138 results about "Diagonal matrix" patented technology

The invention discloses a federal large model adaptive low-rank fine tuning method and device, computer equipment and a storage medium. The method comprises the following steps: decomposing a low-rank adaptive matrix of a large language model into a server shared matrix and a client private matrix; initializing a private matrix and an adaptive diagonal matrix; the client dynamically trims the low-contribution dimension and adjusts the actual effective rank according to the standard deviation of each element in the adaptive diagonal matrix, and combines the shared matrix and the private matrix to obtain an updated private matrix; the server performs aggregation through a rank-aware aggregation strategy, and performs fine adjustment on the shared matrix by using the public data set to obtain a global model; and deploying the global model to a server and each client. By implementing the method, adaptive fine tuning of the large language model can be efficiently realized, meanwhile, the problems of aggregation interference, low resource utilization rate and insufficient generalization ability in a traditional method are solved, and the technical scheme can be applied to the fields of finance and medical health.

The invention discloses a multi-view clustering method based on tensor feature extraction, and the method comprises the steps: inputting a multi-view data matrix, constructing a similarity matrix of each view through a K-NN algorithm and a Gaussian kernel function, and carrying out the spectral clustering to obtain a sample embedding matrix; performing singular value decomposition on an original data matrix of each view, taking first c left singular vectors to construct a feature embedding matrix, applying 2, 1 norm group sparse constraint on the feature embedding matrix, and connecting a sample embedding matrix through a bigraph to extract features; and normalizing the sample embedded matrix, and reconstructing a block diagonal matrix into a third-order tensor. And integrating the sample embedding matrix, the feature embedding matrix and global tensor learning to construct a target function, and optimizing through an alternating direction multiplier method until convergence. And finally, the normalized samples are embedded into the matrix to form block diagonals to form a consistent similarity graph, and a clustering result is obtained by using an N-Cut or k-means algorithm.

The invention belongs to the related technical field of novel power system analysis, and discloses a stability analysis method and analysis system for a multi-following-network-construction-type converter system, and the stability analysis method comprises the steps: calculating admittance matrixes Qeq and Qml used for evaluating the stability of a following-network-type converter; and performing joint diagonalization processing on the matrixes Qeq and Qml to obtain corresponding diagonal matrixes Lambda eq and Lambda ml, extracting diagonal elements of the matrixes to form n groups of characteristic parameters (Lambda i and mu i), judging whether the (Lambda i and mu i XRPC0) are positioned above the critical stability curve of the following grid type converter or not, if so, indicating that the system is stable, and if not, indicating that the system is unstable. Based on the method, the stability criterion of the multi-following-network-construction-type converter system can be simplified, and the influence of different control modes of the construction-type converter on the stability of the following-network-type equipment can be clarified, so that the reactive power control strategy of the construction-type converter can be optimized, and the supporting capability of the construction-type converter on the power grid can be enhanced.

The invention relates to the technical field of array signal processing, in particular to a space-frequency power inversion anti-interference method fusing SMI-LDL decomposition. The problems that an existing space-time anti-interference technology is high in calculation complexity, and real-time processing is difficult to achieve in limited resources of a navigation receiver are mainly solved. The method comprises the following steps: firstly, converting a radio frequency signal received by an array into a digital intermediate frequency signal and carrying out sliding window partitioning processing; windowing the data block and performing FFT (Fast Fourier Transform) to obtain a frequency domain array; then calculating an auto-covariance matrix R of other array elements except the reference array element and a cross-covariance matrix r of the reference array element and other array elements; lDL decomposition is carried out on the auto-covariance matrix to obtain a lower triangular matrix L and a diagonal matrix D, and inversion is carried out on the lower triangular matrix L and the diagonal matrix D respectively, so that huge operand caused by direct inversion of the covariance matrix is avoided; and finally, calculating an optimal weighting vector according to a power inversion criterion, and performing spatial filtering on the frequency domain data.

The invention relates to the technical field of deep neural network training, and discloses a deep neural network training diagnosis method and system based on gradient visualization and loss curved surface analysis, and the method comprises the steps: obtaining a parameter snapshot of a neural network trained to t-th iteration, sampling k random detection vectors, and calculating a Hessian vector product; performing Lanczos iteration on each random detection vector to obtain k symmetric tridiagonal matrixes and calculating a characteristic value density spectrum; mapping the k symmetric tridiagonal matrixes into orthogonal projection base vectors, constructing a two-dimensional projection plane, determining a saddle point state according to the integral of the characteristic value density spectrum in a negative value region, determining a flat region according to the peak value of the characteristic value density spectrum in a zero value region, and determining a sharp minimum value according to the peak value of the characteristic value density spectrum in a positive value region; according to the method, the descending path with the steepest curvature can be captured, and the dominant mode of the dynamics can be optimized, so that the projected loss curved surface truly reflects the geometric structure change in the training process, and the pathological diagnosis of the training process based on the second-order geometric information is realized.

The invention discloses a space-time elastic weight consolidated edge federal continuous learning method, which is applied to a system comprising a server and a plurality of edge devices, is used for processing space-time heterogeneity time sequence data, and comprises the following steps: initializing training, broadcasting a previous time sequence global time Fisher diagonal matrix (the first time sequence is not broadcasted, the second time sequence is not broadcasted, and the third time sequence is not broadcasted) by the server; however, the global model needs to be randomly initialized and broadcasted); in the model training stage, based on local data, a global time Fisher diagonal matrix and the like, an edge device updates a local model through a loss function containing a time / space regular term, calculates a local space Fisher diagonal matrix, uploads the local space Fisher diagonal matrix, and then a server weights and aggregates the global model according to the data volume and issues the global model, and circulates until convergence; and in the global time Fisher diagonal matrix calculation stage, the equipment calculates a local time Fisher diagonal matrix based on a convergence model, and uploads and aggregates the local time Fisher diagonal matrix for the next time sequence. Historical data does not need to be stored, original data does not need to be transmitted, storage calculation / communication overhead is reduced, privacy is protected, and the model convergence speed and precision are improved.

The invention discloses a hybrid antenna array direction of arrival estimation method based on noise marginalization SBL. The method comprises the following steps: initializing system parameters and a sampling grid set; establishing a hybrid antenna array receiving signal model, and initializing a hybrid beam forming matrix into a block diagonal matrix meeting constant modulus constraint; constructing a hierarchical probability model under a Bayesian framework, and introducing a noise precision parameter into signal prior; integral operation is carried out on the noise precision parameter, so that the signal posterior distribution is converted into student t distribution; an objective function is constructed, an expectation maximization algorithm is adopted to iteratively update a signal energy spectrum, and the process does not involve noise parameter estimation; an alternating iteration strategy is adopted, the signal energy is fixedly updated through inner circulation, and optimization is performed through a gradient descent method after outer circulation is fixed; after convergence, constructing a target function of off-grid estimation by reconstructing a covariance matrix; and searching the off-grid direction of the maximized objective function near a spectrum peak to obtain a final DOA estimation value.

The invention discloses a method for generating an amplitude preparation circuit and a quantum state preparation method and device, and the method comprises the steps: setting a main diagonal element of a block matrix as a to-be-prepared amplitude, and setting other elements as 0, so that the block matrix is equivalent to a diagonal matrix, thereby facilitating the construction of a unitary matrix through employing the block matrix, and in the unitary matrix, the unitary matrix is not damaged; the to-be-prepared amplitude is arranged at the upper left corner of the unitary matrix, so that the amplitude preparation of the to-be-prepared quantum state can be carried out by utilizing a circuit corresponding to the unitary matrix, and the preparation of the to-be-prepared quantum state by utilizing a large-scale operator can also be understood, thereby being beneficial to more efficiently and accurately preparing the to-be-prepared quantum state.

The invention discloses a field programmable gate array (FPGA) implementation method for Hermite matrix eigenvalue decomposition, which comprises the following steps of: performing real number processing on a Hermite matrix according to a corresponding relationship between the Hermite matrix and eigenvalues and eigenvectors; grouping the dimension real matrix obtained by the real number processing; calculating rotation matrixes of diagonal units and non-diagonal units; performing Jacobi rotation operation on the diagonal units and the non-diagonal units, and updating the feature vector matrix according to a rotation matrix; after a group of Jacobi rotation is completed, data exchange is carried out according to grouping of a parallel Jacobi algorithm; and multi-stage cleaning can be carried out according to actual requirements. According to the method, a parallel Jacobi algorithm is selected, a series of matrix rotation is adopted, the matrix is converted into a diagonal matrix, and therefore the eigenvalue and the eigenvector of the matrix are calculated. According to the method, the parallel computing advantages of the FPGA and the Jacobi algorithm are fully utilized, and the real-time performance of the algorithm is effectively improved.

This invention discloses a GNSS interference source localization method based on ADS-B data. The method involves acquiring ADS-B data, saving data points affected by GNSS interference, and, if no NIC is available, constructing ADS-B data with a NIC. The message data is then sorted by ICAO and timestamp. A diagonal matrix W is calculated based on the ICAO, timestamp, NIC, a table showing the correspondence between NIC and received interference power, and the hyperparameter value τ. A residual vector R is calculated based on the message data and the optimization vector, and the optimized vector is then output. This invention analyzes large-scale aviation ADS-B data, sorts and classifies the original message data to determine whether flights are subject to GNSS interference, and abstracts the interference source localization problem into a least-squares problem. An optimization function is constructed, and an iterative optimization algorithm is used to calculate the possible GNSS interference source locations and transmission power, thus more efficiently locating GNSS interference sources.

A computer-implemented method for finetuning a neural network. The method includes: providing an input to a layer of the neural network; determining a block-diagonal matrix; determining a first matrix by multiplying the block-diagonal matrix with a weight matrix of the layer, wherein the result of the multiplication is obtained by multiplying at least a plurality of blocks of the block-diagonal matrix with a respective part of the weight matrix in parallel computing operations and combining the result to form the first matrix; determining an output of the layer by multiplying the first matrix with the input of the layer; determining an output of the neural network based on the output of the layer; adapting elements of the block-diagonal matrix based on a difference of the output of the neural network and a desired output with respect to the input datum.

A system includes a machine-learning model implemented on a data processing apparatus, which features a parallel processor with a memory hierarchy. The machine-learning model is a recurrent neural network (RNN) with a multi-head architecture, comprising multiple sub- vectors that process parallel data streams. The RNN's weight matrix is structured as a block-diagonal matrix, allowing for parallel processing of the sub-vectors. A fused computational kernel executes an entire time-series processing loop for the multi-head RNN, maintaining the weight matrix blocks in on-chip memory and performing matrix multiplications and element-wise operations for each sub-vector in a single kernel execution.

The invention discloses a channel estimation circuit and a channel estimation method based on memristors, and relates to the field of wireless communication and integrated circuits, and the circuit comprises three memristor arrays which are respectively used for mapping a first real number matrix, a second real number matrix and a diagonal matrix, the first real number matrix is composed of absolute values of non-positive elements of a channel estimation pilot frequency sequence cross-correlation mapping matrix, and the second real number matrix is composed of non-diagonal elements in non-negative elements of the channel estimation pilot frequency sequence cross-correlation mapping matrix; the diagonal matrix is composed of diagonal elements in non-negative elements of a channel estimation pilot frequency sequence cross-correlation mapping matrix; the switch module controls the memristor to be connected to or disconnected from the circuit; the inverter array is connected between the first memristor array and the second memristor array and is used for realizing matrix subtraction and positive and negative value compensation; the operational amplifier array is connected with the row lines and the column lines of the memristor array to form a feedback loop, channel estimation values are output, the integration level is high, the calculation speed is high, and energy consumption is low.

The application discloses a kind of based on Koopman and CEF model electric carbon collaborative scheduling method, system, medium and equipment, belong to electric power system optimization field, the method is: according to CEF model obtains the original expression of carbon intensity constraint;According to branch outflow power distribution matrix and diagonal matrix, reconstruct the original expression, obtain the nonlinear mapping relationship expression between node carbon emission intensity and node power injection, and according to low rank kernel approximation improved Koopman operator and node power injection dataset are processed, obtain linear mapping relationship expression;According to linear mapping relationship expression, construct electric carbon collaborative scheduling model, and based on electric power system current operation data, solve scheduling model, obtain scheduling optimization strategy;According to the strategy, regulate electric power system operation, complete electric carbon collaborative scheduling.Therefore, by implementing the present application, the problem of insufficient timeliness of electric power system in combination with carbon emission flow for electric carbon collaborative scheduling in the prior art can be solved.

Disclosed is an operation method for executing an addition operation on quantized matrices. This operation method comprises the steps in which: an NPU matrix multiplication unit executes a matrix multiplication operation on a first matrix and a second matrix, wherein the first matrix has a size of R0*2C0 and is obtained by concatenating a first input tensor and a second input tensor, each of which is composed of quantized values and has a size of R0*C0, and the second matrix is obtained by concatenating a first diagonal matrix having a size of C0*C0 and having all main diagonal element values equal to integer N1 and a second diagonal matrix having a size of C0*C0 and having all main diagonal element values equal to integer N2; and an NPU vector processing unit calculates elements of a non-quantized tensor obtainable by adding the second input tensor to the first input tensor, by adding real number B to a product of real number R and a third matrix calculated by the matrix multiplication operation.

The application provides a pulse interference suppression method and related equipment, and relates to the technical field of wireless communication, and the method comprises the following steps: detecting pulse interference points by performing pulse interference detection on a to-be-processed signal sequence based on a Myriad filter; and performing local smoothing repair on the pulse interference points based on an improved local weighted regression algorithm to obtain a smoothed signal sequence; the improved local weighted regression algorithm is an improved robust repair weight diagonal matrix based on a probability density function of a fitted Gaussian distribution; and the probability density function of the fitted Gaussian distribution is determined according to the amplitude of non-pulse interference points in the to-be-processed signal sequence. The application reduces the calculation complexity and improves the noise reduction efficiency through pulse interference detection and local smoothing repair; and the robust repair weight diagonal matrix is introduced based on the LOESS method, so that the noise reduction effect is improved.

The application relates to the technical field of audio processing, and provides a speech dereverberation method and device, computer equipment, a readable storage medium and a program product. The method comprises the following steps: performing two-stage filter dereverberation operation according to a plurality of speech frequency domain delay signals, a first-stage observation equation and a second-stage observation equation to obtain an estimated value of a second-stage current frame speech frequency domain dereverberation signal, so as to obtain a speech time domain dereverberation signal of a current frame; when performing the current-stage filter dereverberation operation, obtaining a current-stage state space observation value of the current frame according to the plurality of speech frequency domain delay signals, the current-stage observation equation and spatial regression coefficients required in the current stage; obtaining a priori estimation value of a current-stage error covariance diagonal matrix of the current frame according to a posteriori estimation value of a previous frame error covariance diagonal matrix in the current stage; and obtaining an estimated value of a current-stage speech frequency domain dereverberation signal in the current stage according to the current-stage state space observation value. The method can reduce the occupied storage resources.

The application discloses an optical matrix vector multiplier based on a unitary matrix-diagonal matrix decomposition. The multiplier comprises a Mach-Zehnder interferometer array for realizing a synthetic unitary matrix Omega and a modulation unit for realizing a corresponding diagonal matrix Sigma, wherein a target weight matrix M satisfies a decomposition form of M=ΩΣ. The method fuses two unitary matrices required for mapping in a traditional singular value decomposition into a single synthetic unitary matrix Omega, so that a unitary transformation can be completed by only one interferometer array of optical hardware, and a complete matrix multiplication is realized in cooperation with the modulation unit. Through algorithm-hardware collaborative design, the number of basic optical interference units required is significantly reduced, the hardware complexity, manufacturing cost and system power consumption of the optical neural network are greatly reduced while the computing performance is maintained, and an effective solution is provided for efficient optical computing acceleration of artificial intelligence.

The application provides a multi-signal spectrum separation method, device, equipment and medium, which is used in the technical field of radio monitoring and can solve the technical problem of low spectrum separation accuracy caused by the limitation of channel number and poor adaptability of directional antenna array. The method comprises the following steps: calculating a real-time conjugate transpose signal and a time-delay conjugate transpose signal under multiple different time delays according to a real-time composite signal, and determining a corresponding covariance matrix and multiple pseudo-covariance matrices; determining a matrix product according to the conjugate transpose matrix of an initial demixing matrix, obtaining multiple initial product matrices, and judging whether the initial product matrices are all approximate diagonal matrices; iteratively processing the initial demixing matrix to obtain a target demixing matrix; determining a corresponding array manifold matrix based on the target demixing matrix, and determining the signal amplitude of each signal at the frequency point corresponding to the array manifold matrix and the mixed amplitude and phase vector corresponding to each frequency point; thus, the spectrum separation accuracy is improved.

The embodiment of the invention discloses a data processing method, a quantum circuit generation method and a related device, and relates to the technical field of quantum computing, a to-be-processed data set can be utilized to generate a difference matrix, the difference matrix can be converted into a diagonal matrix, and then a unitary matrix corresponding to the diagonal matrix is constructed; then, a quantum circuit can be generated based on the unitary matrix, and the generated quantum circuit can prepare a diagonal matrix, thereby obtaining an element target value in the diagonal matrix, and the element target value in the diagonal matrix indicates a processing result for the to-be-processed data set. According to the method, the to-be-processed data set is converted into the difference matrix, so that the to-be-processed data set can be processed by using the quantum circuit, and the difference matrix is converted into the diagonal matrix, and the diagonal matrix is used for constructing the unitary matrix, so that the finally obtained quantum circuit can be simpler. In this way, the processing of the data to be processed can be more efficient and accurate.

The application discloses a spectrum graph convolution network heterogeneous graph representation learning method based on path collaborative graph enhancement, relates to the technical field of graph neural networks, and comprises the following steps: obtaining to-be-processed heterogeneous graph data, projecting node features of different types into a unified latent feature space by using type-aware linear transformation; calculating structure prior weights; constructing a path collaborative graph, learning path interaction weights by using a graph attention network; constructing a collaborative polynomial spectrum filter; performing spectrum graph convolution based on path collaborative graph enhancement, introducing a learnable positive definite diagonal matrix into the collaborative polynomial spectrum filter, performing weighting and feature transformation on the filtered node features, and obtaining final node representation. The application can learn the importance of meta-paths in a fine-grained manner and capture semantic interaction between meta-paths, solves the problems that existing spectrum heterogeneous graph convolution cannot distinguish the importance of fine-grained paths and lacks semantic collaboration, effectively improves the classification performance of heterogeneous graph nodes, and has a good application prospect.

The application discloses a method for calculating equivalent resistance based on a many-to-many mode, which comprises: filling a conductance matrix of a corresponding resistance network to obtain an extended matrix based on a node to be solved of an equivalent resistance, preordering the extended matrix to determine a permutation matrix P; performing LDL T decomposition on the extended matrix to calculate a lower triangular matrix L and a diagonal matrix D required for calculating the equivalent resistance and determining a non-zero element position in a sparse matrix F; calculating a matrix element of a target matrix Z according to the non-zero element position in the sparse matrix F and the lower triangular matrix L and the diagonal matrix D; and calculating the equivalent resistance according to the target matrix Z. For this purpose, the application does not need to solve all matrix elements, but only needs to calculate matrix elements consistent with the non-zero element position distribution of F, i.e. Z, so as to effectively reduce the calculation amount. Since Z is a sparse matrix and a general dense matrix, the total calculation amount is greatly reduced due to the fewer non-zero elements of Z.

The invention relates to a positioning method and device, electronic equipment and a computer storage medium. The method comprises the following steps: acquiring a variance-covariance matrix of a carrier phase observation value acquired by the positioning device; performing LD transformation on the matrix to obtain a lower triangular matrix and a diagonal matrix; and storing the effective elements in the lower triangular matrix and the effective elements in the diagonal matrix into the RAM, loading the effective elements in the lower triangular matrix and the diagonal matrix and the unit matrix from the RAM by adopting the DAM, and calculating according to the effective elements in the lower triangular matrix and the diagonal matrix and the unit matrix by adopting a decorrelation algorithm to obtain a positioning result. According to the method, only the effective elements in the lower triangular matrix and the diagonal matrix are stored, storage is reduced, reading and calculation are facilitated, meanwhile, the effective elements in the lower triangular matrix, the effective elements in the diagonal matrix and the unit matrix are stored in the RAM through the DAM, system control of a CPU is reduced, calculation power is increased, and efficiency is improved.

This invention proposes a 3D Gaussian splatter style transfer method based on learning orthogonal color bases. The method includes: obtaining a local mixing coefficient matrix, a global color base matrix, and a singular value diagonal matrix through a pre-trained 3D Gaussian splatter model, while simultaneously acquiring the original content image; obtaining a final global color base matrix through coarse-stage global color base optimization; refining the local mixing coefficients through a fine-stage local mixing coefficient matrix; updating the pre-trained 3D Gaussian splatter model using the final global color base matrix and the final local mixing coefficient matrix; and generating style transfer results using the stylized 3D Gaussian splatter model. This invention transforms high-dimensional color space optimization into low-parameter subspace optimization through SVD decomposition, significantly improving the optimization speed.

The invention relates to an underground 5G Massive MIMO (Multiple Input Multiple Output) transmitting antenna selection method. The selection method comprises the following steps: determining an underground 5G Massive MIMO transmitting antenna selection model according to a target problem, wherein the target problem comprises maximization of a sum capacity, maximization of a minimum characteristic value and maximization of an F norm of a transmission channel; introducing a diagonal matrix, and converting the selection model into a convex optimization problem model; and calculating and solving the convex optimization problem model to obtain an MIMO transmitting antenna selection scheme. According to the underground 5G Massive MIMO transmitting antenna selection method, the method can be used for maximizing the sum capacity, maximizing the minimum characteristic value, maximizing the F norm of the transmission channel and the like, and the underground 5G Massive MIMO transmitting antenna selection method has certain universality, low operation complexity and better solvability.

The application discloses a channel estimation method and related device, wherein the method comprises: performing minimum mean square error (MMSE) channel estimation based on the product of the first amplitude factor and the first noise power of the first dimension, the first channel autocorrelation matrix of the first dimension, and the first diagonal matrix to obtain the channel estimation value matrix of the first dimension; wherein the channel estimation value matrix of the first dimension is obtained by performing MMSE channel estimation in the non-last step of the multi-dimensional step-by-step MMSE channel estimation; the first amplitude factor is a positive number less than or equal to 1; and performing MMSE channel estimation based on the channel estimation value matrix of the first dimension, the second channel autocorrelation matrix of the last dimension, the second noise power and the second diagonal matrix to obtain the multi-dimensional channel estimation value matrix. The method can improve the performance of the multi-dimensional step-by-step MMSE channel estimation.

The invention relates to the technical field of risk prediction, and provides an electricity consumption risk prediction method and device in the electrical and mechanical industry, electronic equipment and a storage medium. According to the implementation scheme, the method comprises the following steps: based on historical input-output data and historical electricity consumption data of each product department in a work period in an electromechanical industry input-output table, calculating a Legon inverse matrix and an electricity consumption coefficient diagonal matrix; performing matrix multiplication on the Legon inverse matrix, the power consumption coefficient diagonal matrix and the outlet change column vector to obtain the total energy consumption change amount; taking the total energy consumption variation as the input of a target risk prediction model to obtain a risk probability value output by the target risk prediction model; and based on the risk probability value, determining an electricity consumption risk prediction result of the electromechanical industry in the prediction period. According to the embodiment of the invention, the method achieves the accurate prediction of the fluctuation of the power consumption of the industry and the reliable evaluation of the potential risk of the fluctuation under the change of the tax.

A computer-implemented method for memory management in a computer system configured for generating a signature of a binary data message m using a key B of a predetermined lattice-based structure is proposed, which comprises: determining coefficients of a 2×2 signature generation matrix SG, wherein the non-diagonal coefficients of the signature generation matrix SG are complex polynomials with a non-zero imaginary part, and the diagonal coefficients of the signature generation matrix SG are real polynomials; and determining a LDL representation of the signature generation matrix SG according to which SG is represented by a matrix product L.D.L*, wherein L is a 2×2 lower triangular matrix with ones on the diagonal, D is a 2×2 diagonal matrix, and L* is the adjoint of L; wherein the storing in a memory buffer of the computer system of the coefficients of the signature generation matrix SG and the coefficients of the matrices of the LDL representation is managed based on that the signature generation matrix SG has real diagonal coefficients, and the memory buffer is used alternatively to store the coefficients of the signature generation matrix SG or the coefficients of the matrix D of the LDL representation.

The invention provides a test paper automatic detection method, electronic equipment and a storage medium, and belongs to the technical field of test paper instant detection. The detection method comprises the following steps: acquiring a plurality of detection points and color characteristics of the detection points in a test paper reaction region; and calculating the distance between the detection point and the center of the reaction area so as to endow the detection point with a decision weight. And combining the color features of the plurality of detection points into an observation matrix, and combining the basis matrixes of the plurality of detection points based on the decision weight into a block diagonal matrix. And based on the observation matrix and the block diagonal matrix, obtaining an optimal coefficient matrix of the color features of the detection points so as to reconstruct the color features of the detection points. And respectively establishing a background model of each detection point, and verifying the consistency of each background model so as to filter the color of the test paper. And estimating the concentration of the detection point according to the color feature of the detection point, and carrying out substance identification through a discrimination function and a decision weight. And outputting the concentration and name of the substance in the reaction area. According to the method, the accuracy of a detection result can be improved.

Systems and methods are provided for simplifying the generation / application of machine learning models in a network or other deployment of elements or objects of interest. Data (which can be multi-variate, high dimensional, time-series) regarding or associated with such objects may be represented as random matrices, which can then be transformed diagonal variance matrices. Upper and lower confidence bounds can be determined with which to test similarity between the now, diagonal matrices. Based on the determined similarity or dissimilarity, one or more clusters of matrices, representative of the objects of interest, can be determined. In this way, machine learning models can be trained and developed to be operationalized for the clustered matrices (objects) rather than individual matrices (objects).