CN111710366A - Method for processing arbitrary-order segmented polynomial signals - Google Patents
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- CN111710366A CN111710366A CN202010575631.1A CN202010575631A CN111710366A CN 111710366 A CN111710366 A CN 111710366A CN 202010575631 A CN202010575631 A CN 202010575631A CN 111710366 A CN111710366 A CN 111710366A
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Abstract
The invention relates to a method for processing a piecewise polynomial signal of any order, which aims to solve the problem of poor segmentation effect of the traditional piecewise polynomial signal. The invention provides a method for processing a piecewise polynomial signal of any order, which comprises the following steps: firstly, extracting signals from an atomic force microscope or a high-throughput genome sequencer; then, carrying out segmentation fitting on the signals according to a function model, carrying out dynamic planning and matrix decomposition through a computer algorithm program, and drawing new signals after segmentation fitting according to the positions of output segmentation values; and finally, according to the position of the breakpoint of the new signal detection, segmenting a proper region required by extension length and continuous length estimation to finish protein unfolding, or segmenting a proper region required by Young modulus estimation, or detecting a copy number variation interval and a variation type.
Description
Technical Field
The invention relates to a method for segmenting and fitting signals by using piecewise polynomial of any order.
Background
In engineering practice and scientific experiments, it is often necessary to fit experimental data, where polynomial curve fitting is a more common data fitting method. When the number of data points is large, the polynomial order is too low, the fitting accuracy and effect are not ideal, the curve order needs to be increased to improve the fitting accuracy and effect, and the higher order brings computational complexity and other disadvantages.
The existing high-order piecewise polynomial signal analysis appears in many scientific fields, such as data analysis of protein folding by Atomic Force Microscope (AFM), measurement of young modulus, and detection of Copy Number Variation (CNV) by Next Generation Sequencing (NGS), and the key of signal analysis is to segment the signal, i.e. breakpoint detection, and once segmentation is determined, each segment can be analyzed (curve fitting, parameter estimation, etc.). The conventional signal segmentation and fitting usually adopts a classical segmentation algorithm (CBS), but the segmentation algorithm has a poor segmentation effect, cannot quickly find a breakpoint, and is sensitive to noise.
Disclosure of Invention
The invention aims to provide a method for processing a piecewise polynomial signal of any order, which is used for overcoming the problem of poor segmentation effect of the traditional piecewise polynomial signal.
The technical scheme adopted by the invention is as follows: a method for processing an arbitrary-order segmented polynomial signal, comprising the steps of:
1) signal acquisition
Acquiring original signal y output by atomic force microscope0Carrying out normalization processing to obtain a signal y; or obtaining a short-reading fasta format file output by the high-throughput genome sequencer, and extracting a signal y from the short-reading fasta format file;
2) carrying out segmentation fitting on the signal y obtained in the step 1) according to a function model as follows:
the function model is
Wherein:
v is a signal dividing position;
(vk-1+1，vk) Is the fitting error of the k-th segment in the signal y;
lambda is a penalty value of a given parameter, and any positive number is taken for adjusting the quality of segmentation fitting;
k is the number of signal segments;
3) initialization of vector sum matrix
The optimized value vector Φ (1) ═ 0;
the partition value position vector q {1} - [ ];
vector S ═ 1;
matrix array
Matrix Ω (1) ═ G0]；
Vector e (1) ═ 0;
4) circularly executing the steps A1 to A7, wherein the loop flag i is 1 (N-P), and the loop is circulated for (N-P) times, wherein N is the length of the signal y, P is the polynomial order,
A1) and (4) reassigning each element t in the vector S according to the following formula to obtain the vector
The elements in (1):
A2) according to the vector after reassignment
Matrix solving
Where j is the index position of the vector S;
A3) according to a matrix
Re-dividing the signal y and locating the new division
Storing the position vector q { i +1} of the segmentation value;
A4) selecting a mark position j meeting the conditions of the first and the second simultaneously, reserving corresponding position elements in a matrix omega, a matrix e, a matrix B and a matrix S meeting the conditions of the mark position j, and deleting the other elements; wherein:
the condition is as follows: j is more than or equal to 1 and less than or equal to S, and S is the number of elements in the vector S
A5) respectively calculating three variables of A, Gamma and rho according to the reserved elements;
A＝[α1，α2，...，αs]
wherein:
li＝i-S(j)+2+P；
a is a matrix of P +1 rows and s columns, each column having the form of α;
l is the length of the sub-signal, and the calculation formula of l in each column is i-S (j) +2+ P;
A6) according to three variables of A, gamma and rho, respectively updating a matrix B, a matrix omega and a vector e according to the following formula;
B＝B+yv+1A
e＝e+ρ⊙(yv+11s-(T⊙BT)1P+1)2
A7) obtain an updated matrix B of
The matrix omega is [ omega, G ]0]And the vector e is [ e, O]And inserts a loop flag i into the vector S retained in step a4) so that the vector S is [ S, i + 1]]；
5) Taking the (N +1-P) th bit in the phi vector as an output optimized value, adding a numerical value (P-1) to the (N +1-P) th bit in the q vector as an output segmentation value position, wherein the output segmentation value position is an actual segmentation position of the signal segmentation position upsilon; according to the position of the output segmentation value, drawing a new signal y after segmentation fitting1；
6) According to the new signal y1Finding out two breakpoint positions, and segmenting out a proper region required by the estimation of the straightening length and the continuous length;
or, according to the new signal y1Finding two breakpoint positions, and segmenting a proper region required by Young modulus estimation;
or, according to the new signal y1And detecting the copy number variation interval and the variation type.
Further, the original signal y output by the atomic force microscope in step 1)0As a set of force curves y0(z) wherein y0Is the interaction force between the probe and the sample, and z is the offset distance; the signal y in the step (1) is an original signal y output by an atomic force microscope0The normalized value is obtained by linear interpolation.
Further, in step 1), the specific way to extract the signal y from the short-read fasta format file is as follows: firstly, a SAM format file or a compressed BAM format file is obtained from a short-read fasta format file through comparison software, and then a reading depth signal y is obtained from the SAM format file or the compressed BAM format file by utilizing a calculation program. The comparison software is MAQ software or bowtie software, and the calculation program is samtools program;
further, in the curve of the force0(z) when the process is performed, the polynomial order P in step 4) is 2 or 3.
Further, when detecting copy number variation on data of the high throughput genome sequencer, the polynomial order P in step 4) takes 0.
Furthermore, the present invention can process 0 to any order segmented polynomial signals, and the processing of higher order segmented polynomial signals is better. Meanwhile, the invention can reduce the cost of the atomic force microscope and the high-throughput sequencing data analysis.
Compared with the prior art, the invention has the following beneficial effects.
The invention relates to a method for processing a piecewise polynomial signal of any order, which is based on a least square sparse model punished by an L-0 norm, improves the fidelity of fitting by a least square method, optimizes the number of partitions punished by the L-0 norm, obtains the optimal partition (namely the optimal solution) by a dynamic planning and matrix decomposition method, accelerates the operation speed and shortens the operation time.
The processing method of the segmented polynomial signal of any order can realize polynomial fitting of any order, namely P can be any nonnegative integer, for example, the value of P is 2 or 3 in the force curve analysis of an atomic force microscope, the value of P is 0 in the analysis of the copy number variation of the next generation sequencing technology data detection, and the application range is wide.
The processing method of the random-order segmented polynomial signal has good segmentation effect in atomic force microscope protein unfolding data analysis and Young modulus measurement, improves the accuracy of breakpoint detection, and reduces the cost of data analysis; the detection accuracy of the copy number variation is improved by using a detection technology based on a new generation sequencing technology.
Drawings
FIG. 1 is an algorithm program diagram of dynamic programming and matrix decomposition according to the present invention.
FIG. 2 is a signal diagram showing unfolding of the protein in example 1 of the present invention.
FIG. 3 is a graph showing the results of the segmentation and fitting process for unfolding protein in example 1, wherein a plurality of line segments parallel to the vertical axis are the segmentation positions for unfolding protein.
FIG. 4 is a graph showing comparative analysis of the unfolded signal of the protein and the result of the segmentation-fitting process in example 1 of the present invention, in which the abscissa is the probe offset distance and the ordinate is the interaction force between the probe and the sample.
FIG. 5 is a data analysis diagram of the conventional software Fordis in example 1.
FIG. 6 is a graph of the yeast stress test signal for Young's modulus measurement in example 2.
Fig. 7 is a diagram showing the result of the segmentation and fitting process for measuring the young's modulus in embodiment 2 of the present invention, in which two asterisk positions are segmentation positions.
FIG. 8 is a graph showing the results of signal fitting errors in the measurement of Young's modulus in example 2.
Fig. 9 is a graph of comparative analyses of the yeast stress test signal, the result of the division fitting process, and the result of the signal fitting error (magnified ten times) for measuring young's modulus in example 2, in which the abscissa is the probe offset distance and the ordinate is the interaction force between the probe and the sample.
FIG. 10 is a signal diagram of copy number variation detection based on next generation sequencing technology in example 3 of the present invention.
FIG. 11 is a graph showing the results of detecting copy number variation based on the circular binary partitioning (CBS) algorithm in example 3.
FIG. 12 is a diagram showing the results of detecting copy number variation based on the next-generation sequencing technology in example 3 of the present invention.
FIG. 13 is a graph of a comparative analysis of FIGS. 10, 11 and 12 in detecting copy number variation in example 3, wherein the abscissa is locus and the ordinate is read depth.
Detailed Description
The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention and the accompanying drawings. It will be clear that the described embodiments are not limitative of the invention.
Example 1
The invention can analyze the data of protein unfolding, and uses the cyclic nucleotide negative channel subunit alpha 1(CNGA1) of Xenopus laevis oocytes collected by an atomic force microscope, the force curve of the atomic force microscope comprises a plurality of break points, two adjacent break points can be fitted by a Worm Like Chain (WLC) model or a free chain (FJC) model, and the continuous length (persistence length) and the unbent length (contourlength) can be estimated by fitting the models.
The present embodiment is a method for processing a second-order piecewise polynomial signal, including the following steps:
(1) signal acquisition
Acquiring original signal y output by atomic force microscope0And then normalization processing is carried out, as shown in fig. 2, to obtain a signal y;
(2) carrying out segmentation fitting on the signal y obtained in the step 1) according to a function model as follows:
the function model is
Wherein:
v is a signal dividing position;
(vk-1+1，vk) Is the fitting error of the k-th segment in the signal y;
lambda is a penalty value of a given parameter, and any positive number is taken for adjusting the quality of segmentation fitting;
k is the number of signal segments;
(3) calling the function model, performing dynamic planning and matrix decomposition through a computer algorithm program shown in figure 1, outputting a phi vector optimization value, and outputting a q vector segmentation value position, namely an actual segmentation position upsilon; and drawing a new signal y after segmentation fitting according to the output actual segmentation position upsilon1For new signal y1And (6) carrying out analysis.
In a computer algorithm program:
(8) comprises the following steps:
(9) comprises the following steps: b ═ B + yv+1A
(10) Comprises the following steps:
(11) comprises the following steps:
(12) comprises the following steps:
(13) is e ═ e + ρ ⊙ (y)v+11s-(T⊙BT)1P+1)2
(14) Comprises the following steps:
as shown in fig. 3 and 4, the force curve y can be detected by performing segmentation fitting using a second-order (P ═ 2) piecewise polynomial signal to analyze the data for protein unfolding1The invention has better segmentation effect at the breakpoint of the probe offset distance of 30 nm.
As a result of data analysis of the conventional software Fordis shown in FIG. 5, a breakpoint at a probe offset distance of 30nm cannot be detected.
Example 2
Young's modulus can also be measured using the force curve of an atomic force microscope. FIG. 6 is a graph of yeast stress test signals for measuring Young's modulus, and FIG. 7 is a graph of the results of a segmentation fitting process for measuring Young's modulus. The two star positions are segmentation positions, the force curve is on the left side of the star before the probe is offset by 600nm, and the interaction force between the probe and the sample is 0 because the probe is not in contact with the sample; and to the right of the second asterisk after the probe is offset by 600nm in the force curve, a linear region of load saturation due to excessive pressure. Only in the range where the force is small (between the two asterisks) is a suitable fitting region for the young's model. The location of the second asterisk is difficult to detect using conventional methods.
The method can automatically and quickly find two star breakpoints, thereby segmenting a proper region required by the Young modulus estimation. The force curve has high measurement quality and low noise, and the fitting error of the force curve is small. FIG. 8 is a graph showing the result of the fitting error of the signal in measuring Young's modulus in example 2, i.e., the result of the fitting error between the graph of the yeast stress test signal in measuring Young's modulus in FIG. 6 and the graph of the split fitting process result in measuring Young's modulus in FIG. 7.
Fig. 9 is a comparative analysis graph of the yeast pressure test signal, the division fitting processing result, and the signal fitting error (magnified ten times) result of measuring young's modulus in example 2, in which the abscissa is the probe offset distance and the ordinate is the interaction force between the probe and the sample, it can be seen that the effect of dividing and fitting the new signal of the piecewise polynomial using the signal processing method of the present invention is the best.
Example 3
The embodiment is a method for processing a zero-order segmented polynomial signal, applied to a new generation sequencing technology, and comprising the following steps:
1) signal acquisition
A short read fasta format file output by the high throughput genome sequencer was obtained and signal y extracted therefrom, as shown in fig. 10.
The specific way to extract the signal y from the short-read fasta format file is as follows: firstly, a SAM format file or a compressed BAM format file is obtained from a short-read fasta format file through comparison software, and then a reading depth signal y is obtained from the SAM format file or the compressed BAM format file by utilizing a calculation program.
2) Carrying out segmentation fitting on the signal y obtained in the step 1) according to a function model as follows:
the function model is
Wherein:
v is a signal dividing position;
(vk-1+1，vk) Is the fitting error of the k-th segment in the signal y;
lambda is a penalty value of a given parameter, and any positive number is taken for adjusting the quality of segmentation fitting;
k is the number of signal segments;
2) calling the function model, performing dynamic planning and matrix decomposition through a computer algorithm program shown in figure 1, outputting a phi vector optimization value, and outputting a q vector segmentation value position, namely an actual segmentation position upsilon; and drawing a new signal y after segmentation fitting according to the output actual segmentation position upsilon1For new signal y1And (6) carrying out analysis.
In a computer algorithm program:
(8) comprises the following steps:
(9) comprises the following steps: b ═ B + yv+1A
(10) Comprises the following steps:
(11) comprises the following steps:
(12) comprises the following steps:
(13) is e ═ e + ρ ⊙ (y)v+11s-(T⊙BT)1P+1)2
(14) Comprises the following steps:
this example uses a zero-order (P ═ 0) piecewise polynomial signal for segmentation fitting to detect copy number variations from the new generation sequencing technology data. In contrast, as shown in FIG. 11, a classical segmentation algorithm was used to cycle through binary segmentations, which can be seen to have false detections at a locus of about 920. And on the same computer, the cycle split is 35 seconds; as shown in FIGS. 12 and 13, all copy number variations of the present invention can be detected, the calculation time of the present invention is 0.5 seconds, and the calculation time of the present invention is efficient and fast.
The above description is only an embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structural changes made by using the contents of the present specification and the drawings, or applied directly or indirectly to other related technical fields, are included in the scope of the present invention.
Claims (7)
1. A method for processing an arbitrary-order segmented polynomial signal, comprising the steps of:
1) signal acquisition
Acquiring original signal y output by atomic force microscope0Carrying out normalization processing to obtain a signal y; or obtaining a short-reading fasta format file output by the high-throughput genome sequencer, and extracting a signal y from the short-reading fasta format file;
2) carrying out segmentation fitting on the signal y obtained in the step 1) according to a function model as follows:
the function model is
Wherein:
v is a signal dividing position;
(vk-1+1，vk) Is the fitting error of the k-th segment in the signal y;
lambda is a penalty value of a given parameter, and any positive number is taken for adjusting the quality of segmentation fitting;
k is the number of signal segments;
3) initialization of vector sum matrix
The optimized value vector Φ (1) ═ 0;
the partition value position vector q {1} - [ ];
vector S ═ 1;
matrix array
Matrix Ω (1) ═ G0]；
Vector e (1) ═ 0;
4) circularly executing the steps A1 to A7, wherein the loop flag i is 1 (N-P), and the loop is circulated for (N-P) times, wherein N is the length of the signal y, P is the polynomial order,
A1) and (4) reassigning each element t in the vector S according to the following formula to obtain the vector
The elements in (1):
A2) according to the vector after reassignment
Matrix solving
Where j is the index position of the vector S;
A3) according to a matrix
Re-dividing the signal y and locating the new division
Storing the position vector q { i +1} of the segmentation value;
A4) selecting a mark position j meeting the conditions of the first and the second simultaneously, reserving corresponding position elements in a matrix omega, a vector e, a matrix B and a vector S meeting the conditions of the mark position j, and deleting the other elements; wherein:
the condition is as follows: j is more than or equal to 1 and less than or equal to S, and S is the number of elements in the vector S
Condition ② is:
A5) respectively calculating three variables of A, Gamma and rho according to the reserved elements;
A＝[α1，α2，...，αs]
wherein:
a is a matrix of P +1 rows and s columns, each column having the form of α;
l is the length of the sub-signal, and the calculation formula of l in each column is i-S (j) +2+ P;
A6) according to three variables of A, gamma and rho, respectively updating a matrix B, a matrix omega and a vector e according to the following formula;
B＝B+yυ+1A
e＝e+ρ⊙(yv+11s-(T⊙BT)1P+1)2
A7) obtain an updated matrix B of
The matrix omega is [ omega, G ]0]And the vector e is [ e, O]And inserting a loop flag i into the vector S retained in step a4) so that the vector S is
5) Taking the (N +1-P) th bit in the phi vector as an output optimized value, adding a numerical value (P-1) to the (N +1-P) th bit in the q vector as an output segmentation value position, wherein the output segmentation value position is an actual segmentation position of the signal segmentation position upsilon; according to the position of the output segmentation value, drawing a new signal y after segmentation fitting1；
6) According to the new signal y1Finding out two breakpoint positions, and segmenting out a proper region required by the estimation of the straightening length and the continuous length;
or, according to the new signal y1Finding two breakpoint positions, and segmenting a proper region required by Young modulus estimation;
or, according to the new signal y1And detecting the copy number variation interval and the variation type.
2. The method of claim 1, wherein the method further comprises: step 1) original signal y output by atomic force microscope0As a set of force curves y0(z) wherein y0Is the interaction force between the probe and the sample and z is the offset distance.
3. The method according to claim 1 or 2, wherein the step of processing the arbitrary-order segmented polynomial signal comprises: the signal y in the step 1) is an original signal y output by an atomic force microscope0The normalized value is obtained by linear interpolation.
4. The method of claim 1, wherein the method further comprises: in step 1), the specific way to extract the signal y from the short-read fasta format file is as follows: firstly, obtaining an SAM format file or a compressed BAM format file from a short-read fasta format file through comparison software, then obtaining a read-depth signal y from the SAM format file or the compressed BAM format file by utilizing a calculation program, and finally, taking the read-depth signal y as a signal y.
5. The method of claim 4, wherein the method further comprises: the comparison software is MAQ software or bowtie software, and the calculation program is samtools program.
6. The method of claim 2, wherein the method further comprises: in the curve of the pair force y0(z) when the process is performed, the polynomial order P in step 4) is 2 or 3.
7. The method of claim 1, wherein the method further comprises: when detecting copy number variation on the data of the high-throughput genome sequencer, the polynomial order P in step 4) is taken as 0.
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