasar light curves in the four categories show irregular changes, with both high and low amplitudes and frequencies, and no suitable physical phenomenon has been found to match them. This category contains 5,256 quasars.

[0042] These results not only reveal the different patterns of quasar light variations, but also provide important data support for subsequent research, helping scientists to deeply explore the physical properties of quasars and their evolution process, and promote further research in this field.

[0043] Figure 2 It is a scatter plot of the light variation data before fitting in the present invention. We plot the light variation data into a scatter plot, normalize the data, fix the horizontal axis to the MJD time from 58200 to 60400, and fix the vertical axis span to the minimum observed brightness value to the minimum observed brightness value + 1.5 magnitudes, which includes a total of 2200 days of light variation.

[0044] Figure 3 This is the light curve diagram after fitting by the present invention. In the diagram, the original scattered data and confidence interval are cancelled, and only the fitted light curve is retained, which is convenient for in-depth study of the light variation situation.

[0045] Figure 4 This is the structure diagram of the feature extraction network BYOL-t proposed in the present invention. The network implements a self-supervised learning model, combines the pre-trained ResNet-50 and Transformer layers, and uses the BYOL (Bootstrap Your OwnLatent) algorithm to extract image features.

[0046] ResNet (Residual Network) is a deep convolutional neural network. Its main innovation is the introduction of residual connection (skip connection), which solves the gradient vanishing problem in deep network training. Through this structure, ResNet can effectively learn deeper features and achieve excellent performance in many computer vision tasks.

[0047] In this invention, ResNet-50 is used as a basic feature extractor, responsible for extracting rich feature representations from the input image.

[0048] Transformer was originally used for natural language processing, but its self-attention mechanism has been widely used in image processing tasks. Transformer can capture the relationship between different regions in an image, thereby extracting global context information.

[0049] The Transformer layer in the present invention is composed of a multi-head self-attention mechanism and a feedforward neural network. It enhances the network's modeling ability for input features, allowing the model to better understand complex image content.

[0050] BYOL is a self-supervised learning algorithm that performs feature learning by creating two networks (one is the main network and the other is the target network). This method does not rely on negative samples, but optimizes the representation of the main network by predicting the features of the target network for the same input image.

[0051] In this invention, BYOL is used as the main method of self-supervised learning, and the model acquires the ability to represent images through self-learning without the need for labeled data.

[0052] The network design makes full use of the latest technology in the field of deep learning, and provides a powerful self-supervised learning framework by combining convolutional networks and Transformers. It is suitable for feature extraction and learning tasks of large-scale unlabeled image data, and can show superior performance in many computer vision applications.

[0053] Figure 5 This is a quasar light curve anomaly diagram fitted by the present invention in combination with the common physical characteristics of quasars. By referring to the common physical characteristics of quasars, five common abnormal phenomena of light curves are fitted:

[0054] 1. Microlensing Effect

[0055] Phenomenon: Gravitational amplification of background quasar light by foreground objects.

[0056] Time scale: months to years.

[0057] Magnitude variation: Usually varies from 0.1 to 1.0 magnitude, and can reach 2.0 magnitude in extreme cases.

[0058] Features: The light curve is relatively smooth, gradually rising or falling, and gradually returning after staying at the peak for a period of time.

[0059] 2. Accretion Disk Instability

[0060] Phenomenon: Instability occurs inside the accretion disk of a quasar, causing matter to suddenly increase or decrease, affecting the luminosity.

[0061] Time scale: weeks to months.

[0062] Magnitude variation: Usually between 0.2 and 0.5 magnitude, but larger instability events can cause variations of 0.5 to 1.0 magnitude. Characteristics: The light curve may show a rapid rise or fall followed by a gradual recovery.

[0063] 3. Jet Activity

[0064] Phenomenon: The relativistic jet activity of quasars can cause changes in luminosity, which is especially evident in different bands of electromagnetic waves.

[0065] Time scale: days to months.

[0066] Magnitude variation: usually between 0.1 and 0.5 magnitude, and in extreme cases can reach over 1.0 magnitude.

[0067] Characteristics: Rapid light changes, which may be a sudden increase or decrease in brightness within a short period of time, with more drastic changes.

[0068] 4. Baryon Acoustic Oscillations (BAO)

[0069] Phenomenon: The residual effects of density fluctuations in the early universe may appear as periodic fluctuations in the light variations of quasars.

[0070] Time scale: Long-term effects, usually appearing over years to decades.

[0071] Magnitude variation: Usually small, varying by about 0.1 magnitude.

[0072] Characteristics: Slow and periodic small fluctuations.

[0073] 5. Dust Obscuration

[0074] Phenomenon: The dust cloud near the quasar blocks part of the light, causing the luminosity to weaken.

[0075] Time scale: months to years.

[0076] Magnitude variation: Usually between 0.1 and 1.0 magnitude, and can reach 2.0 magnitude in extreme cases.

[0077] Features: The brightness decreases slowly, recovers slowly, and the overall change curve is smoother.

[0078] Figure 6 It is a representative example of quasars in Class 1 clustered by the present invention. Its horizontal axis is fixed to the MJD time from 58200 to 60400, and its vertical axis span is fixed to the minimum observed magnitude value to the minimum observed magnitude value + 1.5 magnitudes. This figure represents the light curve shapes of most quasars in this clustering result.

[0079] Figure 7It is a more representative example of quasars in the two categories clustered by the present invention. Its horizontal axis is fixed to the mjd time from 58200 to 60400, and the vertical axis span is fixed to the minimum observed magnitude value to the minimum observed magnitude value + 1.5 magnitude. This figure represents the light curve shape of most quasars in this clustering result.

[0080] Figure 8 It is a more representative example of quasars among the three categories clustered by the present invention. Its horizontal axis is fixed to the mjd time from 58200 to 60400, and the vertical axis span is fixed to the minimum observed magnitude value to the minimum observed magnitude value + 1.5 magnitude. This figure represents the light curve shape of most quasars in this clustering result.

[0081] Fig. 9 It is a more representative example of quasars among the four categories clustered by the present invention. Its horizontal axis is fixed to the mjd time from 58200 to 60400, and the vertical axis span is fixed to the minimum observed magnitude value to the minimum observed magnitude value + 1.5 magnitude. This figure represents the light curve shape of most quasars in this clustering result.

Claims

1. A quasar analysis method based on light variable data, characterized in that it comprises the following steps: 1.

1. Retrieve the celestial coordinates (ra, dec) of the quasar from the SDSS DR16 dataset; 1.

2. Use the retrieved ra and dec coordinates to cross-match on the ZTF star catalog to obtain the corresponding light variable data; 1.

3. De-noising the acquired light-variable data using the local outlier factor (LOF) algorithm and a statistically based outlier detection method; 1.

4. Use the Gaussian process regression model to fit the denoised light curve data to generate a smooth light curve; 1.

5. Use the self-supervised learning model (BYOL) with the Transformer layer added to extract features from the fitted light curve; 1.

6. Apply K-means algorithm and hierarchical clustering algorithm to perform cluster analysis on the extracted features; 1.

7. Select the best clustering method and number of clusters based on the clustering evaluation index to obtain accurate and distinctive clustering results. 1.

8. Based on the comparison between the clustering results and the common physical characteristics of quasars, consistency was found.

2. The method according to claim 1, characterized in that The local outlier factor algorithm calculates the local density of data points and identifies outliers that are significantly different from surrounding data to improve data quality.

3. The method according to claim 1, characterized in that The Gaussian process regression model described is a non-parametric model that can automatically adjust its smoothness according to the input data to capture the main trends and uncertainties of light-varying data.

4. The method according to claim 1, characterized in that: The self-supervised learning model (BYOL) can effectively extract deep features in light-varying data and enhance the ability to understand time series data through label-free learning.

5. The method according to claim 1, characterized in that The K-means algorithm quickly identifies similarities between light curves by dividing data points into multiple clusters.

6. The method according to claim 1, characterized in that The hierarchical clustering algorithm constructs a hierarchical tree structure of data points, thereby providing a more intuitive clustering result and facilitating the analysis of the relationship between quasars.

7. The method according to claim 1, characterized in that The clustering evaluation indicators include silhouette coefficient, Davies-Bouldin index and Calinski-Harabasz index to ensure the reliability and effectiveness of the clustering results.

8. The method according to claim 1, characterized in that The cluster analysis results can reveal different patterns of quasar light variations and provide data support for subsequent scientific research.

9. The method according to claim 1, characterized in that: The light variation data include the brightness observation values ​​of quasars at different times, forming the basis for studying the behavior of quasars.

10. The method according to claim 1, characterized in that The quasar analysis method can be applied to multiple fields, including but not limited to astronomy, astrophysics, astronomical observation, etc.

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