Method for pushing data by combining microfluidic system with large model

Abstract

The invention discloses a method for pushing data by combining a microfluidic system with a large model. The method comprises the following steps: step 1, carrying out diversity evaluation in a rearrangement stage of intelligent recommendation; and step 2, based on rule constraint, a heuristic algorithm or a depth model, performing intelligent recommendation rearrangement according to a diversity evaluation result, and performing accurate control by adopting a micro-fluidic chip built-in rule diversity scattering algorithm. Diversity regulation and control are carried out in the final link rearrangement stage of intelligent recommendation, diversity definition is matched with diversity perception of a user, various rule diversity scattering algorithms are built in by adopting a micro-fluidic chip technology, accurate control is carried out through a chip, damage to an original sequence is reduced, correlation can be reserved to the maximum extent, and the accuracy of recommendation is improved. The phenomenon that contents with the same attribute are gathered is avoided, and the use efficiency is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent recommendation, and in particular relates to a method for pushing data in combination with a microfluidic system and a large model. Background Art

[0002] Reranking is the last link in the recommendation system chain. It has the right to adjust the refined ranking results. The diversity of the adjusted results is an important consideration indicator and optimization task for reranking. The recommendation system starts from the starting point of reranking diversity adjustment, diversity evaluation indicators, diversity scattering strategy rules, and diversity optimization model strategy to carry out the relevant work of diversity processing in the reranking stage. Diversity refers to the degree of differentiation between the recommended display content. The diversity of recommended content is an important evaluation indicator to measure the quality of a recommendation system. Practice has proved that diversity will have a relatively large impact on the product's short-term user experience and long-term user retention goals. The whole link modules such as recall rough ranking, refined ranking, and reranking in the recommendation system need to consider diversity issues. Reranking is the final adjustment of the recommendation results, and generally requires more refined diversity regulation. In the refined ranking stage before reranking, whether it is content representation or audience users, the content will be relatively similar, so there will be a large amount of homogeneous content in the ranking results. If diversity regulation is not performed in the reranking stage, similar content will be clustered and recommended content will be redundant, which will seriously affect the recommendation efficiency and user experience. It is particularly important for the recommendation system to take into account diversity regulation in the reranking stage. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for pushing data in a microfluidic system combined with a large model in view of the above-mentioned deficiencies in the prior art.

[0004] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0005] A method for pushing data of a microfluidic system combined with a large model comprises the following steps:

[0006] Step 1: Perform diversity evaluation in the re-ranking phase of intelligent recommendation;

[0007] Step 2: Based on rule constraints, heuristic algorithms or deep models, intelligent recommendations are rearranged according to the diversity evaluation results, and the rule diversity scattering algorithm built into the microfluidic chip is used for precise control.

[0008] To optimize the above technical solutions, the specific measures taken also include:

[0009] The diversity evaluation indicators described in the above step 1 include: coverage, K-times repetition rate, SSD, Hellinger distance, n-NDCG, and manual evaluation indicators; among them, the coverage rate is the proportion of content recommended and exposed to users in the overall recommended content library, which is used to measure the recommendation system's distribution ability for long-tail content; the K-times repetition rate is the proportion of content of the same category appearing K times in the same batch of recommendation requests from users or in the same Session; SSD is the proportion of the current recommended content in the recommendation list that is not in the previous recommendation results, which is used to measure the temporal diversity of the recommendation results; the Hellinger distance is the difference between the actual diversity distribution and the ideal diversity distribution; the manual evaluation indicator is an indicator that is combined with the product positioning and business goals, and is manually evaluated by professional product or operation personnel for diversity.

[0010] The above-mentioned manual evaluation index is obtained by using simulation software to generate simulation data close to manual evaluation and then using real-time federated learning to replace manual evaluation, and obtaining the optimal manual evaluation index through multiple iterations; the process of real-time federated learning is:

[0011] In the Nth training iteration, the terminal performs local training using locally collected images / videos based on the global model downloaded from the FL server, and then reports the intermediate training results of the Nth iteration to the FL server through the 5G line channel. At the same time, the FL server sends the global model and training configuration of the (N+1)th iteration to the terminal. When the FL server aggregates the gradients collected in the Nth iteration, the terminal can perform training for the (N+1)th iteration, and the federated aggregation outputs an updated global model for the next iteration training, and distributes the model together with the updated training configuration to the terminal.

[0012] The rule diversity scattering algorithm described in the above step 2 includes bucket scattering method, weight distribution method and sliding window method.

[0013] The above-mentioned bucketing and scattering method divides the items into buckets according to the attributes that need to be scattered. Items with the same attribute value are placed in the same bucket. The attributes of items in different buckets are different. The order of placement in the buckets is consistent with the order of precise sorting, and then the items are taken out from each bucket in turn.

[0014] The above weight distribution method calculates a scattered weighted score for each item, and sorts the items from low to high according to the scattered weighted score to complete the scattered; the calculation formula of the scattered weighted score is:

[0015]

[0016] Where W i is the weight of each attribute, representing the priority of attribute-dispersed requirements; Count(i) is the number of times items with the same attribute have been recommended.

[0017] The above sliding window method controls the number of times items with the same attributes appear in a fixed-length sliding window. When items with the same attributes appear more than a certain number of times, they are swapped out of the window.

[0018] The above step 2 uses the rule diversity scattering algorithm built into the microfluidic chip for precise control, as follows:

[0019] First, the built-in migration algorithm is used to evenly distribute the data with the same attribute content in the sliding window method to 8 directions with different probability densities, and the center point retains the optimal solution of the migration process;

[0020] Secondly, the weight distribution method is migrated to the data in each direction through the execution of pseudocode.

[0021] The above migration means that at a certain moment and a certain spatial grid node, the isotropic probability density function of the point after collision is transferred to the corresponding position of the adjacent grid node, and the value at the position is replaced; at the same time, the point also accepts the values ​​transferred from other adjacent grid nodes and replaces the corresponding local values.

[0022] In the above migration process, the probability density distribution at the center point does not change, and only the changes in the distribution in the eight probability density directions are considered.

[0023] The present invention has the following beneficial effects:

[0024] In view of the problem that diversity is not regulated in the re-ranking stage, similar contents are clustered and recommended contents are redundant, which seriously affects the recommendation efficiency and user experience, the present invention performs diversity regulation in the re-ranking stage, the last link of intelligent recommendation. The main diversity evaluation indicators include: coverage, K-times repetition rate, SSD, Hellinger distance, n-NDCG, and manual evaluation.

[0025] The present invention aims to reduce the user's perception of recommended content when the model's definition of diversity does not match the user's perception of diversity. It uses simulation software to generate simulation data close to artificial ones and then uses federated learning technology to replace manual evaluation, and obtains the optimal manual evaluation index through multiple iterations.

[0026] The present invention adopts microfluidic chip technology to build in various rule diversity scattering algorithms and accurately controls them through the chip, which reduces the damage to the original order, can retain the correlation to the maximum extent, avoids the phenomenon of clustering of contents with the same attributes, and has high utilization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a flow chart of the method of the present invention;

[0028] Figure 2Schematic diagram of the real-time federated learning process;

[0029] Figure 3 The following is a migration diagram;

[0030] Figure 4 It is a schematic diagram of probability density direction and probability density distribution;

[0031] Figure 5 It is a schematic diagram of the migration operation in the x direction;

[0032] Figure 6 Schematic diagram of the shift assignment in the y-direction migration operation. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0034] Although the steps in the present invention are arranged with numbers, they are not used to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a certain step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" used in this article involves and covers any and all possible combinations of one or more of the associated listed items.

[0035] like Figure 1 As shown, a method for pushing data of a microfluidic system combined with a large model of the present invention comprises the following steps:

[0036] Step 1: Perform diversity evaluation in the re-ranking phase of intelligent recommendation;

[0037] Step 2: Based on rule constraints, heuristic algorithms or deep models, intelligent recommendations are rearranged according to the diversity evaluation results, and the rule diversity scattering algorithm built into the microfluidic chip is used for precise control.

[0038] In the embodiments, the methods for regulating diversity in the rearrangement stage can be roughly divided into three categories: (1) rule-based constraints; (2) heuristic algorithms; and (3) deep models.

[0039] The present invention performs diversity regulation in the final re-ranking stage of intelligent recommendation. The main diversity evaluation indicators include: coverage, K-times repetition rate, SSD, Hellinger distance, n-NDCG, and manual evaluation. When the model's definition of diversity does not match the user's perception of diversity, it will easily reduce the user's perception of the recommended content. First, simulation software is used to generate simulation data close to artificial, and then federated learning technology is used to replace manual evaluation. The optimal manual evaluation index is obtained through multiple iterations.

[0040] Rule constraints are basically based on some manually set rules, such as labeling by label category, breaking up by author, etc. Heuristic algorithms that are widely used in the industry include MMR, DPP, Deep-DPP, etc. Deep models use re-ranking models to integrate context-aware information or add diversity constraints to the target.

[0041] Technical innovation 1. Diversity control is carried out in the final re-ranking stage of intelligent recommendation. The main diversity evaluation indicators include: coverage, K-times repetition rate, SSD, Hellinger distance, n-NDCG, and manual evaluation.

[0042] Furthermore, diversity evaluation indicators:

[0043] Different users have different perceptions of diversity. When the model's definition of diversity does not match the user's perception of diversity, it will easily reduce the user's perception of the recommended content. The definition and evaluation of diversity is also a major problem in the recommendation system. The diversity evaluation indicators publicly used in the industry are also varied. The following introduces 6 commonly used diversity evaluation indicators.

[0044] (1) Coverage: The proportion of content recommended to users to the total recommended content library. This indicator is mainly used to measure the recommendation system’s ability to distribute long-tail content.

[0045] (2) K-time repetition rate: the ratio of K-times repetition rate in the same batch of recommendation requests from users, or the ratio of K-times repetition rate in the same category of content within the same Session.

[0046] (3) SSD (Self System Diversity): SSD is mainly used to measure the temporal diversity of recommendation results. SSD refers to the proportion of the current recommended content in the recommendation list that is not in the previous recommended results. As shown in formula (1), it is the previous recommended content of R. The smaller the SSD value, the better the temporal diversity of the recommendation list.

[0047]

[0048] Rt-1 is the previous recommendation of R.

[0049] (4) Hellinger distance: As shown in formula (2), Hellinger distance is used to measure the difference between two probability distributions. In the application of recommendation diversity, it can be used to measure the difference between the actual diversity distribution and the ideal diversity distribution.

[0050]

[0051] (5) α-NDCG: NDCG is one of the commonly used indicators to measure the accuracy of sorting. α-NDCG: NDCG measures the diversity of sorting results while ensuring accuracy. When the α-NDCG value is relatively high, it means that both the accuracy and diversity of the sorting are relatively good.

[0052] (6) Manual evaluation: Business personnel conduct sampling evaluation on the diversity of recommendation results. Usually, different users have different perceptions of diversity, and the evaluation of diversity is somewhat subjective. Diversity also needs to be combined with product positioning and business goals. Professional product or operation personnel should conduct manual evaluation of diversity on a regular or routine basis.

[0053] The present invention adopts simulation software to generate simulation data close to artificial ones and then adopts federated learning technology to replace manual evaluation, and obtains the optimal manual evaluation index through multiple iterations.

[0054] Federated machine learning (Federated Machine Learning / Federated Learning), also known as federated learning, joint learning, and alliance learning, is a machine learning framework that can effectively help multiple institutions use data and conduct machine learning modeling while meeting user privacy protection, data security and other requirements.

[0055] like Figure 2 As shown in the figure, the real-time federated learning process is:

[0056] In the Nth training iteration, the terminal performs local training using locally collected images / videos based on the global model downloaded from the FL server. The terminal then reports the intermediate training results of the Nth iteration (such as the gradient of the DNN) to the FL server through the 5G line channel. At the same time, the FL server sends the (N+1)th global model and training configuration to the terminal. While the FL server aggregates the gradients collected in the Nth iteration, the terminal can perform training for the (N1)th iteration. Federated Aggregation outputs an updated global model for the next iteration of training, and distributes the model to the terminal together with the updated training configuration.

[0057] In order to make full use of the training resources on the terminal and minimize the training delay, Figure 2 The training sequence shown requires that the training result report of the (N-1)th iteration and the global model distribution and training parameter configuration of the (N+1)th iteration be completed during the training process of the UE's Nth iteration. Of course, in the actual training process, it is also possible to consider using a relaxed sequence, at the cost of sacrificing the convergence speed of the training, that is, performing non-real-time federated learning.

[0058] In the embodiment, the rule diversity is broken up:

[0059] The rule-based scattering methods mainly include bucket scattering method, weight distribution method and sliding window method.

[0060] Although the sliding window method solves the drawbacks of the bucket-splitting method and can maximize the preservation of relevance in order to reduce the damage to the original order, it will also cause the phenomenon of clustering of contents with the same attributes;

[0061] The weight allocation method can only solve this problem manually, resulting in poor efficiency.

[0062] The present invention adopts all the above methods of microfluidic chip built-in migration technology and accurately controls them through the chip. First, the built-in migration algorithm evenly distributes the data with the same attribute content clustered in the sliding window method to 8 directions with different probability distributions, and the center point retains the optimal solution of the migration process.

[0063] Secondly, the weight distribution method is migrated to the data in each direction through the execution of pseudocode.

[0064] Furthermore, each item has several attributes that need to be isolated, such as category, author, similar images and texts, etc. Scattering generally adjusts the input ordered sequence and outputs a sequence of items with similar attributes separated. Scattering does not conflict with the heuristic algorithm or model strategy of diversity. Scattering can be used as a prerequisite for the heuristic algorithm or model strategy to provide a basic guarantee for the diversity of recommendations.

[0065] Scattering can be based on rules or on the distance represented by the item's latent vector. The rule-based approach is relatively simple and controllable, but when there are many item attribute enumeration values, it is necessary to adjust the rules for different attribute scattering through multiple experiments, and the scalability is not strong. Scattering based on latent vectors has strong generalization ability, but is prone to Bad Cases, and the basic guarantee is uncontrollable. The current mainstream method is still rule-based scattering. There are three main rule-based scattering methods.

[0066] 1). Bucket-based method

[0067] The bucketing method divides items into buckets according to the attributes that need to be scattered. Items with the same attribute value are placed in the same bucket, and the attributes of items in different buckets are different. The order of placing items in the buckets is generally consistent with the order of fine sorting, and then the items are taken out from each bucket in turn. This method is somewhat similar to merge sorting, which is simple to implement and has a better scattering effect. However, it is easy to cluster at the end, which greatly changes the original sequence.

[0068] 2). Weight distribution method

[0069] The weight distribution method calculates a score for each item, and the calculation method is shown in formula (3). Where W is the weight of each attribute, representing the priority of the attribute dispersal demand. Count is the number of times the same attribute item has been recommended. Formula (3)(x) is the weighted score for dispersal, and the items are sorted from low to high according to it to complete the dispersal. This method is also relatively easy to implement, and it can fully consider the superposition of multiple attributes. It is also highly scalable, but it is necessary to manually adjust the weight parameters to adjust the effect of dispersal.

[0070]

[0071] 3). Sliding Window Method

[0072] The sliding window method controls the number of times items with the same attribute appear in a fixed-length sliding window (Session). When items with the same attribute appear more than a certain number of times, they are swapped out of the window. This method only uses local frequency calculations, and the amount of calculation is relatively low. At the same time, the damage to the original sequence is relatively small, and the relevance can be retained to the maximum extent, but the phenomenon of the same attribute content being clustered may also occur.

[0073] The present invention uses microfluidic chip technology to build in migration logic flow and precisely control it through the chip, as follows:

[0074] Microfluidics chip technology integrates the basic operating units of sample preparation, reaction, separation, detection, etc. in the biological, chemical, and medical analysis process into a micrometer-scale chip to automatically complete the entire analysis process. Usually, in a microfluidic system, valves are used to realize switches to control the flow direction of the fluid and play a role in controlling flow limitation; pumps are used to drive the fluid, and the pumps play the role of transmitting and distributing the liquid flow, which is the premise and basis for realizing microfluidic control: the flow and mixing of fluids can also be controlled by channel design.

[0075] The process of using microfluidic chip migration technology is as follows:

[0076] First, the built-in migration algorithm is used to evenly distribute the data with the same attribute content in the sliding window method to 8 directions with different probability densities, and the center point retains the optimal solution of the migration process.

[0077] Secondly, the weight distribution method is migrated to the data in each direction through the execution of pseudocode.

[0078] Migration is the evolution of the flow field in space, such as Figure 3As shown. The role of migration: at a certain moment and a certain point in space, the probability density function of the point after collision is transferred to the corresponding position of the adjacent grid node and replaces the value at that position; at the same time, the point also accepts the value transferred from other adjacent grid nodes and replaces the corresponding local value. After all values ​​are migrated and replaced, the density, velocity, etc. of the flow field can be updated, thereby realizing the evolution of the flow field in space. The migration formula is

[0079] f i (x+e i ·Δt, t) = f i (x, t) Formula (4)

[0080] The velocity distribution in the ninth direction (at the center point) does not change during the migration. Therefore, when implementing the migration steps, only the changes in the velocity distribution in eight directions are considered. The corresponding grid parameters are as follows: Figure 4 shown.

[0081] Implementation process and pseudo code of migration: Assume that the coordinates of the grid point at position "9" in the figure are (i, j), f should migrate one grid to the right, so it needs to be assigned to point (i+1, j); f should migrate to the upper right, that is, it needs to migrate to point (i+1, j+1). Migration in other directions also has similar steps. Therefore, from the implementation process of migration, its essence is the "shift" operation of the array. In the program implementation, the shift operation can be performed in a loop, or it can be implemented by manipulating the address of the array elements. For the latter, the corresponding MATLAB code is as follows:

[0082] 1 function F1=stream(F1,1x,1y)

[0083] 2 F1(:,:,4)=F1([2:1x1],[1y1:1y-1],4);

[0084] 3 F1(;,:,3)=F1(:,[1y1:1y-1],3);

[0085] 4 F1(:,:,2)=F1([1×1:1x-1],[1y1:1y-1],2);

[0086] 5 F1(;,:,5)=F1([2:1×1],:,5);

[0087] 6 F1(;,:,1)=F1([1×1:1x-1],:,1);

[0088] 7 F1(:,:,6)=F1([2:1×1],[2:1y1],6);

[0089] 8 F1(:,:,7)=F1(:,[2:1y1],7);

[0090] 9F1(;,:,8)=F1([1×1:1x-1],[2:1y1],8);

[0091] Take the second line of code "F1(:,:,4)=F1([2:1x1],[1y1:1y-1],4)" as an example. Figure 4 It can be seen that the fourth direction is the direction of the upper left position, and the value of this direction needs to be obtained by migrating the fourth direction of the point (i+1,j-1). The left side of the code equal sign represents the node that receives the migration, and the right side of the equal sign is the node that sends the migration value. It can also be noted here that both the left and right sides of the equal sign operate on the F1 array, but this will not affect the modification of its local element values. Let's analyze how this line of code implements the "shift" assignment. The shift assignment in the x-direction migration operation is as follows Figure 5 As shown, the shift assignment in the y-direction migration operation is as follows Figure 6 shown.

[0092] However, the above shift operations also have certain problems. For example, for the last shift in the x direction and the first shift in the y direction, there is a "head-to-tail cross-border" problem. This can be solved by reassigning and overwriting during boundary processing.

[0093] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0094] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for pushing data in a microfluidic system combined with a large model, characterized in that: The following steps are involved: Step 1: Perform diversity evaluation in the re-ranking phase of intelligent recommendation; Step 2: Based on rule constraints, heuristic algorithms or deep models, intelligent recommendations are rearranged according to the diversity evaluation results, and the rule diversity scattering algorithm built into the microfluidic chip is used for precise control.

2. A method for pushing data in combination with a microfluidic system according to claim 1, characterized in that: The diversity evaluation indicators described in step 1 include: coverage, K-times repetition rate, SSD, Hellinger distance, n-NDCG, and manual evaluation indicators; among them, coverage is the proportion of content recommended to users in the overall recommendation content library, which is used to measure the recommendation system's distribution ability for long-tail content; K-times repetition rate is the proportion of content of the same category appearing K times in the same batch of recommendation requests from users or in the same Session; SSD is the proportion of current recommended content in the recommendation list that is not in the previous recommendation results, which is used to measure the temporal diversity of recommendation results; Hellinger distance is the difference between the actual diversity distribution and the ideal diversity distribution; manual evaluation indicators are indicators that are combined with product positioning and business goals, and are manually evaluated by professional product or operation personnel on diversity.

3. A method for pushing data in combination with a microfluidic system according to claim 2, characterized in that: The method for obtaining the manual evaluation index is: using simulation software to generate simulation data close to manual evaluation and then using real-time federated learning to replace manual evaluation, and obtaining the optimal manual evaluation index through multiple iterations; the process of real-time federated learning is: In the Nth training iteration, the terminal performs local training using locally collected images / videos based on the global model downloaded from the FL server, and then reports the intermediate training results of the Nth iteration to the FL server through the 5G line channel. At the same time, the FL server sends the global model and training configuration of the (N+1)th iteration to the terminal. When the FL server aggregates the gradients collected in the Nth iteration, the terminal can perform training for the (N+1)th iteration, and the federated aggregation outputs an updated global model for the next iteration training, and distributes the model together with the updated training configuration to the terminal.

4. A method for pushing data in combination with a microfluidic system according to claim 1, characterized in that: The rule diversity scattering algorithm described in step 2 includes bucket scattering method, weight distribution method and sliding window method.

5. A method for pushing data in combination with a microfluidic system according to claim 4, characterized in that: The bucketing and scattering method divides the items into buckets according to the attributes that need to be scattered. Items with the same attribute value are placed in the same bucket. The attributes of items in different buckets are different. The order of placing them in the buckets is consistent with the order of precise sorting, and then the items are taken out from each bucket in turn.

6. A method for pushing data in combination with a microfluidic system according to claim 4, characterized in that: The weight distribution method calculates a weighted score for each item, and sorts the items from low to high according to the weighted score to complete the dispersal; the calculation formula of the weighted score is: Where W i is the weight of each attribute, representing the priority of attribute-dispersed requirements; Count(i) is the number of times items with the same attribute have been recommended.

7. A method for pushing data in combination with a microfluidic system according to claim 4, characterized in that: The sliding window method controls the number of times items with the same attributes appear in a fixed-length sliding window. When items with the same attributes appear more than a certain number of times, they are swapped out of the window.

8. The method for pushing data of a microfluidic system combined with a large model according to claim 1, characterized in that: Step 2 uses the built-in rule diversity scattering algorithm of the microfluidic chip for precise control, as follows: First, the built-in migration algorithm is used to evenly distribute the data with the same attribute content in the sliding window method to 8 directions with different probability densities, and the center point retains the optimal solution of the migration process; Secondly, the weight distribution method is migrated to the data in each direction through the execution of pseudocode.

9. A method for pushing data in combination with a microfluidic system according to claim 8, characterized in that: The migration means that at a certain moment and a certain spatial grid node, the probability density function of the point after collision is transferred to the corresponding position of the adjacent grid node, and the value at the position is replaced; at the same time, the point also accepts the values ​​transferred from other adjacent grid nodes and replaces the corresponding local values.

10. The method for pushing data of a microfluidic system combined with a large model according to claim 8, characterized in that: During the migration process, the probability density distribution at the center point does not change, and only the changes in the distribution in the eight probability density directions are considered.

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