Patent Description:
A clinical decision support (CDS) system is a health information algorithm that analyzes data about a patient in view of health knowledge in order to provide information to a healthcare professional with the goal of improving health care. The information may be, for example, a diagnosis, a recommended course of action, or both. Most healthcare professionals do not simply assent to and apply the outcome of the CDS, but instead add the output of the CDS to their analysis and decision-making process, based on previous experience with the CDS. Indeed, empirical experience suggests that there are some patient features that may result in higher misclassification, including both false positive and false negative recommendations. For example, certain medications, interventions, and/or chronic conditions could lead to false recommendations of the CDS algorithm.

The output of simple CDS algorithms, including false positives and false negatives, is easily interpreted by the healthcare professional, who has a gained understanding of when the output from the CDS algorithm should be ignored, or when the response to the algorithm should be modified. However, as more complex and sophisticated CDS services are offered, it has become increasingly difficult for healthcare professionals to interpret the CDS output as confidently as was possible with simple algorithms. As a result, a healthcare professional might not fully understand when the output of the CDS algorithm should be used, trusted, or ignored. Additionally, relying on healthcare professionals to spend time interpreting the output of a complex CDS service will not only increase the already heavy workload in most healthcare settings, but will also lead to reduced confidence in the output of CDS algorithms. <CIT> discloses a CDS system, which is trained with training data including actual patient outcomes. Correlations between physiological data and outcomes are identified, so that predictions can be made of patient outcomes, or decision support can be provided.

In view of the foregoing, it would be beneficial to provide methods and systems that improve clinical decision support algorithms to provide reliable and actionable information to healthcare professionals.

Accordingly, the present disclosure is directed to methods and systems for adding a confidence score to the output of a clinical decision support algorithm. Various embodiments and implementations herein are directed to a system that clusters the output of a CDS algorithm analyzing training data into multi-dimensional parameter space based on accuracy, and calculates a confidence score for each cluster. The confidence score for a given cluster indicates the reliability of the prediction from the CDS algorithm falling within the region of multi-dimensional parameter space corresponding to the given cluster. Once the system is trained, it receives output from a CDS algorithm, compares the output to the generated clusters, associates the output with a confidence score corresponding to the cluster to which the output falls within, and provides the confidence score to the healthcare professional.

Generally in one aspect, a method for training a score system is provided. The method includes the steps of: (i) providing a scoring system comprising a scoring module; (ii) receiving a training dataset comprising a plurality of patient data and treatment outcomes; (iii) analyzing, using a clinical decision support algorithm, the training dataset to generate a plurality of clinical decision support recommendations; (iv) clustering, using the scoring module, the plurality of clinical decision support recommendations into a plurality of clusters; and (v) identifying, using the scoring module, one or more features of at least one of the plurality of clusters, and generating, based on the identified one or more features, one or more inclusion criteria for the at least one of the plurality of clusters.

According to an embodiment, clustering is based at least in part on a comparison of each of the clinical decision support recommendations to the treatment outcomes in the training data.

According to an embodiment, the identifying step further includes generating, based on the identified one or more features, one or more exclusion criteria for the at least one of the plurality of clusters.

According to an embodiment, the method further includes the steps of: obtaining health data about a patient; analyzing, using a clinical decision support algorithm, the health data to generate a clinical decision support recommendation for the patient; assigning, using a scoring module, the clinical decision support recommendation to one of the plurality of clusters based on the extracted inclusion criteria; and assigning, using the scoring module, a confidence score to the clinical decision support recommendation based at least in part on the assignment of the recommendation to the one of the plurality of clusters.

According to an embodiment, the method further includes the step of communicating the confidence score to a user.

According to an embodiment, the confidence score is a quantitative score.

According to a second aspect, a method for training a scoring system is provided. The method includes the steps of: (i) providing a scoring system comprising a scoring module; (ii) receiving a training dataset comprising a plurality of patient data and treatment outcomes; (iii) clustering, using the scoring module, the training dataset into a plurality of clusters; (iv) analyzing, using a clinical decision support algorithm, the training dataset to generate a plurality of clinical decision support recommendations, wherein said clustering step and said analyzing step are performed separately; and (v) identifying, using the scoring module, one or more features of at least one of the plurality of clusters, and generating, based on the identified one or more features, one or more inclusion criteria for the at least one of the plurality of clusters.

According to an embodiment, the identifying step further comprises identifying the at least one of the plurality of clusters as a cluster with a plurality of false recommendations, based on the plurality of clusters compared to the plurality of clinical decision support recommendations.

According to an embodiment, the method further includes the step of identifying, using the scoring module, at least one of the plurality of clusters as a noisy cluster, wherein said identified noisy cluster is the cluster from which the one or more exclusion criteria are generated.

According to an embodiment, the analyzing step comprises the steps of analyzing, using a clinical decision support algorithm, each of the plurality of clusters individually to generate a plurality of clinical decision support recommendations for each of the plurality of clusters; and further wherein the method comprises the step of identifying, using the scoring module, at least one of the plurality of clusters with a low area under the curve score, based on least in part on the plurality of clusters and the plurality of clinical decision support recommendations.

According to an embodiment, the method further includes the steps of: (i) obtaining health data about a patient; (ii) analyzing, using a clinical decision support algorithm, the health data to generate a clinical decision support recommendation for the patient; (iii) assigning, using the scoring module, the clinical decision support recommendation to one of the plurality of clusters based on the extracted inclusion criteria; and (iv) assigning, using the scoring module, a confidence score to the clinical decision support recommendation based at least in part on the assignment of the recommendation to the one of the plurality of clusters.

According to another aspect, a method for providing a confidence score is provided. The method includes the steps of: (i) obtaining health data about a patient; analyzing, using a clinical decision support algorithm, the health data to generate a clinical decision support recommendation for the patient; assigning, using a scoring module, the clinical decision support recommendation to one of a plurality of clusters based on inclusion criteria, wherein the inclusion criteria is generated by: (i) clustering, using the scoring module, a training dataset or clinical decision support recommendations into a plurality of clusters; and (ii) identifying, using the scoring module, one or more features of at least one of the plurality of clusters, and generating, based on the identified one or more features, one or more inclusion criteria for the at least one of the plurality of clusters; assigning, using the scoring algorithm, a confidence score to the clinical decision support recommendation based at least in part on the assignment of the recommendation to the one of the plurality of clusters; and communicating the confidence score to a user.

According to an embodiment, the confidence score is a quantitative score comprising an indication of whether to utilize the clinical decision support recommendation.

As used herein for purposes of the present disclosure, the term "processor" is used generally to describe various apparatus components relating to the operation of the recommendation apparatus, system, or method. A processor can be implemented in numerous ways (e.g., such as with dedicated hardware) to perform various functions discussed herein. A "processor" can employ one or more microprocessors that may be programmed using software (e.g., microcode) to perform various functions discussed herein. A processor may also be implemented as a combination of dedicated hardware to perform some functions. Examples of processor components that may be employed in various embodiments of the present disclosure include, but are not limited to, conventional microprocessors, application specific integrated circuits (ASICs), and field-programmable gate arrays (FPGAs).

In various implementations, a processor may be associated with one or more storage media (generically referred to herein as "memory," e.g., volatile and non-volatile computer memory such as RAM, PROM, EPROM, and EEPROM, floppy disks, compact disks, optical disks, magnetic tape, etc.). In some implementations, the storage media may be encoded with one or more programs that, when executed on one or more processors and/or controllers, perform at least some of the functions discussed herein. Various storage media may be fixed within a processor or controller or may be transportable, such that the one or more programs stored thereon can be loaded into a processor or controller so as to implement various aspects discussed herein. The terms "program" or "computer program" are used herein in a generic sense to refer to any type of computer code (e.g., software or microcode) that can be employed to program one or more processors or controllers. As used herein, the term "non-transitory machine-readable medium" will be understood to encompass both volatile and non-volatile memories, but to exclude transitory signals.

The term "user interface" as used herein refers to an interface between a human user or operator and one or more devices that enables communication between the user and the device(s). Examples of user interfaces that may be employed in various implementations of the present disclosure include, but are not limited to, switches, potentiometers, buttons, dials, sliders, track balls, display screens, various types of graphical user interfaces (GUIs), touch screens, microphones and other types of sensors that may receive some form of human-generated stimulus and generate a signal in response thereto.

Various embodiments may further include non-transitory computer-readable storage media, having embodied thereon a firewall program executable by a processor to perform methods described herein.

It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the subject matter disclosed herein.

Also, the drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles demonstrated herein.

The present disclosure describes various embodiments of a method and system for providing reliable and actionable information to healthcare professionals. More generally, Applicant has recognized and appreciated that it would be beneficial to provide a method or system that augments the output of clinical decision support algorithms with a confidence score. A particular goal of utilization of certain embodiments of the present disclosure is to provide a reporting system that provides the output of a CDS algorithm and a confidence score to a healthcare professional.

In view of the foregoing, various embodiments and implementations are directed to a method and system that clusters output from a CDS algorithm analyzing training data into multi-dimensional parameter space based on accuracy, and calculates a confidence score for each cluster. The confidence score for a given cluster indicates the reliability of the prediction from the CDS algorithm falling within the region of multi-dimensional parameter space corresponding to the given cluster. The trained algorithm can then receive output from a CDS algorithm, compare the output to the generated clusters, and associate the output with a confidence score corresponding to the cluster to which the output falls within. The confidence score can then be reported to the healthcare professional, who can interpret the CDS in light of that score.

Referring to <FIG>, in one embodiment, is a method <NUM> for training a clustering algorithm. The method clusters the output of a CDS algorithm analyzing training data into multi-dimensional parameter space based on accuracy, and calculates a confidence score for each cluster. The confidence score for a given cluster indicates the reliability of the prediction from the CDS algorithm falling within the region of multi-dimensional parameter space corresponding to the given cluster. Once the system is trained, it associates the output of a CDS algorithm with a confidence score, and can lead to patient-centric personalized CDS healthcare output across the care continuum.

At step <NUM> of the method, a scoring service, system, or device is provided. The scoring service, system, or device may be any of the systems described or otherwise envisioned herein. For example, the scoring service may be a cloud-based service provided to healthcare professionals, such as a software as a service option, and can thus be hosted on one or more specialized remote servers. Alternatively, the scoring service may hosted locally to the healthcare professional, such as on a specialized computer or server at a hospital or any other healthcare setting.

At step <NUM> of the method, training data is obtained. The training data will be utilized to train a clustering algorithm, based on a comparison of the output of a CDS algorithm providing diagnoses and/or recommendations to actual diagnoses and/or treatment decisions. Accordingly, the training data can comprise clinical and/or non-clinical measurements or other data from patients, as well as treatment decisions and outcomes. The training data can be obtained from one or more sources, and may be generalized for all locations, settings, or one or more other variables. Alternatively, the training data may be obtained from a specific location that will be most applicable to the location where the clustering algorithm will be implemented. For example, the training data may be specific to a hospital or other healthcare facility, and/or to a physician or other healthcare professional. The training data can comprise, for example, health data, background information, demographics, and clinical measurements for a plurality of patients. Each of these patients in the training data can be associated with one or more treatment decisions that were made, as well as one or more outcomes of those treatment decisions.

At step <NUM> of the method, a CDS algorithm analyzes the training data to produce one or more diagnoses and/or one or more treatment recommendations. According to an embodiment, the CDS algorithm analyzing the training data is the same CDS algorithm that will be utilized by the healthcare professional in conjunction with the scoring algorithm. Alternatively, the CDS algorithm is different from the CDS algorithm that will be utilized by the healthcare professional in conjunction with the scoring algorithm. The CDS will analyze information within the training data which is normally provided to a CDS, such as health data, background information, demographics, and clinical and/or non-clinical measurements or other data about patients.

At step <NUM> of the method, a clustering algorithm clusters the output of the CDS algorithm. According to an embodiment, the clustering algorithm is a known clustering system, approach, or algorithm, including but not limited to K-means, spectral clustering, and other clustering approaches. The clustering algorithm can cluster the output of the CDS algorithm based on a comparison of the CDS-based diagnosis and/or recommended treatment to the known diagnosis and treatment decisions. Accordingly, the clustering algorithm may cluster the output of the CDS algorithm into groups associated with accuracy compared to the known diagnosis and treatment decisions, such as True Positive (TP), True Negative (TN), False positive (FP), and False Negatives (FN). According to an embodiment, the clusters can then optionally be fixed, such that the clustering can be validated on an independent set of patients prior to deployment.

At step <NUM>, a clustering algorithm identifies or extracts one or more features of one or more of the clusters, where a feature is strongly correlated with the cluster. The identified or extracted features provide inclusion and exclusion criteria which can be utilized by the scoring algorithm and/or the CDS algorithm for analysis of future data. For example, identified or extracted features may be associated with the False Positive (FP) and/or False Negative (FN) cluster. According to an embodiment, the output of the clustering algorithm are clusters and one or more identified or extracted features associated with one or more of those clusters. Each cluster may be associated with a generated, identified, or extracted feature, or alternatively only one or a few of the clusters may be associated with a generated, identified, or extracted feature.

There are multiple methods for clustering, feature identification, and calculation of confidence scores. In addition to the method described above, the clustering algorithm could first be applied to the training data. Accordingly, at step <NUM> of the method, the clustering algorithm is applied to the given data to generate one or more clusters.

At step <NUM>, the CDS algorithm is utilized to analyze the data within each of the clusters. Each cluster is analyzed separately. This results in an area under the curve (AUC) score for each cluster.

At step <NUM>, clusters with low AUC scores are identified. This may be based on a learned threshold or a predetermined threshold. For example, a healthcare professional or setting may determine a particular threshold based on one or more factors internal or external factors. As an example, a hospital or healthcare professional may intentionally set a threshold very high to filter out as many false positives and/or false negatives as possible. Alternatively, the hospital or healthcare professional may intentionally set a threshold low with the understanding that there might be more false positives and/or false negatives in the output to the healthcare professional. The threshold may be a learned threshold, with a goal to make the clusters as distinct and/or reliable as possible. Accordingly, the threshold may change over time or in response to one or more internal and/or external factors.

At step <NUM>, the scoring algorithm identifies or extracts one or more features of one or more of the clusters, where a feature is strongly correlated with the cluster. The identified or extracted features provide inclusion and exclusion criteria which can be utilized by the scoring algorithm and/or the CDS algorithm for analysis of future data.

Referring to <FIG>, in one embodiment, is a schematic representation of the method described by steps <NUM> through <NUM>. Training data, which can be stored in a database <NUM>, is clustered at step <NUM> by a clustering algorithm, which may be a known clustering algorithm such as K-means, spectral clustering, and other clustering approaches. This results in a plurality of clusters <NUM>. At step <NUM>, the CDS algorithm is utilized to analyze the data within each of the clusters, resulting in an AUC score for each cluster. In <FIG>, for example, each of the three clusters receives an AUC score, with these particular clusters receiving scores of <NUM>, <NUM>, and <NUM>. The clusters with low AUC scores are then identified in step <NUM>, and in step <NUM> one or more features are identified or extracted from one or more of the clusters in order to generate a set of exclusion and inclusion criteria which can be utilized to analyze and classify subsequent data.

As noted above, there are multiple methods for clustering, feature identification, and calculation of confidence scores. In addition to the methods described above, the CDS algorithm and the clustering algorithm could be separately applied to the training data at the same time. Accordingly, steps <NUM> and <NUM> are performed separately on the same training data. At step <NUM> of the method, the training data is analyzed using the CDS algorithm, and evaluate the predictions against the known labels, where each data point belongs to one of the four sets: True Positive (TP), True Negative (TN), False positive (FP), or False Negative (FN). At step <NUM> of the method, the training data is clustered using the clustering algorithm to divide the data into meaningful clusters. Steps <NUM> and <NUM> are either performed separately on the same training data at the same time, or at different times.

According to this embodiment, at step <NUM> the system utilizes the output from the CDS algorithm at step <NUM> and the clustering algorithm at <NUM>, and identifies one or more clusters with high false prediction densities, which are candidates for exclusion while the remainder are candidates for inclusion. The method then proceeds to step <NUM> to identify or extract one or more features from one or more of the clusters in order to generate a set of exclusion and inclusion criteria which can be utilized to analyze and classify subsequent data.

Referring to <FIG>, in one embodiment, is a schematic representation of the method described by steps <NUM>, <NUM>, <NUM>, and <NUM> in which the CDS algorithm and the clustering algorithm are separately applied to the training data. Training data, which can be stored in a database <NUM>, is analyzed with the CDS algorithm at step <NUM> to generate an output <NUM>, and separately the training data is analyzed with the clustering algorithm to generate a plurality of clusters <NUM>. At step <NUM> the system utilizes the output from the CDS algorithm at step <NUM> and the clustering algorithm at <NUM>, and identifies one or more clusters with high false prediction densities, which are candidates for exclusion while one or more of the other clusters are candidates for inclusion. At step <NUM>, one or more features are identified or extracted from one or more of the clusters in order to generate a set of exclusion and inclusion criteria which can be utilized to analyze and classify subsequent data.

Once the clustering algorithm has created clusters and generated, identified, or extracted one or more features of these clusters to generate a set of exclusion and inclusion criteria, this resulting output can be utilized to analyze and classify subsequent data. Additionally, how well the subsequent data fits within a cluster, and thus how accurate the determination by the CDS is based on the training data, may be determined based on a confidence score which is provided to the healthcare professional.

Referring to <FIG>, in one embodiment, is a method <NUM> for providing a confidence score to the output of a CDS algorithm. At step <NUM> of the method, the scoring service, system, or device is provided. The scoring service, system, or device may be any of the systems described or otherwise envisioned herein. For example, the scoring service may be a cloud-based service provided to healthcare professionals, such as a software as a service option, and can thus be hosted on one or more specialized remote servers. Alternatively, the scoring service may hosted locally to the healthcare professional, such as on a specialized computer or server at a hospital or any other healthcare setting.

At step <NUM> of the method, input to a CDS algorithm is obtained or provided. For example, the input may comprise health data, background information, demographics, clinical and/or non-clinical measurements, and/or other data from or about a patient or subject. At step <NUM> of the method, the CDS algorithm is applied to the input, and an output is generated. The output may be, for example, a diagnosis and/or a treatment recommendation, among other outputs of the CDS.

At step <NUM> of the method the scoring algorithm determines to which of the clusters, which were generated by the clustering algorithm using the training data, the output of the CDS and/or the patient data belongs. Some output of the CDS algorithm will not fit into any of the clusters, and this information could be reported to the healthcare professional.

At step <NUM> of the method, a confidence score is assigned to the output of the CDS algorithm, based at least in part on the cluster membership of the given patient data and/or the output of the CDS algorithm. According to an embodiment, the confidence score is quantitative and/or qualitative. For example, the confidence score can be a positive number between <NUM> and <NUM>. Alternatively, the confidence score may be a "yes" or a "no. " A "<NUM>" or "yes" may indicate that the output of the CDS algorithm can be utilized with confidence, while a "<NUM>" or a "no" may indicate that the output of the CDS algorithm cannot be utilized with confidence. The "<NUM>" or "no" cases may be excluded from further CDS evaluation and can be flagged to alert physicians.

Accordingly, the output of the scoring algorithm and method <NUM> may be, for example, a decision whether or not to utilize the CDS algorithm for a particular patient or on specific patient data. Alternatively, the output of the scoring algorithm and method <NUM> may be, for example, a confidence score associated with a decision whether or not to utilize the CDS algorithm. Alternatively, the output of the scoring algorithm and method <NUM> may be, for example, a confidence score associated the output of the CDS algorithm, enabling the healthcare professional to determine whether the CDS algorithm output is reliable.

Referring to <FIG>, in one embodiment, is a simplified flowchart of method <NUM>. New patient record <NUM> is received, and its assignment in a cluster is made at step <NUM> of the method. A confidence score is applied by the scoring algorithm at step <NUM>, and at step <NUM> of the method the confidence score (here, a "yes" or a "no") is communicated to the healthcare professional. According to an embodiment, therefore, the output of the system is a decision whether to analyze the patient record with the CDS algorithm in association with a confidence score in that determination. According to another embodiment, the output of the system is the output of the CDS algorithm along with a confidence score in that output.

According to an embodiment, the system and method described or otherwise envisioned herein generates a generic platform capable of finding exclusion and/or inclusion criteria for any CDS algorithm. Accordingly, the system and method is not restricted to existing CDS algorithms.

Referring to <FIG>, in one embodiment, is a scoring system <NUM>. The scoring service, system, or device may be any of the systems described or otherwise envisioned herein. For example, the scoring service may be a cloud-based service provided to healthcare professionals, such as a software as a service option, and can thus be hosted on one or more specialized remote servers. Alternatively, the scoring service may hosted locally to the healthcare professional, such as on a specialized computer or server at a hospital or any other healthcare setting.

According to an embodiment, scoring system <NUM> comprises a training database <NUM>, which includes training data. The training data can comprise, for example, health data, background information, demographics, and clinical measurements for a plurality of patients. Each of these patients in the training data can be associated with one or more treatment decisions that were made, as well as one or more outcomes of those treatment decisions. Training database <NUM> may be local or remote, and thus the system may comprise a network <NUM> configured to communicate by wired and/or wireless communication with the scoring system.

According to an embodiment, scoring system <NUM> comprises a scoring module <NUM> which is configured to train a clustering algorithm using training data from training database <NUM>, and which is further configured to analyze new patient data from a patient <NUM>. According to an embodiment, scoring module <NUM> can comprise a processor <NUM> which is configured or programmed to carry out one or more processes of or for the scoring module. For example, the processor may be configured or programmed to receive and analyze the training data from training database <NUM>, and to receive and analyze the patient data from patient <NUM>. Processor <NUM> may be programmed using software to perform various functions discussed herein, and can be utilized in combination with a memory <NUM> and/or database <NUM>. Memory <NUM> and/or database <NUM> can store data, including one or more commands or software programs for execution by processor <NUM>, as well as various types of data. For example, memory <NUM> may comprise a non-transitory computer readable storage medium that includes a set of instructions that are executable by processor <NUM>, and which cause the system to execute one or more of the steps of the methods described herein.

According to an embodiment, the scoring module <NUM> can comprise a communications module <NUM> to facilitate wired and/or wireless communication between the report generator and other devices and/or networks, such as network <NUM>. Communication module <NUM> may be facilitated through the use of one or more antennas, for example. Communication module <NUM> can facilitate communication with one or more networks or with other devices, for example, by using wireless methods that are known, including but not limited to Wi-Fi, Bluetooth, <NUM>, <NUM>, LTE, and/or ZigBee, among others.

Scoring module <NUM> may comprise a user interface and display <NUM> to receive input from a healthcare provider <NUM>, and/or to provide output or other information to healthcare provider <NUM>. The user interface may be a button or multiple buttons, a microphone, a key stroke input, a slider, a touchscreen, or any of a variety of other inputs. The display may be, for example, an LED-based, LCD-based, or e-paper type display. In other embodiments, the display may be a touch screen display that allows the user to directly interact with a wearable device through physical contact and/or gestures.

According to an embodiment, system <NUM> can optionally comprise a display device <NUM>, which may also serve as a user input device. The device <NUM> may be, for example, a smartphone or other portable device. According to yet another embodiment, the device <NUM> may be a computer such as a desktop, laptop, tablet, or other permanent or semi-permanent computing device. The device <NUM> may receive input from healthcare provider <NUM>. The device <NUM> may also display information to healthcare provider <NUM> or any other intended or authorized entity.

Only terms clearly indicated to the contrary, such as "only one of' or "exactly one of," or, when used in the claims, "consisting of," will refer to the inclusion of exactly one element of a number or list of elements.

Only the transitional phrases "consisting of" and "consisting essentially of' shall be closed or semi-closed transitional phrases, respectively.

Claim 1:
A computer-implemented method (<NUM>) for training a scoring system (<NUM>), the method comprising the steps of:
providing (<NUM>) a scoring system comprising a scoring module (<NUM>);
receiving (<NUM>) a training dataset comprising a plurality of patient data and treatment outcomes;
analyzing (<NUM>), using a clinical decision support algorithm, the training dataset to generate a plurality of clinical decision support recommendations;
clustering (<NUM>), using the scoring module, the plurality of clinical decision support recommendations into a plurality of clusters, wherein clustering is based at least in part on a comparison of each of the clinical decision support recommendations to the treatment outcomes in the training data such that the clusters are based on the accuracy of the output of the clinical decision support algorithm; and
identifying (<NUM>), using the scoring module, one or more features of at least one of the plurality of clusters, and generating, based on the identified one or more features, one or more inclusion criteria for the at least one of the plurality of clusters.