A numerical regression method for autism assessment scale based on KAN network

Abstract

This invention provides a numerical regression method for autism assessment scales based on KAN networks. By collecting multi-channel electroencephalogram (EEG) data and combining it with behavioral scale scores, and utilizing the feature extraction and modeling capabilities of KAN networks, it achieves high-precision prediction of autism scale scores for autism patients and increases the interpretability of the model, intuitively demonstrating the impact of each feature on the scale score. This method effectively improves the accuracy and consistency of scale scores, reduces reliance on expert manual assessment, and has broad clinical application potential for early screening, diagnostic support, and personalized intervention analysis for autism.

Description

Technical Field

[0001] This invention relates to the field of electroencephalogram (EEG) signal processing technology, and in particular to a numerical regression method for an autism assessment scale based on a KAN network. Background Technology

[0002] Autism Spectrum Disorder (ASD) is a common neurodevelopmental disorder characterized by impairments in social interaction, language communication, and repetitive, stereotyped behaviors. With the increasing incidence of ASD in recent years, early screening and personalized diagnosis play a crucial role in the rehabilitation and intervention of autistic patients. Currently, the diagnosis and assessment of ASD largely rely on clinical observation and scale evaluation. Autism assessment scales (such as ADOS, CARS, and SRS) are commonly used clinical diagnostic tools that can quantify patients' performance in social, language, and behavioral aspects. Although scale evaluation has high diagnostic value, its operation is complex and relies on expert subjective judgment, making it difficult to adapt to the needs of large-scale screening and standardized diagnosis.

[0003] In recent years, with the development of artificial intelligence technology, numerical regression models have been gradually introduced into the prediction and analysis of autism scale scores to address the limitations of existing scale assessments that rely on experts, thereby improving diagnostic efficiency and consistency. Numerical regression models can automatically generate scale scores or perform predictive analysis by analyzing patients' multimodal data, such as behavioral characteristics, language features, and electroencephalogram (EEG) signals. However, traditional machine learning regression methods typically rely heavily on data features and lack model interpretability, making them difficult to apply to autism scale score prediction. Summary of the Invention

[0004] This invention provides a numerical regression method for autism assessment scales based on KAN networks to address the shortcomings of existing technologies.

[0005] In a first aspect, the present invention provides a numerical regression method for an autism assessment scale based on a KAN network, comprising:

[0006] Collect electroencephalogram (EEG) signal data from the target subjects;

[0007] The EEG signal data is preprocessed to obtain preprocessed EEG signal data;

[0008] Extract the EEG features from the preprocessed EEG signal data;

[0009] Using the aforementioned EEG features, the KAN network was trained and optimized to generate a numerical regression model for an autism assessment scale.

[0010] An interpretability analysis was performed on the regression results output by the numerical regression model of the autism assessment scale to obtain the key EEG channel characteristics of the scale scores.

[0011] According to the present invention, a numerical regression method for an autism assessment scale based on a KAN network is provided, which involves collecting electroencephalogram (EEG) signal data of the target subject, including:

[0012] High-density 62-channel 1000Hz resting-state EEG signal data were acquired;

[0013] The autism assessment scale was used to quantify and score the behavioral characteristics of the subjects, forming structured scale data.

[0014] According to the numerical regression method for an autism assessment scale based on a KAN network provided by the present invention, the electroencephalogram (EEG) signal data is preprocessed to obtain preprocessed EEG signal data, including:

[0015] The EEG signal data is downsampled, filtered, and artifact removed sequentially to obtain filtered EEG signal data.

[0016] The filtered EEG signal data is segmented into multiple EEG segments using a fixed time window;

[0017] Discrete Fourier transform and bandpass filtering are performed on the multiple EEG segments respectively to obtain the EEG frequency domain signal, while the EEG time domain signal is preserved;

[0018] The frequency domain EEG signal and the time domain EEG signal are randomly mixed according to the subjects and divided into training set, validation set and test set.

[0019] According to the numerical regression method for an autism assessment scale based on a KAN network provided by the present invention, the electroencephalogram (EEG) features of the preprocessed EEG signal data are extracted, including:

[0020] Based on time-domain and frequency-domain methods, neural activity features are extracted from the preprocessed EEG signal data, and these neural activity features constitute the EEG features.

[0021] According to the present invention, a numerical regression method for an autism assessment scale based on a KAN network is provided, which uses the aforementioned EEG features to train and optimize the KAN network to generate a numerical regression model for an autism assessment scale, including:

[0022] The KAN network is defined as comprising an input layer, multiple hidden layers, and an output layer;

[0023] The KAN network is trained using the aforementioned EEG features with the goal of minimizing the mean squared error.

[0024] The parameters of the KAN network were optimized using backpropagation and gradient descent to obtain the numerical regression model of the autism assessment scale.

[0025] According to the numerical regression method for an autism assessment scale based on a KAN network provided by the present invention, the interpretability analysis of the regression results output by the numerical regression model of the autism assessment scale is performed to obtain the key EEG channel features of the scale scores, including:

[0026] Obtain the regression results of the numerical regression model of the autism assessment scale;

[0027] The regression results were used to analyze the contribution of different features to the scale score, and key EEG channel features were identified by visualizing the KAN weights and function importance.

[0028] Weighted visualization was used to highlight the key EEG channel features.

[0029] Secondly, the present invention also provides a numerical regression system for an autism assessment scale based on a KAN network, comprising:

[0030] The acquisition module is used to acquire electroencephalogram (EEG) signal data from the target subject.

[0031] The preprocessing module is used to preprocess the EEG signal data to obtain preprocessed EEG signal data.

[0032] The extraction module is used to extract the EEG features from the preprocessed EEG signal data;

[0033] The training module is used to train and optimize the KAN network using the EEG features to generate a numerical regression model for an autism assessment scale.

[0034] The regression module is used to perform interpretability analysis on the regression results output by the numerical regression model of the autism assessment scale, and to obtain the key EEG channel features of the scale score.

[0035] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the numerical regression method for autism assessment scales based on KAN networks as described above.

[0036] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the numerical regression method for autism assessment scales based on KAN networks as described above.

[0037] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the numerical regression method for autism assessment scales based on KAN networks as described above.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] This invention utilizes the structured design and nonlinear decomposition capabilities of the KAN network, enabling the model to effectively capture complex features in the EEG data of autistic patients and achieve high-precision scale score prediction. Through feature selection and optimization of the regression model, the model maintains excellent predictive performance even with limited data samples, improving the algorithm's adaptability and practicality.

[0040] This invention significantly enhances the interpretability of the model while improving the accuracy of scale score prediction. By analyzing the feature weights and importance in the KAN network, the impact of different EEG features on scale scores can be intuitively demonstrated, making it easier for clinicians to understand the model's decision-making process and providing a more transparent and feasible reference for personalized intervention and diagnosis.

[0041] The lightweight design of this invention reduces the demand for computing resources, consuming fewer computing resources than traditional neural networks. This allows the model to be deployed on lower-configuration hardware, making it suitable for practical application scenarios. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0043] Figure 1 This is a flowchart illustrating the numerical regression method for autism assessment scales based on KAN networks provided by this invention.

[0044] Figure 2 This is a schematic diagram of the overall structure provided by the present invention;

[0045] Figure 3 This is a schematic diagram of the structure of the numerical regression system for autism assessment scales based on KAN networks provided by the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0047] To address the problems of existing technologies, this invention proposes a numerical regression method for autism assessment scales based on Kolmogorov-Arnold Networks (KAN). This method utilizes KAN networks to effectively model patients' EEG data and scale characteristics. It not only automatically extracts and aggregates key features from EEG data but also provides good model interpretability, thus providing a scientific basis for the assessment and personalized intervention of autism patients. This invention effectively overcomes the limitations of traditional models in large-scale screening through KAN networks, improving the efficiency and accuracy of autism assessment and providing an innovative and practical solution for the early diagnosis and intervention of autism.

[0048] Figure 1 This is a flowchart illustrating the numerical regression method for autism assessment scales based on KAN networks provided in this embodiment of the invention. Figure 1 Shown, including:

[0049] Step 100: Collect EEG signal data from the target subject;

[0050] Step 200: Preprocess the EEG signal data to obtain preprocessed EEG signal data;

[0051] Step 300: Extract the EEG features from the preprocessed EEG signal data;

[0052] Step 400: Using the aforementioned EEG features, train and optimize the KAN network to generate a numerical regression model for the autism assessment scale;

[0053] Step 500: Perform interpretability analysis on the regression results output by the numerical regression model of the autism assessment scale to obtain the key EEG channel features of the scale score.

[0054] Specifically, the numerical regression method for autism assessment scales based on KAN networks proposed in this embodiment of the invention includes the following steps:

[0055] Step 1: Data Collection

[0056] This method uses high-density 62-channel EEG data and autism assessment scale data as the data source for model training and prediction. The EEG data acquisition frequency was set to 1000Hz to ensure high temporal resolution. The scale data includes multiple sub-scores related to ASD symptoms to quantify patients' performance in social, language, and behavioral aspects.

[0057] Step 2: Data Preprocessing

[0058] For EEG signals and scale data, the preprocessing steps include the following parts:

[0059] EEG signal processing: Using downsampling, bandpass filtering, and artifact removal algorithms to remove artifact noise such as electrooculography and electromyography, thereby improving signal quality.

[0060] Time window segmentation: The preprocessed EEG signal is divided into several time segments according to a fixed time window in order to perform feature extraction.

[0061] Frequency domain transformation: Performing discrete Fourier transform on time segment data to highlight frequency domain characteristics.

[0062] Data matrixing of autism assessment scales: The autism assessment scale data is converted into matrix form and standardized to be combined with EEG data features for easier input into subsequent models.

[0063] Step 3: Extraction of EEG features

[0064] In the preprocessed EEG data, various features in the time and frequency domains are extracted, including neural activity features such as power spectrum, entropy, and phase coupling, to construct a rich feature set. This feature set, together with the scale data matrix, constitutes the input features.

[0065] Step 4: KAN Network Model Construction and Training

[0066] Network architecture initialization: Based on the multi-layer structure of the KAN network, the initial model includes an input layer, multiple hidden layers and an output layer, which aims to decompose and regress complex nonlinear features.

[0067] Training and optimization: The KAN network is trained using input feature data. The model objective is to minimize the mean squared error (MSE) to improve the accuracy of scale score prediction.

[0068] Parameter optimization: The parameters of the KAN network are optimized through backpropagation and gradient descent to generate a stable regression model.

[0069] Step 5: Interpretability Analysis

[0070] Based on the regression results of the KAN network, the contribution of each feature to the scale score was analyzed, and the symptom representations corresponding to different features were identified. By analyzing the weights and feature importance of the KAN network, key EEG features affecting the scale score were identified, providing clinicians with diagnostic support and a reference for personalized intervention.

[0071] This invention utilizes the KAN network to perform deep feature extraction and modeling of multi-channel EEG signals and scale data to efficiently predict the scale scores of autism patients, thereby achieving accurate assessment and providing interpretable analysis for clinical practice.

[0072] Based on the above embodiments, step 1 includes:

[0073] 1.1 EEG signal acquisition process

[0074] EEG signal acquisition is usually carried out in a professional EEG acquisition room. Sensors are attached to the surface of the subject's scalp to record the brain's electrophysiological activity data during rest or task states, and the signals acquired in real time are transmitted to a computer for storage.

[0075] 1.2 Preliminary Preparations and Environment Setup

[0076] To ensure signal acquisition quality, subjects are required to remove items that may interfere with signal acquisition, such as glasses and earrings. Additionally, during the acquisition process, subjects will wear a headgear made of a special material to ensure the electrodes fit snugly against the scalp and minimize external interference.

[0077] 1.3 Electrode Arrangement and Conductivity Treatment

[0078] Electrodes corresponding to 62 channels, a reference electrode, and a ground wire were passed through the headgear to ensure a tight fit between the electrodes and the subject's scalp. To further reduce resistance and improve signal acquisition stability, conductive paste was applied to the contact points.

[0079] 1.4 Signal Acquisition and Recording

[0080] The data collection process requires subjects to maintain steady breathing, sit still, and keep their eyes open for 3-5 minutes. The collected EEG signals will be stored along with the subject's basic information for subsequent analysis.

[0081] 1.5 Scale Data Collection

[0082] Autism assessment scales (such as ADOS, CARS, SRS, etc.) were used to quantify and score the behavioral characteristics of the participants, forming structured scale data. The scale data included scores for multiple dimensions such as social skills, language development, and behavioral characteristics.

[0083] Based on the above embodiments, step 2 includes:

[0084] 2.1 Data downsampling and filtering

[0085] First, the acquired EEG data is downsampled to 256Hz to enhance its noise resistance and reduce storage and computational resource consumption. Next, bandpass filtering (0.5-45Hz) is used to remove interference signals from non-EEG frequency bands, effectively preserving the main components of EEG activity. Furthermore, artifact removal algorithms are used to eliminate artifact signals such as electrooculogram (EOG) and electromyogram (EMG) signals from the data to ensure data purity.

[0086] 2.2 Data Fragmentation Processing

[0087] Each subject's complete EEG recording was segmented into 4-second intervals, serving as the basic unit for subsequent processing. During the discrimination process, the voting results of multiple segments were used to generate the subject's final classification judgment, thereby improving the robustness of individual classifications.

[0088] 2.3 Feature Extraction and Matrixing

[0089] Discrete Fourier Transform (DFT) was performed on the segmented EEG signal fragments to enhance frequency domain features. The scale data was matrixed to standardize the scoring data for subsequent model input.

[0090] 2.4 Dataset Partitioning

[0091] All samples were randomly mixed according to the number of people and divided into a training set, a validation set, and a test set (in a ratio of 3:1:1). The training set was used for model training, the validation set was used for parameter optimization, and the test set was used for evaluating the final model performance.

[0092] Based on the above embodiments, step 3 includes:

[0093] Using time and frequency domain methods, neural activity features such as power spectrum, entropy, and phase coupling are extracted. After feature selection, a complete set of EEG features is constructed for predicting scale scores.

[0094] Based on the above embodiments, step 4 includes:

[0095] 4.1 Network Architecture Initialization

[0096] Based on the Kolmogorov-Arnold representation theorem, a KAN network architecture is designed to enable regression by decomposing complex multivariate features. The model's input layer contains EEG features, and the output layer is used to regress and predict scale scores.

[0097] 4.2 Model Training and Optimization

[0098] Based on the mean squared error (MSE) optimization objective, model parameters are adjusted through backpropagation to achieve high-precision prediction of scale scores. The formula used is:

[0099]

[0100] in, The univariate function in KAN is parameterized using B-splines or other learnable functions, enabling the model to learn complex nonlinear relationships.

[0101] Based on the above embodiments, step 5 includes:

[0102] 5.1 Feature Importance Analysis

[0103] Based on the KAN network regression results, the contribution of different features to the scale scores was analyzed. By visualizing the importance of KAN weights and functions, key EEG channels or features were identified, providing interpretive support for the diagnosis of autism.

[0104] 5.2 Feature Visualization and Interpretation

[0105] Weighted visualization techniques (such as transparency mapping) are used to highlight important features, making it easier for clinicians to identify important signals.

[0106] The present invention will now be illustrated with specific embodiments, such as... Figure 2 Shown, including:

[0107] The first step is data acquisition. EEG signal acquisition is typically conducted in a specialized EEG acquisition room. To ensure signal quality, the acquisition environment must be quiet and the power supply voltage stable. Subjects with sparse or soft hair are preferred. Before wearing the EEG acquisition headgear, the scalp must be cleaned and headwear removed to ensure a good electrode fit. The electrodes are accurately attached to specific locations on the subject's scalp, and a special conductive gel is applied to the electrode contacts to reduce contact resistance, ensuring that the impedance of each electrode is below 100kΩ (ideally below 30kΩ). During data acquisition, the subject is required to keep their eyes open, remain silent, relax as much as possible, and breathe steadily. Air conditioning or other methods are used to prevent signal drift caused by sweating. Finally, 3 to 5 minutes of EEG data are collected and stored along with the subject's basic information.

[0108] In this embodiment, the default frequency of the acquired EEG data is 1000Hz, which far exceeds the basic data accuracy requirements of deep neural networks. To enhance noise resistance, downsampling is used to reduce the frequency to 256Hz. Subsequently, a bandpass filter is used to remove noise interference from 0-0.5Hz and above 45Hz. The EEG recordings of each subject are divided into 4-second segments as processing units for subsequent analysis; segments shorter than 4 seconds are discarded. During classification, the classification results of more than half of all segments for an individual are used as the overall classification result. Segments with heavy noise or significant signal drift are removed after manual screening. Then, a Discrete Fourier Transform is performed on each EEG segment to convert the signal from the time domain to the frequency domain, making the features more significant and retaining the effective frequency band of 0.5-45Hz while preserving the original time domain features. The autism assessment scale data is converted into matrix form and standardized to ensure consistency with EEG data features, facilitating its integration into the model input and unified processing. Finally, the samples were randomly mixed by individual (non-fragment) and divided into training, validation and test sets in a 3:1:1 ratio. The former two were used for model training and optimization, and the latter was used for model testing.

[0109] Multiple time-domain and frequency-domain features were extracted from the preprocessed EEG fragment data to establish a rich feature set. The extracted features include: (1) Power spectrum: analyzing the power distribution of each frequency band to reflect the activity state of specific brain regions. (2) Entropy features: used to quantify the complexity of EEG signals and help identify autism-related EEG changes. (3) Phase coupling features: calculating the phase consistency between different frequency bands and channels to capture the synergistic information of cross-regional EEG activity. These features, together with the scale data matrix, constitute the input feature set of the model, aiming to provide a more comprehensive representation of EEG data for accurate regression prediction of scale scores.

[0110] The goal of the model in this invention is to achieve high-precision prediction of autism scale scores. During model training, based on the EEG feature data and scale score labels in the training set, the KAN network parameters are optimized using the backpropagation algorithm to reduce the mean squared error (MSE). During training, a validation set is used to evaluate and adjust hyperparameters (such as learning rate, batch size, dropout rate, etc.) to further optimize the model's regression performance on the test set. Finally, through multiple rounds of iteration and hyperparameter tuning, a balance is achieved between generalization ability, accuracy, and stability, providing a reliable guarantee for subsequent scale score prediction.

[0111] Based on the regression results of the KAN network, interpretability analysis was performed on the features to identify the EEG features that contributed most to the scale scores. By analyzing the feature weights and importance in the KAN network, the association between different EEG features and autism symptoms can be determined. Visualizing the contribution of key features facilitates clinicians' intuitive understanding of the model's predictive basis, providing a scientific reference for diagnostic support and personalized intervention.

[0112] The numerical regression system for autism assessment scales based on KAN networks provided by this invention is described below. The numerical regression system for autism assessment scales based on KAN networks described below can be referred to in correspondence with the numerical regression method for autism assessment scales based on KAN networks described above.

[0113] Figure 3 This is a schematic diagram of the structure of the numerical regression system for autism assessment scales based on KAN networks provided in an embodiment of the present invention, as shown below. Figure 3 As shown, it includes: acquisition module 31, preprocessing module 32, extraction module 33, training module 34, and regression module 35, wherein:

[0114] The acquisition module 31 is used to acquire EEG signal data of the target subject; the preprocessing module 32 is used to preprocess the EEG signal data to obtain preprocessed EEG signal data; the extraction module 33 is used to extract the EEG features of the preprocessed EEG signal data; the training module 34 is used to train and optimize the KAN network using the EEG features to generate a numerical regression model of the autism assessment scale; the regression module 35 is used to perform interpretability analysis on the regression results output by the numerical regression model of the autism assessment scale to obtain the key EEG channel features of the scale score.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A numerical regression method for an autism assessment scale based on a KAN network, characterized in that, include: Collect electroencephalogram (EEG) signal data from the target subjects; The EEG signal data is preprocessed to obtain preprocessed EEG signal data; Extract the EEG features from the preprocessed EEG signal data; Using the aforementioned EEG features, the KAN network was trained and optimized to generate a numerical regression model for an autism assessment scale. An interpretability analysis was performed on the regression results output by the numerical regression model of the autism assessment scale to obtain the key EEG channel characteristics of the scale scores. Extracting the EEG features from the preprocessed EEG signal data includes: Based on time-domain and frequency-domain methods, neural activity features are extracted from the preprocessed EEG signal data, and the neural activity features are used to constitute the EEG features, which include power spectrum, entropy and phase coupling. Using the aforementioned EEG features, the KAN network is trained and optimized to generate a numerical regression model for an autism assessment scale, including: The KAN network is defined as comprising an input layer, multiple hidden layers, and an output layer; The KAN network is trained using the aforementioned EEG features with the goal of minimizing the mean squared error. The parameters of the KAN network were optimized by backpropagation and gradient descent to obtain the numerical regression model of the autism assessment scale. An interpretability analysis was performed on the regression results output by the numerical regression model of the autism assessment scale to obtain key EEG channel features of the scale scores, including: Obtain the regression results of the numerical regression model of the autism assessment scale; The regression results were used to analyze the contribution of different features to the scale score, and key EEG channel features were identified by visualizing the KAN weights and function importance. Weighted visualization was used to highlight the key EEG channel features.

2. The numerical regression method for autism assessment scales based on KAN networks according to claim 1, characterized in that, Collect electroencephalogram (EEG) signal data from the target subjects, including: High-density 62-channel 1000Hz resting-state EEG signal data were acquired; The autism assessment scale was used to quantify and score the behavioral characteristics of the subjects, forming structured scale data.

3. The numerical regression method for autism assessment scales based on KAN networks according to claim 1, characterized in that, The EEG signal data is preprocessed to obtain preprocessed EEG signal data, including: The EEG signal data is downsampled, filtered, and artifact removed sequentially to obtain filtered EEG signal data. The filtered EEG signal data is segmented into multiple EEG segments using a fixed time window; Discrete Fourier transform and bandpass filtering are performed on the multiple EEG segments respectively to obtain the EEG frequency domain signal, while the EEG time domain signal is preserved; The frequency domain EEG signal and the time domain EEG signal are randomly mixed according to the subjects and divided into training set, validation set and test set.

4. A numerical regression system for an autism assessment scale based on a KAN network, based on the numerical regression method for an autism assessment scale based on a KAN network as described in any one of claims 1 to 3, characterized in that, include: The acquisition module is used to acquire electroencephalogram (EEG) signal data from the target subject. The preprocessing module is used to preprocess the EEG signal data to obtain preprocessed EEG signal data. The extraction module is used to extract the EEG features from the preprocessed EEG signal data; The training module is used to train and optimize the KAN network using the EEG features to generate a numerical regression model for an autism assessment scale. The regression module is used to perform interpretability analysis on the regression results output by the numerical regression model of the autism assessment scale, and to obtain the key EEG channel features of the scale score.

5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the numerical regression method for autism assessment scales based on KAN networks as described in any one of claims 1 to 3.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the numerical regression method for autism assessment scales based on KAN networks as described in any one of claims 1 to 3.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the numerical regression method for autism assessment scales based on KAN networks as described in any one of claims 1 to 3.

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