A method for evaluating target spatial spectrum characteristics combined with masking effect based on hyperspectral anomaly detection

Abstract

The present invention discloses a method for evaluating target spatial-spectral features combined with masking effects based on hyperspectral anomaly detection, comprising the following steps: step 1, feature band screening; step 2, spatial feature extraction; step 3, spectral feature extraction; step 4, spatial-spectral feature combined with masking effect evaluation; step 5, objective image evaluation based on a hyperspectral anomaly detection model; step 6, modifying parameter weights: The method disclosed in the present invention is suitable for hyperspectral imaging with gradually increasing spatial resolution at this stage, adds spatial dimension feature information extraction, and improves the hyperspectral masking effect evaluation performance.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent information remote sensing observation, object recognition and analysis technology, and particularly relates to a target space-spectrum feature combined with masking effect evaluation method based on hyperspectral anomaly detection in this field. Background Art

[0002] In recent years, hyperspectral imaging remote sensing observation methods have developed rapidly. This technology organically combines imaging technology and spectral technology, and simultaneously obtains two-dimensional spatial geometric information and one-dimensional spectral information of the detection object to form a three-dimensional data cube, providing continuous narrow-band image data. In particular, spectral information is an inherent attribute of natural objects, also known as spectral fingerprint. It has good application prospects and great significance for the classification and identification of objects, and has become one of the important means of modern earth remote sensing observation.

[0003] An analysis of the fields of intelligent remote sensing observation, object identification, and analysis reveals that traditional hyperspectral-based masking effect evaluation methods often employ spectral information matching measures, performing single-dimensional analysis based on only three influencing factors: spectral channel, spectral distance, and spectral angle. With the improvement of the resolution of hyperspectral imagers, spatial information should also be incorporated into masking evaluation indicators, combined with spectral information for comprehensive evaluation. Furthermore, in hyperspectral masking effect evaluation systems based on the combination of spatial and spectral features, the determination of parameter weights is susceptible to the influence of expert expertise and subjective judgment, resulting in a lack of objectivity. Therefore, it is particularly urgent and important to research and implement a masking effect evaluation method based on hyperspectral anomaly detection that combines target spatial and spectral features to address the various issues existing in existing technologies. Summary of the Invention

[0004] This invention overcomes the shortcomings of existing technologies, such as unitary evaluation methods, incomplete evaluation elements, and relatively subjective evaluation criteria. It provides a method for evaluating masking effects based on target spatial-spectral features combined with hyperspectral anomaly detection. This method enables joint feature extraction and comprehensive evaluation in both spatial and spectral dimensions. It also extracts features in optimized screening bands based on prior knowledge. Finally, the output of the hyperspectral anomaly detection model is used to modify the subjective scoring weights of experts, making the evaluation results more informative and objective.

[0005] The present invention adopts the following technical solutions:

[0006] A method for evaluating target spatial spectrum characteristics combined with masking effect based on hyperspectral anomaly detection is improved in that it includes the following steps:

[0007] Step 1, characteristic band screening:

[0008] Analyze hyperspectral imaging data, perform full-channel dimensionality reduction and optimal band screening through band screening and dimensionality reduction algorithms, and use orthogonal transformation;

[0009] Set the reconstruction threshold to t = 95% and select the minimum dimension d that makes the equation valid ′ :

[0010]

[0011] In the above formula, d is the feature dimension, d′ is the feature dimension after dimensionality reduction, and λ i ,i=1,2,… is the eigenvector;

[0012] Analyze the material properties of the target and background objects. For the known material properties of the target, use prior knowledge to add the grayscale image spatial feature calculation information of the material's best reflection characteristic band.

[0013] Step 2, spatial feature extraction:

[0014] Convert the optimally filtered grayscale images of each band into L * a * b * Color space; calculate the L of the minimum bounding rectangle of the target and the surrounding 8 neighborhoods in each band; * a * b * Spatial brightness contrast; the brightness contrast of the 8 neighborhoods is determined by the minimum-maximum normalization method to determine the weight of each neighborhood, and the proportion of the eigenvector corresponding to the band in the dimensionality reduction is determined by the minimum-maximum normalization method; the brightness contrast of the 8 neighborhoods is determined by the Z-Score normalization method to determine the weight;

[0015] Calculate the Hu invariant moments of the target area and the surrounding 8 neighborhoods in the 3*3 area where the target and background are located; calculate the similarity measure of the Hu invariant moments of the target and background in all preferred bands:

[0016]

[0017] In the above formula, Q T,i is the Hu moment of the single-band target area, Q B,i is the Hu moment of the background area;

[0018] The Hu moments of the 8 neighborhoods are normalized by the minimum-maximum method to determine the weight of each region, and the dimension ratio of the eigenvector corresponding to the band in the dimensionality reduction process is also used to determine the weight by the minimum-maximum method; the Hu moments of the 8 neighborhoods are normalized by the Z-Score method to determine the weight;

[0019] Calculate the structural similarity (SSIM) of the target area and its 8 surrounding neighborhoods in terms of brightness, contrast, and structure respectively; calculate the SSIM of the target area and the surrounding 8 neighborhood background areas, and compare the SSIM of each neighborhood area with that of the target area;

[0020] The structural similarity of the 8-neighborhood is determined by the minimum-maximum normalization method to determine the weight of each region, and the proportion of the corresponding feature vector of the band in the dimensionality reduction is also determined by the minimum-maximum normalization method to determine the weight of the band; the visual features of the 8-neighborhood are determined by the Z-Score normalization method;

[0021] Calculate the Bhattacharyya distance between the edge direction histogram of the target area and the edge direction histogram of the surrounding 8 neighborhoods in the 3*3 area where the target and background are located; calculate the mean error of the Bhattacharyya distance between the target area and the surrounding 8 neighborhoods:

[0022]

[0023] In the above formula, h(x T ) represents the normalized edge direction statistical histogram of the target area, h(x B,i ) represents the normalized edge direction statistical histogram of the i-th neighborhood background area around the target;

[0024] The weight of each region is determined by the minimum-maximum normalization method for the structural similarity of the 8-neighborhood, and the weight of the band is determined by the minimum-maximum normalization method based on the proportion of the eigenvector corresponding to the band in the dimensionality reduction; the weight of the structural similarity of the 8-neighborhood is determined by the Z-Score normalization method;

[0025] Step 3, spectral feature extraction:

[0026] Calculate the average spectral information of the sum of the spectral responses of each pixel in each band of the target in the area occupied by the hyperspectral image;

[0027] Obtain the standard spectral channel data of each neighborhood in the 8-neighborhood background around the target;

[0028] According to the average spectrum information of the target area, the cosine value of the whitening spectrum angle between the target area and the surrounding 8 neighboring areas is calculated:

[0029]

[0030] In the above formula, p i ,q i Represent the target p i and background q i The average spectral vector of the region;

[0031] Step 4: Evaluation of spatial spectrum features combined with masking effect:

[0032] The brightness contrast, Hu invariant moment, visual similarity and structural similarity of the target and the surrounding background area processed by the Z-Score normalization method are standardized and weighted, and the spatial weight of the principal component after dimensionality reduction is determined by the minimum-maximum normalization method.

[0033] Determine the spectrum weight value based on the cosine value of the whitened spectrum angle processed by the normalization method;

[0034] Standardize and weight the spectral and spatial dimension features and perform joint feature calculations:

[0035]

[0036] In the above formula, w ij is the weight of the area in row i and column j, λ θ is the spectral dimension influencing parameter, t ij -b ij is the spatial dimension influencing parameter, t ij is the feature information of the intermediate target domain, b ij is the background domain feature information;

[0037]

[0038] E tb =|T t -T b |

[0039] In the above formula, E tb is the target spectrum T t With the background spectrum T b The distance normalization result of

[0040] The model is used to quantitatively score the masking effect evaluation of known hyperspectral imaging and obtain the setting range of the model weight;

[0041] Step 5: Objective image evaluation based on the hyperspectral anomaly detection model:

[0042] The collected masked target and background hyperspectral data are used as training sets to design a deep learning model and train a hyperspectral anomaly detection model.

[0043] Based on the different masking levels obtained by training the hyperspectral anomaly detection model, the target and background segmentation thresholds are correspondingly determined, and the highest masking level at which the target is identified as an anomaly by the model is determined;

[0044] Obtain the evaluation results of the objective evaluation model on the hyperspectral image to be detected;

[0045] Step 6: Modify the parameter weights:

[0046] According to the masking effect evaluation result of the hyperspectral data obtained in step 5, the masking degree of the hyperspectral masking effect evaluation result combined with the spatial spectrum feature obtained in step 4 is compared;

[0047] Modify the weight of the evaluation model based on the empty spectrum features and expert scoring;

[0048] The final evaluation result of the masking effect of the hyperspectral imaging to be detected is obtained.

[0049] Furthermore, the band screening dimensionality reduction algorithm in step 1 includes principal component analysis PCA, independent component analysis ICA and deep learning algorithm.

[0050] Furthermore, the reconstruction threshold t in step 1 is 95%.

[0051] Furthermore, step 5 also includes: calibrating the target and the degree of obscuration based on a large amount of outdoor airborne hyperspectral test data; designing and training a hyperspectral-based anomaly detection algorithm through an artificial intelligence algorithm; testing the model trained in step 5 with the marked image, training and calculating and obtaining the segmentation threshold of the target and background in the hyperspectral anomaly detection model for different degrees of obscuration, inputting the hyperspectral data to be detected into the anomaly detection model associated with the degree of obscuration for end-to-end anomaly detection, and obtaining the output results.

[0052] Further, AI algorithms include low-rank sparse matrix factorization, subspace projection, generative adversarial networks, and stacked autoencoders.

[0053] The beneficial effects of the present invention are:

[0054] The method disclosed in the present invention is suitable for hyperspectral imaging with gradually increasing spatial resolution at this stage. It increases the extraction of spatial dimension feature information and improves the performance of hyperspectral masking effect evaluation. At the same time, the objective artificial intelligence evaluation model obtained through large-scale data training is used to guide the modification of weights, making the hyperspectral masking effect evaluation model algorithm based on the combination of spatial and spectral features and the application of expert prior knowledge more scientific and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0056] Figure 2 Detailed processing flow diagram of the method of the present invention. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0058] Example 1, as Figure 1 As shown, this embodiment discloses a method for evaluating target spatial spectrum features combined with masking effects based on hyperspectral anomaly detection. This method can realize joint feature extraction and comprehensive evaluation in spatial and spectral dimensions. At the same time, it can extract features in the optimized screening band based on prior knowledge. Finally, the output results of the hyperspectral anomaly detection model are used to correct the subjective scoring weights of experts, making the evaluation results more referenceable and objective. It includes the following steps:

[0059] Step 1, characteristic band screening:

[0060] Analyze hyperspectral imaging data, perform full-channel dimensionality reduction and optimal band screening through band screening and dimensionality reduction algorithms (including but not limited to principal component analysis (PCA), independent component analysis (ICA), and deep learning algorithms), and use orthogonal transformation;

[0061] From the perspective of reconstruction, the reconstruction threshold is set to t = 95%, and the minimum dimension d′ that makes the equation valid is selected:

[0062]

[0063] In the above formula, d is the feature dimension, d′ is the feature dimension after dimensionality reduction, and λ i ,i=1,2,… is the eigenvector;

[0064] The material properties of the target and background objects are analyzed. For the material properties of the known target, the spatial feature calculation information of the grayscale image of the best reflective characteristic band of the material is added based on prior knowledge. For example, the chlorophyll content target detection adds the 550nm band feature map calculation, the green plants add the 680, 690, and 720nm band map feature calculation, and the exploration of the atmospheric water peak on the target image adds the characteristic grayscale images of the 980nm, 1120nm, 1450nm and 1940nm bands.

[0065] Step 2, spatial feature extraction:

[0066] Convert the optimally filtered grayscale images of each band into L * a * b * Color space; calculate the L of the minimum bounding rectangle of the target and the surrounding 8 neighborhoods in each band; * a * b * Spatial brightness contrast; the brightness contrast of the 8 neighborhoods is determined by the minimum-maximum normalization method to determine the weight of each neighborhood, and the proportion of the eigenvector corresponding to the band in the dimensionality reduction is determined by the minimum-maximum normalization method; the brightness contrast of the 8 neighborhoods is determined by the Z-Score normalization method to determine the weight;

[0067] Calculate the Hu invariant moments of the target area and the surrounding 8 neighborhoods in the 3*3 area where the target and background are located; calculate the similarity measure of the Hu invariant moments of the target and background in all preferred bands:

[0068]

[0069] In the above formula, Q T,i is the Hu moment of the single-band target area, Q B,i is the Hu moment of the background area;

[0070] The Hu moments of the 8 neighborhoods are normalized by the minimum-maximum method to determine the weight of each region, and the dimension ratio of the eigenvector corresponding to the band in the dimensionality reduction process is also used to determine the weight by the minimum-maximum method; the Hu moments of the 8 neighborhoods are normalized by the Z-Score method to determine the weight;

[0071] Calculate the structural similarity (SSIM) of the target area and its 8 surrounding neighborhoods in terms of brightness, contrast, and structure respectively; calculate the SSIM of the target area and the surrounding 8 neighborhood background areas, and compare the SSIM of each neighborhood area with that of the target area;

[0072] The structural similarity of the 8-neighborhood is determined by the minimum-maximum normalization method to determine the weight of each region, and the proportion of the corresponding feature vector of the band in the dimensionality reduction is also determined by the minimum-maximum normalization method to determine the weight of the band; the visual features of the 8-neighborhood are determined by the Z-Score normalization method;

[0073] Calculate the Bhattacharyya distance between the edge direction histogram of the target area and the edge direction histogram of the surrounding 8 neighborhoods in the 3*3 area where the target and background are located; calculate the mean error of the Bhattacharyya distance between the target area and the surrounding 8 neighborhoods:

[0074]

[0075] In the above formula, h(x T ) represents the normalized edge direction statistical histogram of the target area, h(x B,i ) represents the normalized edge direction statistical histogram of the i-th neighborhood background area around the target;

[0076] The weight of each region is determined by the minimum-maximum normalization method for the structural similarity of the 8-neighborhood, and the weight of the band is determined by the minimum-maximum normalization method based on the proportion of the eigenvector corresponding to the band in the dimensionality reduction; the weight of the structural similarity of the 8-neighborhood is determined by the Z-Score normalization method;

[0077] Step 3, spectral feature extraction:

[0078] Calculate the average spectral information of the sum of the spectral responses of each pixel in each band of the target in the area occupied by the hyperspectral image;

[0079] Obtain the standard spectral channel data of each neighborhood in the 8-neighborhood background around the target;

[0080] According to the average spectrum information of the target area, the cosine value of the whitening spectrum angle between the target area and the surrounding 8 neighboring areas is calculated:

[0081]

[0082] In the above formula, p i ,q i Represent the target p i and background q i The average spectral vector of the region;

[0083] Step 4: Evaluation of spatial spectrum features combined with masking effect:

[0084] The brightness contrast, Hu invariant moment, visual similarity and structural similarity of the target and the surrounding background area processed by the Z-Score normalization method are standardized and weighted, and the spatial weight of the principal component after dimensionality reduction is determined by the minimum-maximum normalization method.

[0085] Determine the spectrum weight value based on the cosine value of the whitened spectrum angle processed by the normalization method;

[0086] The spectral angle between the target and the 8-neighborhood background spectrum is standardized and weighted;

[0087] Standardize and weight the spectral and spatial dimension features and perform joint feature calculations:

[0088]

[0089] In the above formula, w ij is the weight of the area in row i and column j, λ θ is the spectral dimension influencing parameter, t ij -b ij is the spatial dimension influencing parameter, t ij is the feature information of the intermediate target domain, b ij is the background domain feature information;

[0090]

[0091] E tb =|T t -T b |

[0092] In the above formula, E tb is the target spectrum T tWith the background spectrum T b The distance normalization result of

[0093] Collect and organize hyperspectral cube data with known masking levels, use the model to quantitatively score the masking effect of the data, and obtain the scoring range of the model weight under different background conditions;

[0094] The model is used to quantitatively score the masking effect evaluation of known hyperspectral imaging and obtain the setting range of the model weight;

[0095] Step 5: Objective image evaluation based on the hyperspectral anomaly detection model:

[0096] The collected masked target and background hyperspectral data are used as training sets to design a deep learning model and train a hyperspectral anomaly detection model.

[0097] The hyperspectral data to be detected is input into an anomaly detection model associated with the masking degree to perform end-to-end anomaly detection and obtain the output result;

[0098] Based on the different masking levels obtained by training the hyperspectral anomaly detection model, the target and background segmentation thresholds are correspondingly determined, and the highest masking level at which the target is identified as an anomaly by the model is determined;

[0099] Obtain the evaluation results of the objective evaluation model on the hyperspectral image to be detected;

[0100] like Figure 2 As shown, it also includes model training: based on a large amount of outdoor airborne hyperspectral test data, calibrate the target and the degree of obscuration; design and train a hyperspectral-based anomaly detection algorithm through artificial intelligence algorithms (including but not limited to low-rank sparse matrix decomposition, subspace projection, generative adversarial network and stacked autoencoder algorithm); test the model trained in step 5 with the marked image, train and calculate and obtain the segmentation threshold of the target and background in the hyperspectral anomaly detection model with different degrees of obscuration, input the hyperspectral data to be detected into the anomaly detection model associated with the degree of obscuration for end-to-end anomaly detection, and obtain the output result.

[0101] Step 6: Modify the parameter weights:

[0102] According to the masking effect evaluation result of the hyperspectral data obtained in step 5, the masking degree of the hyperspectral masking effect evaluation result combined with the spatial spectrum feature obtained in step 4 is compared;

[0103] Modify the weight of the evaluation model based on the empty spectrum features and expert scoring;

[0104] The final evaluation result of the masking effect of the hyperspectral imaging to be detected is obtained.

Claims

1. A method for evaluating target spatial spectrum characteristics combined with masking effect based on hyperspectral anomaly detection, characterized in that: The steps include: Step 1, characteristic band screening: Analyze hyperspectral imaging data, perform full-channel dimensionality reduction and optimal band screening through band screening and dimensionality reduction algorithms, and use orthogonal transformation; Set the reconstruction threshold to t and select the minimum dimension d′ that makes the equation valid: In the above formula, d is the feature dimension, d′ is the feature dimension after dimensionality reduction, and λ i ,i=1,2,… is the eigenvector; Analyze the material properties of the target and background objects. For the known material properties of the target, use prior knowledge to add the grayscale image spatial feature calculation information of the material's best reflection characteristic band. Step 2, spatial feature extraction: Convert the optimally filtered grayscale images of each band into L * a * b * Color space; calculate the L of the minimum bounding rectangle of the target and the surrounding 8 neighborhoods in each band; * a * b * Spatial brightness contrast; the brightness contrast of the 8 neighborhoods is determined by the minimum-maximum normalization method to determine the weight of each neighborhood, and the proportion of the eigenvector corresponding to the band in the dimensionality reduction is determined by the minimum-maximum normalization method; the brightness contrast of the 8 neighborhoods is determined by the Z-Score normalization method to determine the weight; Calculate the Hu invariant moments of the target area and the surrounding 8 neighborhoods in the 3*3 area where the target and background are located; calculate the similarity measure of the Hu invariant moments of the target and background in all preferred bands: In the above formula, Q T,i is the Hu moment of the single-band target area, Q B,i is the Hu moment of the background area; The Hu moments of the 8 neighborhoods are normalized by the minimum-maximum method to determine the weight of each region, and the dimension ratio of the eigenvector corresponding to the band in the dimensionality reduction process is also used to determine the weight by the minimum-maximum method; the Hu moments of the 8 neighborhoods are normalized by the Z-Score method to determine the weight; Calculate the structural similarity SSIM between the target area and the surrounding 8 neighborhoods in terms of brightness, contrast and structure respectively; Calculate the SSIM of the target and the surrounding 8 neighborhood background areas, and compare them with the target area; The structural similarity of the 8-neighborhood is determined by the minimum-maximum normalization method to determine the weight of each region, and the proportion of the corresponding feature vector of the band in the dimensionality reduction is also determined by the minimum-maximum normalization method to determine the weight of the band; the visual features of the 8-neighborhood are determined by the Z-Score normalization method; Calculate the Bhattacharyya distance between the edge direction histogram of the target area and the edge direction histogram of the surrounding 8 neighborhoods in the 3*3 area where the target and background are located; calculate the mean error of the Bhattacharyya distance between the target area and the surrounding 8 neighborhoods: In the above formula, h(x T ) represents the normalized edge direction statistical histogram of the target area, h(x B,i ) represents the normalized edge direction statistical histogram of the i-th neighborhood background area around the target; The weight of each region is determined by the minimum-maximum normalization method for the structural similarity of the 8-neighborhood, and the weight of the band is determined by the minimum-maximum normalization method based on the proportion of the eigenvector corresponding to the band in the dimensionality reduction; the weight of the structural similarity of the 8-neighborhood is determined by the Z-Score normalization method; Step 3, spectral feature extraction: Calculate the average spectral information of the sum of the spectral responses of each pixel in each band of the target in the area occupied by the hyperspectral image; Obtain the standard spectral channel data of each neighborhood in the 8-neighborhood background around the target; According to the average spectrum information of the target area, the cosine value of the whitening spectrum angle between the target area and the surrounding 8 neighboring areas is calculated: In the above formula, p i ,q i Represent the target p i and background q i The average spectral vector of the region; Step 4: Evaluation of spatial spectrum features combined with masking effect: The brightness contrast, Hu invariant moment, visual similarity and structural similarity of the target and the surrounding background area processed by the Z-Score normalization method are standardized and weighted, and the spatial weight of the principal component after dimensionality reduction is determined by the minimum-maximum normalization method. Determine the spectrum weight value based on the cosine value of the whitened spectrum angle processed by the normalization method; Standardize and weight the spectral and spatial dimension features and perform joint feature calculations: In the above formula, w ij is the weight of the area in row i and column j, λ θ is the spectral dimension influencing parameter, t ij -b ij is the spatial dimension influencing parameter, t ij is the feature information of the intermediate target domain, b ij is the background domain feature information; E tb =|T t -T b | In the above formula, E tb is the target spectrum T t With the background spectrum T b The distance normalization result of Use E tb =|T t -T b The model quantitatively scores the masking effect of known hyperspectral imaging and obtains the setting range of the model weight; Step 5: Objective image evaluation based on the hyperspectral anomaly detection model: The collected masked target and background hyperspectral data are used as training sets to design a deep learning model and train a hyperspectral anomaly detection model. Based on the different masking levels obtained by training the hyperspectral anomaly detection model, the target and background segmentation thresholds are correspondingly determined, and the highest masking level at which the target is identified as an anomaly by the model is determined; Obtain the evaluation results of the objective evaluation model on the hyperspectral image to be detected; Step 6: Modify the parameter weights: According to the masking effect evaluation result of the hyperspectral data obtained in step 5, the masking degree of the hyperspectral masking effect evaluation result combined with the spatial spectrum feature obtained in step 4 is compared; Modify the weight of the evaluation model based on the empty spectrum features and expert scoring; The final evaluation result of the masking effect of the hyperspectral imaging to be detected is obtained.

2. The method for evaluating target spatial spectrum characteristics combined with masking effects based on hyperspectral anomaly detection according to claim 1 is characterized by: The band screening and dimensionality reduction algorithms in step 1 include principal component analysis (PCA), independent component analysis (ICA), and deep learning algorithms.

3. The method for evaluating target spatial spectrum characteristics combined with masking effects based on hyperspectral anomaly detection according to claim 1 is characterized by: The reconstruction threshold in step 1 is t=95%.

4. The method for evaluating target spatial spectrum characteristics combined with masking effect based on hyperspectral anomaly detection according to claim 1 is characterized in that: Step 5 also includes: calibrating the target and the degree of obscuration based on a large amount of outdoor airborne hyperspectral test data; designing and training a hyperspectral-based anomaly detection algorithm through an artificial intelligence algorithm; testing the model trained in step 5 with the marked image, training and calculating and obtaining the segmentation threshold of the target and background in the hyperspectral anomaly detection model for different degrees of obscuration, inputting the hyperspectral data to be detected into the anomaly detection model associated with the degree of obscuration for end-to-end anomaly detection, and obtaining the output results.

5. The method for evaluating target spatial spectrum characteristics combined with masking effect based on hyperspectral anomaly detection according to claim 4 is characterized by: AI algorithms include low-rank sparse matrix factorization, subspace projection, generative adversarial networks, and stacked autoencoders.

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