Phenotype classification from persistent Betti curve analysis
A computer-implemented method for data analysis is provided. The computer-implemented method includes splitting data into first and second training data and first and second test data, partitioning the first and second training data into first and second partitions, generating initial Betti curves for the first and second partitions, training a model to recognize Betti curves of the first and second data types on the initial Betti curves, adding each of the first and second test data to each of the first and second partitions to form new first and second partitions, generating new Betti curves for the new first and second partitions, having the model determine whether each of the first and second test data are likely to be first or second data types from new and initial Betti curve deviations and iteratively re-training the model based on determination accuracies.
1 . A computer-implemented method for data analysis, the computer-implemented method comprising:
splitting data into first and second training data and first and second test data;
partitioning the first and second training data into first and second partitions;
generating initial Betti curves for the first and second partitions;
training a model to recognize Betti curves of the first and second data types on the initial Betti curves;
modifying the first and second partitions by adding a data sample of each of the first and second test data to each of the first and second partitions to form new first and second partitions;
generating new Betti curves for the new first and second partitions;
having the model identify deviations between the new Betti curves and the initial Betti curves and make a quantitative or qualitative judgment about those deviations to determine whether each of the first and second test data are likely to be first or second data types;
measuring differences in the prediction performance of the model between all initial Betti curves and new initial Betti curves; and
setting an accuracy threshold and iteratively re-training the model until its accuracy score exceeds the accuracy threshold, the iteratively re-training including ignoring a least likely result, at which point the model can be considered to be a verified model,
wherein the initial Betti curves and the new Betti curves are defined as Betti numbers over filtration steps and the Betti numbers are defined as a number of structures at a given dimension dϵD, where D=Z+0 and the computer-implemented method further comprises:
using the model, following the iteratively re-training of the model, to determine whether newly received data is associated with the first or second data types;
automatically activating a treatment course for a patient from whom the newly received data is drawn in accordance with the newly received data being determined to be associated with the first or second data types; and,
in accordance with the newly received data being determined to be associated with the first or second data types, where the training of the model comprises training the model toward classes related to drug response mechanisms and where a patient is already treated with a drug C:
monitoring a therapeutic response of the patient to drug C treatment;
identifying, from results of the monitoring, that the therapeutic response of the patient to the drug C treatment resembles a non-responsive Betti curve; and
automatically terminating treatment of the patient with the drug C treatment based on the therapeutic response of the patient to the drug C treatment resembling the non-responsive Betti curve.
2 . The computer-implemented method according to claim 1 , wherein:
the first data type is associated with a first cancer and the second data type is associated with a second cancer,
Betti numbers are defined as the number of structures at a given dimension dϵD, a Betti number Bpd is learned for each phenotype pϵP of the first cancer and the second cancer, where Bpd is calculated from a fixed number of samples Npd, which is dependent on a size of p and which is constructed from samples non-exclusively drawn from p to capture a noisy space reflective of a heterogeneous nature of each of the first cancer and the second cancer, and
the training of the model comprises training a model Md for Bpd for each dϵD and testing the model Md during a testing phase, the testing comprising adding an unlabeled sample t with an identical feature space to each Npd to give N′pd and recalculating Bpd as B′pd for each given dimension d.
3 . The computer-implemented method according to claim 1 , wherein the training comprises re-sampling of the data.
4 . The computer-implemented method according to claim 1 , wherein the iteratively re-training of the model comprises ignoring a least likely result and, in an event the training of the model uses six total Betti curves and the determining reveals that, for a given data sample of breast cancer, deviations between one pair of the new Betti curves and the initial Betti curves associated with lung cancer exceeded all the other deviations, the computer-implemented method further comprises discarding that one pair during the re-training to recognize Betti curves for data samples associated with characteristics of breast cancer.
5 . The computer-implemented method according to claim 1 , further comprising generating a report in accordance with the newly received data being determined to be associated with the first or second data types.
6 . A computer program product for data analysis, the computer program product comprising one or more computer readable storage media having computer readable program code collectively stored on the one or more computer readable storage media, the computer readable program code being executed by a processor of a computer system to cause the computer system to perform a method comprising:
splitting data into first and second training data and first and second test data;
partitioning the first and second training data into first and second partitions;
generating initial Betti curves for the first and second partitions;
training a model to recognize Betti curves of the first and second data types on the initial Betti curves;
modifying the first and second partitions by adding a data sample of each of the first and second test data to each of the first and second partitions to form new first and second partitions;
generating new Betti curves for the new first and second partitions;
having the model identify deviations between the new Betti curves and the initial Betti curves and make a quantitative or qualitative judgment about those deviations to determine whether each of the first and second test data are likely to be first or second data types;
measuring differences in the prediction performance of the model between all initial Betti curves and new initial Betti curves; and
setting an accuracy threshold and iteratively re-training the model until its accuracy score exceeds the accuracy threshold, the iteratively re-training including ignoring a least likely result, at which point the model can be considered to be a verified model,
wherein the initial Betti curves and the new Betti curves are defined as Betti numbers over filtration steps and the Betti numbers are defined as a number of structures at a given dimension dϵD, where D=Z+0 and the computer-implemented method further comprises:
using the model, following the iteratively re-training of the model, to determine whether newly received data is associated with the first or second data types;
automatically activating a treatment course for a patient from whom the newly received data is drawn in accordance with the newly received data being determined to be associated with the first or second data types; and,
in accordance with the newly received data being determined to be associated with the first or second data types, where the training of the model comprises training the model toward classes related to drug response mechanisms and where a patient is already treated with a drug C:
monitoring a therapeutic response of the patient to drug C treatment;
identifying, from results of the monitoring, that the therapeutic response of the patient to the drug C treatment resembles a non-responsive Betti curve; and
automatically terminating treatment of the patient with the drug C treatment based on the therapeutic response of the patient to the drug C treatment resembling the non-responsive Betti curve.
7 . The computer program product according to claim 6 , wherein:
the first data type is associated with a first cancer and the second data type is associated with a second cancer,
Betti numbers are defined as the number of structures at a given dimension dϵD, a Betti number Bpd is learned for each phenotype pϵP of the first cancer and the second cancer, where Bpd is calculated from a fixed number of samples Npd, which is dependent on a size of p and which is constructed from samples non-exclusively drawn from p to capture a noisy space reflective of a heterogeneous nature of each of the first cancer and the second cancer, and
the training of the model comprises training a model Md for Bpd for each dϵD and testing the model Md during a testing phase, the testing comprising adding an unlabeled sample t with an identical feature space to each Npd to give N′pd and recalculating Bpd as B′pd for each given dimension d.
8 . The computer program product according to claim 6 , wherein the training comprises re-sampling of the data.
9 . The computer program product according to claim 6 , wherein the iteratively re-training of the model comprises ignoring a least likely result and, in an event the training of the model uses six total Betti curves and the determining reveals that, for a given data sample of breast cancer, deviations between one pair of the new Betti curves and the initial Betti curves associated with lung cancer exceeded all the other deviations, the method further comprises discarding that one pair during the re-training to recognize Betti curves for data samples associated with characteristics of breast cancer.
10 . The computer program product according to claim 6 , wherein the method further comprises generating a report in accordance with the newly received data being determined to be associated with the first or second data types.
11 . A computing system comprising:
a processor;
a memory coupled to the processor; and
one or more computer readable storage media coupled to the processor, the one or more computer readable storage media collectively containing instructions that are executed by the processor via the memory to implement a method for data analysis comprising:
splitting data into first and second training data and first and second test data;
partitioning the first and second training data into first and second partitions;
generating initial Betti curves for the first and second partitions;
training a model to recognize Betti curves of the first and second data types on the initial Betti curves;
modifying the first and second partitions by adding a data sample of each of the first and second test data to each of the first and second partitions to form new first and second partitions;
generating new Betti curves for the new first and second partitions;
having the model identify deviations between the new Betti curves and the initial Betti curves and make a quantitative or qualitative judgment about those deviations to determine whether each of the first and second test data are likely to be first or second data types;
measuring differences in the prediction performance of the model between all initial Betti curves and new initial Betti curves; and
setting an accuracy threshold and iteratively re-training the model until its accuracy score exceeds the accuracy threshold, the iteratively re-training including ignoring a least likely result, at which point the model can be considered to be a verified model,
wherein the initial Betti curves and the new Betti curves are defined as Betti numbers over filtration steps and the Betti numbers are defined as a number of structures at a given dimension dϵD, where D=Z+0 and the computer-implemented method further comprises:
using the model, following the iteratively re-training of the model, to determine whether newly received data is associated with the first or second data types;
automatically activating a treatment course for a patient from whom the newly received data is drawn in accordance with the newly received data being determined to be associated with the first or second data types; and,
in accordance with the newly received data being determined to be associated with the first or second data types, where the training of the model comprises training the model toward classes related to drug response mechanisms and where a patient is already treated with a drug C:
monitoring a therapeutic response of the patient to drug C treatment;
identifying, from results of the monitoring, that the therapeutic response of the patient to the drug C treatment resembles a non-responsive Betti curve; and
automatically terminating treatment of the patient with the drug C treatment based on the therapeutic response of the patient to the drug C treatment resembling the non-responsive Betti curve.
12 . The computing system according to claim 11 , wherein:
the first data type is associated with a first cancer and the second data type is associated with a second cancer,
Betti numbers are defined as the number of structures at a given dimension dϵD, a Betti number Bpd is learned for each phenotype pϵP of the first cancer and the second cancer, where Bpd is calculated from a fixed number of samples Npd, which is dependent on a size of p and which is constructed from samples non-exclusively drawn from p to capture a noisy space reflective of a heterogeneous nature of each of the first cancer and the second cancer, and
the training of the model comprises training a model Md for Bpd for each de D and testing the model Md during a testing phase, the testing comprising adding an unlabeled sample t with an identical feature space to each Npd to give N′pd and recalculating Bpd as B′pd for each given dimension d.
13 . The computing system according to claim 11 , wherein the training comprises re-sampling of the data.
14 . The computing system according to claim 11 , wherein the iteratively re-training of the model comprises ignoring a least likely result and, in an event the training of the model uses six total Betti curves and the determining reveals that, for a given data sample of breast cancer, deviations between one pair of the new Betti curves and the initial Betti curves associated with lung cancer exceeded all the other deviations, the method for data analysis further comprises discarding that one pair during the re-training to recognize Betti curves for data samples associated with characteristics of breast cancer.