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PFSA.m
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classdef PFSA
% Class File Containing the Essential PFSA Functions needed
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: August, 2021
%
% Please cite:
% Chandrachur Bhattacharya and Dr Asok Ray. Thresholdless Classification
% of Chaotic Dynamics and Combustion Instability via Probabilistic Finite
% State Automata." Mechanical Systems and Signal Processing (2021).
%
% Important functions in this class and their syntax given below:
% (For details please type: help PFSA/function_name)
%
% FUNCTIONS IMPORTANT TO THE USER
%
% [model] = Define_PFSA(N,D,part_scheme,global_part,unit_var,analysis_type)
% [model] = Train_PFSA_Bulk(model,training_data,training_label)
% [model] = Init_PFSA_Sequential(model,training_data_raw)
% [model] = Train_PFSA_Sequential(model,training_data,training_label)
% [pred_class] = Test_PFSA(model,testing_data)
%
% There are 2 routes to training and testing PFSA models
%
% ROUTE 1:
% Define_PFSA -> Train_PFSA_Bulk -> Test_PFSA
%
% (Preferred when training data windows are lower in number / data
% pre-organized as [TS_data_window_1; ... ;TS_data_window_n] and
% [label_1; ... ; label_n] format)
%
% ROUTE 2:
% Define_PFSA -> Init_PFSA_Sequential -> Train_PFSA_Sequential -> Test_PFSA
%
% (Preferred when training data windows are large in number / data
% pre-organized as [TS_data_1; ... ;TS_data_n] and
% [label_series_1; ... ; label_series_n] format)
%
% NOTE: Sequential training is sometimes a bit slower than bulk
% training, due to the fact that values are recomputed at every step.
% However, this allows for lesser data manipulation (like needed in
% the 'Bulk' method). This leads to an overall faster training.
%
% FOR A LISTING OF THE OTHER FUNCTIONS IN THIS CLASS PLEASE TYPE:
% help PFSA/More_Info
methods(Static)
function [model] = Define_PFSA(N,D,part_scheme,global_part,unit_var,analysis_type)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: May 6, 2020
%
% FORMAT: [model] = Define_PFSA(training_data,training_label,...
% N,D,partitioning,global_part,unit_var,analysis_type)
% PURPOSE: Creates the PFSA model to be used for the analysis
% Outputs a PFSA model that is used during training
% and testing phases.
% [Needs to be called as an object]
%
% INPUTS: N = Number of partitions of the PFSA
% D = Depth of the PFSA
% global_part = Set to 1 if a global partition is
% desired (recommended), 0 otherwise
% unit_var = Set to 1 if normalization is to be
% done to generate zero mean and unit
% variance (recommended), 0 otherwise
% analysis_type = Choose the PFSA analysis type:
% 's' - Standard PFSA
% 'p' - Projection PFSA (recommended)
% 'b' - Best (tries to choose the
% most accurate of 's' and 'p')
% OUTPUTS: model = Base PFSA model
model.N = N;
model.D = D;
model.part_scheme = part_scheme;
model.global_part = global_part;
model.unit_var = unit_var;
model.analysis_type = analysis_type;
model.classes = 0;
end
function [model] = Train_PFSA_Bulk(model,training_data,training_label)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: May 6, 2020
%
% FORMAT: [model] = Train_PFSA_Bulk(model,training_data,training_label)
% PURPOSE: Trains the PFSA model using the training time
% series data and the corresponding (numeric) class
% label. 'Bulk' implies full training data and labels
% must be provided to the function.
% [Needs to be called as an object]
%
% INPUTS: model = Base PFSA model with parameters.
% This must be generated using the
% function: Define_PFSA(...)
% training_data = Training data time-series as a
% matrix of size (m x n), n is the
% number of samples per time series
% and m is the number of training
% time series
% [NOTE: All the time series must
% have the same length (n)]
% training_label = Corresponding training labels for
% the time series as a vector of size
% (m x 1)
% OUTPUTS: model = Trained PFSA model
N = model.N;
D = model.D;
part_scheme = model.part_scheme;
global_part = model.global_part;
unit_var = model.unit_var;
analysis_type = model.analysis_type;
num_classes = length(unique(training_label));
states = generate_states(PFSA,N,D);
for i = 1:num_classes
pi_train{i} = zeros(N^D,N^D);
mean_train(i) = 0;
std_train(i) = 0;
cnt(i) = 0;
end
if global_part == 1
if unit_var == 1
for i = 1:size(training_data,1)
bounds(i,:) = return_partitions_unit_var(PFSA,training_data(i,:),part_scheme,N);
end
elseif unit_var == 2
for i = 1:size(training_data,1)
bounds(i,:) = return_partitions(PFSA,training_data(i,:),part_scheme,N);
end
else
for i = 1:size(training_data,1)
bounds(i,:) = return_partitions_unit_range(PFSA,training_data(i,:),part_scheme,N);
end
end
% bounds = sign(mean(bounds)).*max(abs(bounds));
bounds = sign(mean(bounds)).*mean(abs(bounds));
% bounds = mean(bounds);
end
for i = 1:size(training_data,1)
if global_part == 1
if unit_var == 1
y = symbolize_partitions_unit_var(PFSA,training_data(i,:),bounds);
elseif unit_var ==2
y = symbolize_partitions(PFSA,training_data(i,:),bounds);
else
y = symbolize_partitions_unit_range(PFSA,training_data(i,:),bounds);
end
else
if unit_var == 1
y = symbolize_unit_var(PFSA,training_data(i,:),part_scheme,N);
else
y = symbolize_unit_range(PFSA,training_data(i,:),part_scheme,N);
end
end
pi_temp = State_Transition_Matrix(PFSA,y,N,D,states);
pi_train{training_label(i)} = pi_train{training_label(i)} + pi_temp;
mean_train(training_label(i)) = mean_train(training_label(i)) + mean(training_data(i,:));
std_train(training_label(i)) = std_train(training_label(i)) + std(training_data(i,:));
cnt(training_label(i)) = cnt(training_label(i)) + 1;
end
for i = 1:num_classes
pi_train{i} = pi_train{i}/cnt(i);
mean_train(i) = mean_train(i)/cnt(i);
std_train(i) = std_train(i)/cnt(i);
if analysis_type == 'p' || analysis_type == 'b'
[Right{i},Val{i},Left{i}] = eig(pi_train{i},'vector');
[~,ind] = sort(real(Val{i}),'descend');
Val{i} = Val{i}(ind);
Right{i} = Right{i}(:,ind);
mult = sign(Right{i}(1,1));
Right{i} = Right{i}*mult;
Left{i} = Left{i}(:,ind);
Left{i} = Left{i}'*mult;
factor = sqrt(abs(Val{i}));
temp = factor'.*Right{i};
for j = 1:1
[Right_Ortho{i,j},~] = qr(temp(:,[[1:j-1],[j+1:end]]));
Right_Ortho{i,j} = sign(real(Right_Ortho{i,j}(1,[1:end-1]))).*Right_Ortho{i,j}(:,[1:end-1]);
end
end
end
model.pi_train = pi_train;
model.mean_train = mean_train;
model.std_train = std_train;
if analysis_type == 'p' || analysis_type == 'b'
model.Right_Ortho = Right_Ortho;
end
if global_part == 1
model.bounds = bounds;
end
model.classes = num_classes;
model.map = [1:num_classes];
end
function [model] = Init_PFSA_Sequential(model,training_data_raw)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: May 6, 2020
%
% FORMAT: [Init_PFSA_Sequential(model,training_data_raw)
% PURPOSE: Initializes the PFSA model using the training raw
% time series data. Here the time-series data need
% not be organized and is inputed as a (p x q)
% matrix, where p is the number of observed raw time
% series (irrespective of regime / class) and q is
% the data samples per time series
% [Needs to be called as an object]
%
% INPUTS: model = Base PFSA model with parameters.
% This must be generated using the
% function: Define_PFSA(...)
% training_data_raw = Training data time-series as a
% matrix of size (p x q), p is the
% number of observed raw time series
% (irrespective of regime / class)
% and q is the data samples per time
% series
% [NOTE: All the time series must
% have the same length (q)]
% OUTPUTS: model = Initialized PFSA model for
% Sequential method
N = model.N;
D = model.D;
part_scheme = model.part_scheme;
global_part = model.global_part;
unit_var = model.unit_var;
states = generate_states(PFSA,N,D);
% training_data_raw = training_data_raw(:);
if global_part == 1
if unit_var == 1
for i = 1:size(training_data_raw,1)
bounds(i,:) = return_partitions_unit_var(PFSA,training_data_raw(i,:),part_scheme,N);
end
elseif unit_var == 2
for i = 1:size(training_data_raw,1)
bounds(i,:) = return_partitions(PFSA,training_data_raw(i,:),part_scheme,N);
end
else
for i = 1:size(training_data_raw,1)
bounds(i,:) = return_partitions_unit_range(PFSA,training_data_raw(i,:),part_scheme,N);
end
end
model.bounds_list = bounds;
bounds = sign(mean(bounds)).*max(abs(bounds));
% bounds = mean(bounds);
if unit_var == 2 || unit_var == 0
bounds = [0:1/(length(bounds)-1):1]*(max(bounds) - min(bounds)) + min(bounds);
end
end
if global_part == 1
model.bounds = bounds;
end
end
function [model] = Train_PFSA_Sequential(model,training_data,training_label)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: May 6, 2020
%
% FORMAT: [model] = Train_PFSA_Sequential(model,training_data,training_label)
% PURPOSE: Trains the PFSA model using the training time
% series data and the corresponding (numeric) class
% label. 'Sequential' implies the training data and
% labels is provided to the function sequqnetially
% (i.e. in an online windowed fashion).
% [Needs to be called as an object]
%
% INPUTS: model = Base PFSA model with parameters.
% This must be generated using the
% function: Define_PFSA(...) and
% initialized by: Init_PFSA_Sequential(...)
% training_data = Training data time-series as a
% vector of size (1 x n), n is the
% number of samples in the time series
% [NOTE: Only a single time series is
% allowed]
% training_label = Corresponding training label for
% the time series as a scalar
% OUTPUTS: model = Trained PFSA model
N = model.N;
D = model.D;
part_scheme = model.part_scheme;
global_part = model.global_part;
unit_var = model.unit_var;
analysis_type = model.analysis_type;
if global_part == 1
bounds = model.bounds;
end
states = generate_states(PFSA,N,D);
if model.classes == 0
num_classes = model.classes;
num_classes = num_classes + 1;
pi_train{1} = zeros(N^D,N^D);
mean_train(1) = 0;
std_train(1) = 0;
cnt(1) = 0;
map(1) = training_label;
elseif ismember(training_label,model.map) == 0
num_classes = model.classes;
pi_train = model.pi_train;
mean_train = model.mean_train;
std_train = model.std_train;
cnt = model.cnt;
map = model.map;
if analysis_type == 'p' || analysis_type == 'b'
Right_Ortho = model.Right_Ortho;
end
num_classes = num_classes + 1;
pi_train{end+1} = zeros(N^D,N^D);
mean_train(end+1) = 0;
std_train(end+1) = 0;
cnt(end+1) = 0;
map(end+1) = training_label;
else
num_classes = model.classes;
pi_train = model.pi_train;
mean_train = model.mean_train;
std_train = model.std_train;
cnt = model.cnt;
map = model.map;
if analysis_type == 'p' || analysis_type == 'b'
Right_Ortho = model.Right_Ortho;
end
end
if global_part == 1
if unit_var == 1
y = symbolize_partitions_unit_var(PFSA,training_data(1,:),bounds);
elseif unit_var ==2
y = symbolize_partitions(PFSA,training_data(1,:),bounds);
else
y = symbolize_partitions_unit_range(PFSA,training_data(1,:),bounds);
end
else
if unit_var == 1
y = symbolize_unit_var(PFSA,training_data(1,:),part_scheme,N);
else
y = symbolize_unit_range(PFSA,training_data(1,:),part_scheme,N);
end
end
pi_temp = State_Transition_Matrix(PFSA,y,N,D,states);
pi_train{training_label(1)} = (pi_train{training_label(1)}*cnt(training_label(1))...
+ pi_temp)/(cnt(training_label(1)) + 1);
mean_train(training_label(1)) = (mean_train(training_label(1))*cnt(training_label(1))...
+ mean(training_data(1,:)))/(cnt(training_label(1)) + 1);
std_train(training_label(1)) = (std_train(training_label(1))*cnt(training_label(1))...
+ std(training_data(1,:)))/(cnt(training_label(1)) + 1);
cnt(training_label(1)) = cnt(training_label(1)) + 1;
if analysis_type == 'p' || analysis_type == 'b'
[Right,Val,Left] = eig(pi_train{training_label(1)},'vector');
[~,ind] = sort(real(Val),'descend');
Val = Val(ind);
Right = Right(:,ind);
mult = sign(Right(1,1));
Right = Right*mult;
Left = Left(:,ind);
Left = Left'*mult;
factor = sqrt(abs(Val));
temp = factor'.*Right;
for j = 1:1
[Right_Ortho{training_label(1),j},~] = qr(temp(:,[[1:j-1],[j+1:end]]));
Right_Ortho{training_label(1),j} = sign(real(Right_Ortho{training_label(1),j}(1,[1:end-1])))...
.*Right_Ortho{training_label(1),j}(:,[1:end-1]);
end
end
model.pi_train = pi_train;
model.mean_train = mean_train;
model.std_train = std_train;
model.cnt = cnt;
if analysis_type == 'p' || analysis_type == 'b'
model.Right_Ortho = Right_Ortho;
end
if global_part == 1
model.bounds = bounds;
end
model.classes = num_classes;
model.map = map;
end
function [pred_class] = Test_PFSA(model,testing_data)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: May 6, 2020
%
% FORMAT: [pred_class] = Test_PFSA(model,testing_data)
% PURPOSE: Classifies the test time series data using the
% trained PFSA model. The output is the (numeric)
% class label.
% [Needs to be called as an object]
%
% INPUTS: model = Trained PFSA model with parameters.
% This must be generated using the
% function: Train_PFSA(...)
% (which needs: Define_PFSA(...))
% testing_data = Testing data time-series as a
% matrix of size (m x n), n is the
% number of samples per time series
% and m is the number of training
% time series.
% [NOTE 1: All the time series must
% have the same length (n)]
% [NOTE 2: To analyse a single window
% (e.g. online) the matrix is
% a vector of size (1 x n)]
% OUTPUTS: pred_class = Corresponding predicted classification
% labels for the test time series
% as a vector of size (m x 1).
% [NOTE: When analysing a single window
% (e.g. online) output is a scalar]
N = model.N;
D = model.D;
part_scheme = model.part_scheme;
global_part = model.global_part;
unit_var = model.unit_var;
analysis_type = model.analysis_type;
pi_train = model.pi_train;
mean_train = model.mean_train;
std_train = model.std_train;
if analysis_type == 'p' || analysis_type == 'b'
Right_Ortho = model.Right_Ortho;
end
if global_part == 1
bounds = model.bounds;
end
map = model.map;
num_classes = model.classes;
states = generate_states(PFSA,N,D);
for i = 1:size(testing_data,1)
if global_part == 1
if unit_var == 1
y = symbolize_partitions_unit_var(PFSA,training_data(i,:),bounds);
elseif unit_var ==2
y = symbolize_partitions(PFSA,training_data(i,:),bounds);
else
y = symbolize_partitions_unit_range(PFSA,training_data(i,:),bounds);
end
else
if unit_var == 1
y = symbolize_unit_var(PFSA,testing_data(i,:),part_scheme,N);
else
y = symbolize_unit_range(PFSA,testing_data(i,:),part_scheme,N);
end
end
pi_temp = State_Transition_Matrix(PFSA,y,N,D,states);
std_temp = std(testing_data(i,:));
mean_temp = mean(testing_data(i,:));
dist_pi = [];
if analysis_type == 's' || analysis_type == 'b'
for j = 1:num_classes
dist_pi(j) = norm([norm(pi_train{j} - pi_temp,2),...
std_temp-std_train(j),mean_temp - mean_train(j)],2);
% dist_pi(j) = norm([norm(pi_train{j} - pi_temp,2),...
% (std_temp-std_train(j))/std_train(j),(mean_temp - mean_train(j))/mean_train(j)],2);
end
end
error = [];
if analysis_type == 'p' || analysis_type == 'b'
[Right_temp,Val_temp,Left_temp] = eig(pi_temp,'vector');
[~,ind] = sort(real(Val_temp),'descend');
Val_temp = Val_temp(ind);
Right_temp = Right_temp(:,ind);
mult = sign(real(Right_temp(1,1)));
Left_temp = (Left_temp(:,ind)*mult)';
for j = 1:num_classes
error(j) = norm([vecnorm((Left_temp(1,:)*Right_Ortho{j,1}),2,2),...
std_temp-std_train(j),mean_temp - mean_train(j)],2);
% error(j) = norm([vecnorm((Left_temp(1,:)*Right_Ortho{j,1}),2,2),...
% 1-min(std_temp/std_train(j),std_train(j)/std_temp),...
% 1-min(mean_temp/mean_train(j),mean_train(j)/mean_temp)],2);
end
% for j = 1:num_classes
% error(j,1) = vecnorm((Left_temp(1,:)*Right_Ortho{j,1}),2,2);
% error(j,2) = std_temp-std_train(j);
% error(j,3) = mean_temp - mean_train(j);
% end
%
% [~,p] = sort(abs(error),'ascend');
%
% r = [];
% for k = 1:3
% r(p(:,k),k) = [1:num_classes];
% end
%
% error = sum(r')';
end
switch analysis_type
case 's'
pred_class(i,1) = map(find(dist_pi == min(dist_pi)));
case 'p'
% [M,F] = mode(r');
% temp_pred = union(find(error == min(error)),find(M == min(M)));
% if length(temp_pred) > 1
% [M,F] = mode(r(temp_pred,:)');
% temp_pred = temp_pred(find(M == min(M)));
% end
% if length(temp_pred) > 1
% for j = 1:num_classes
% error(j) = norm([vecnorm((Left_temp(1,:)*Right_Ortho{j,1}),2,2),...
% std_temp-std_train(j),mean_temp - mean_train(j)],2);
% end
% temp_pred = find(error == min(error));
% end
%
% pred_class(i,1) = map(temp_pred);
pred_class(i,1) = map(find(error == min(error)));
case 'b'
conf_pi = sort((1./dist_pi)./sum(1./dist_pi),'descend');
conf_proj = sort((1./error)./sum(1./error),'descend');
if conf_pi(1) >= conf_proj(1)
pred_class(i,1) = map(find(dist_pi == min(dist_pi)));
else
pred_class(i,1) = map(find(error == min(error)));
end
end
end
end
end
methods
function [] = More_Info()
% OTHER PROGRAM FUNCTIONS
% For further information on these functions please type:
% "help PFSA/function_name"
%
% [arr] = chooseNfromP(obj,N,P)
% [bounds] = return_partitions_unit_var(obj,x,t,n)
% [bounds] = return_partitions_unit_range(obj,x,t,n)
% [y] = normalize_unit_var(obj,x)
% [y] = normalize_unit_range(obj,x)
% [bounds] = return_partitions_unit_var(obj,x,t,n)
% [bounds] = return_partitions_unit_range(obj,x,t,n)
% [A] = State_Transition_Matrix(obj,y,n,D,states)
% [A] = State_Transition_Matrix_D1(obj,y,n)
% [y] = symbolize_partitions_unit_range(obj,x,bounds)
% [y] = symbolize_partitions_unit_var(obj,x,bounds)
% [y] = symbolize_unit_var(obj,x,t,n)
% [y] = symbolize_unit_range(obj,x,t,n)
% [states] = generate_states(obj,n,D)
% [P] = State_Probability_Vector(obj,y,n,D,states)
end
function [arr] = chooseNfromP(obj,N,P)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [arr] = chooseNfromP(obj,N,P)
% PURPOSE: This function chooses N numbers from P numbers randomly
% INPUTS: N = No. of Numbers to be chosen,
% P = Total Numbers
% OUTPUTS: arr = Array of N selected numbers
% MATLAB functions called: ceil isempty intersect
% Non-MATLAB functions called: None
n = 1;
arr = [];
while n<=N
temp = ceil(rand*P);
if isempty(intersect(temp,arr))==1
arr(n) = temp;
n = n+1;
end
end
end
function [y] = normalize_unit_var(obj,x)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = normalize_unit_var(obj,x)
% PURPOSE: This function returns the normalized time-series to have zero
% mean and unit variance
% INPUTS: x = Raw time-series
% OUTPUTS: y = Normalized time-series
% MATLAB functions called: mean std
% Non-MATLAB functions called: None
y = (x-mean(x))/std(x);
end
function [y] = normalize_unit_range(obj,x)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = normalize_unit_range(obj,x)
% PURPOSE: This function returns the normalized time-series
% to have unit range
% INPUTS: x = Raw time-series
% OUTPUTS: y = Normalized time-series
% MATLAB functions called: max min
% Non-MATLAB functions called: None
range = max(x) - min(x) + 1e-9;
y = (x-min(x))/range;
end
function [bounds] = return_partitions_unit_var(obj,x,t,n)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [bounds] = return_partitions_unit_var(obj,x,t,n)
% PURPOSE: This function returns the partition boundaries for a given raw
% data time series after normalizing the data to have zero mean
% and unit variance
% INPUTS: x = Raw time-series,
% t = Type of partitioning schemes (MEP: 'm', Uniform: 'u',
% K-means: 'k'),
% n = Alphabet size
% OUTPUTS: bounds = normalized partition boundary values
% MATLAB functions called: min max sort size kmeans find
% Non-MATLAB functions called: normalizeTS
x = normalize_unit_var(PFSA,x);
bounds = zeros(1,n);
switch t
case 'u'
bounds = [0:1/n:1]*(max(x) - min(x)) + min(x);
case 'm'
x1 = sort(x);
K = max(size(x1));
bounds(1) = min(x1);
for i=1:n
bounds(i+1) = x1(ceil(i*K/n));
end
case 'k'
y = kmeans(x',n,'MaxIter',10000);
bounds(1) = min(x);
for i=1:n
bounds(i+1) = max(x(find(y == i)));
end
bounds = sort(bounds);
end
end
function [bounds] = return_partitions_unit_range(obj,x,t,n)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [bounds] = return_partitions_unit_range(obj,x,t,n)
% PURPOSE: This function returns the partition boundaries for a given raw
% data time series after normalizing the data to have zero mean
% and unit variance
% INPUTS: x = Raw time-series,
% t = Type of partitioning schemes (MEP: 'm', Uniform: 'u',
% K-means: 'k'),
% n = Alphabet size
% OUTPUTS: bounds = normalized partition boundary values
% MATLAB functions called: min max sort size kmeans find
% Non-MATLAB functions called: normalizeTS
x = normalize_unit_range(PFSA,x);
bounds = zeros(1,n);
switch t
case 'u'
bounds = [0:1/n:1]*(max(x) - min(x)) + min(x);
case 'm'
x1 = sort(x);
K = max(size(x1));
bounds(1) = min(x1);
for i=1:n
bounds(i+1) = x1(ceil(i*K/n));
end
case 'k'
y = kmeans(x',n,'MaxIter',10000);
bounds(1) = min(x);
for i=1:n
bounds(i+1) = max(x(find(y == i)));
end
bounds = sort(bounds);
end
end
function [bounds] = return_partitions(obj,x,t,n)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified:August 4, 2021
% FORMAT: [bounds] = return_partitions(obj,x,t,n)
% PURPOSE: This function returns the partition boundaries for a given raw
% data time series without normalizing the data
% INPUTS: x = Raw time-series,
% t = Type of partitioning schemes (MEP: 'm', Uniform: 'u',
% K-means: 'k'),
% n = Alphabet size
% OUTPUTS: bounds = partition boundary values
% MATLAB functions called: min max sort size kmeans find
% Non-MATLAB functions called: normalizeTS
bounds = zeros(1,n);
switch t
case 'u'
bounds = [0:1/n:1]*(max(x) - min(x)) + min(x);
case 'm'
x1 = sort(x);
K = max(size(x1));
bounds(1) = min(x1);
for i=1:n
bounds(i+1) = x1(ceil(i*K/n));
end
case 'k'
y = kmeans(x',n,'MaxIter',10000);
bounds(1) = min(x);
for i=1:n
bounds(i+1) = max(x(find(y == i)));
end
bounds = sort(bounds);
end
end
function [A] = State_Transition_Matrix(obj,y,n,D,states)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [A] = State_Transition_Matrix(obj,y,n,D,states)
% PURPOSE: This function returns the state transition matrix for the PFSA
% given a symbol sequence, Markov depth, alphabet size and the
% list of states
% INPUTS: y = Symbol sequence,
% n = Alphabet size,
% D = Markov depth,
% states = List of states (can be generated by function
% 'generate_states')
% OUTPUTS: A = State transition matrix
% MATLAB functions called: length find size
% Non-MATLAB functions called: State_Transition_Matrix_D1
% LIMITATIONS: If D>1, n is restricted to 9
if D == 1
[A] = State_Transition_Matrix_D1(obj,y,n);
else
A = zeros(n^D,n^D);
P = zeros(length(states),1);
for i = D:length(y)-1
temp1 = 0;
temp2 = 0;
for j = D:-1:1
temp1 = temp1 + 10^(j-1)*y(i-j+1);
temp2 = temp2 + 10^(j-1)*y(i-j+2);
end
A(find(states==temp1),find(states==temp2)) = A(find(states==temp1),find(states==temp2))+1;
P(find(states==temp1)) = P(find(states==temp1)) + 1;
end
for i = 1:size(A,1)
A(i,:) = (A(i,:)+1)/(P(i)+n);
end
P = (P+1)/(length(states) + sum(P));
end
end
function [A] = State_Transition_Matrix_D1(obj,y,n)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [A] = State_Transition_Matrix_D1(obj,y,n)
% PURPOSE: Sub-sub-routine to find the transition matrix when Markov
% depth (D) is 1
% INPUTS: y = Symbol sequence,
% n = Alphabet size,
% OUTPUTS: A = State transition matrix
% MATLAB functions called: None
% Non-MATLAB functions called: None
A = zeros(n);
pre = [1:n];
P = zeros(n,1);
for i = 1:length(y)-1
A(y(i),y(i+1)) = A(y(i),y(i+1)) + 1;
P(y(i)) = P(y(i)) + 1;
end
for i = 1:size(A,1)
A(i,:) = (A(i,:)+1)/(P(i)+n);
end
end
function [y] = symbolize_partitions_unit_range(obj,x,bounds)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = symbolize_partitions_unit_range(obj,x,bounds)
% PURPOSE: This function returns the symbol sequence obtained from
% normalizing and partitioning the raw data time-series using
% preset partition boundaries
% INPUTS: x = Raw time-series,
% bounds = Preset partition boundaries
% OUTPUTS: y = Computed symbol sequence (of same length as 'x')
% MATLAB functions called: length
% Non-MATLAB functions called: normalizeTS
x = normalize_unit_range(PFSA,x);
y = zeros(length(x),1);
for i = 1:length(bounds)-1
y(find(x>=bounds(i) & x<=bounds(i+1))) = i;
end
y(find(x<=bounds(1))) = 1;
y(find(x>=bounds(end))) = length(bounds)-1;
end
function [y] = symbolize_partitions_unit_var(obj,x,bounds)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = symbolize_partitions_unit_var(obj,x,bounds)
% PURPOSE: This function returns the symbol sequence obtained from
% normalizing and partitioning the raw data time-series using
% preset partition boundaries
% INPUTS: x = Raw time-series,
% bounds = Preset partition boundaries
% OUTPUTS: y = Computed symbol sequence (of same length as 'x')
% MATLAB functions called: length
% Non-MATLAB functions called: normalizeTS
x = normalize_unit_var(obj,x);
y = zeros(length(x),1);
for i = 1:length(bounds)-1
y(find(x>=bounds(i) & x<=bounds(i+1))) = i;
end
y(find(x<=bounds(1))) = 1;
y(find(x>=bounds(end))) = length(bounds)-1;
end
function [y] = symbolize_partitions(obj,x,bounds)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = symbolize_partitions_unit_var(obj,x,bounds)
% PURPOSE: This function returns the symbol sequence obtained from
% normalizing and partitioning the raw data time-series using
% preset partition boundaries
% INPUTS: x = Raw time-series,
% bounds = Preset partition boundaries
% OUTPUTS: y = Computed symbol sequence (of same length as 'x')
% MATLAB functions called: length
% Non-MATLAB functions called: normalizeTS
y = zeros(length(x),1);
for i = 1:length(bounds)-1
y(find(x>=bounds(i) & x<=bounds(i+1))) = i;
end
y(find(x<=bounds(1))) = 1;
y(find(x>=bounds(end))) = length(bounds)-1;
end
function [y] = symbolize_unit_var(obj,x,t,n)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = symbolize_unit_var(obj,x,t,n)
% PURPOSE: This function returns the symbol sequence obtained from
% normalizing to unit range of data and partitioning
% INPUTS: x = Raw time-series,
% t = Type of partitioning schemes (MEP: 'm', Uniform: 'u',
% K-means: 'k'),
% n = Alphabet size
% OUTPUTS: y = Computed symbol sequence (of same length as 'x')
% MATLAB functions called: length
% Non-MATLAB functions called: normalize
x = normalize_unit_var(obj,x);
y = zeros(length(x),1);
switch t
case 'u'
for i = 1:n
y(find(x>=(min(x)+(i-1)/n) & x<(min(x)+i/n))) = i;
end
y(find(y==0)) = n;
case 'm'
x1 = sort(x);
K = max(size(x1));
lim(1) = min(x1);
for i=1:n
lim(i+1) = x1(ceil(i*K/n));
end
for i = 1:n
y(find(x>=lim(i) & x<=lim(i+1))) = i;
end
case 'k'
y = kmeans(x',n,'MaxIter',10000);
end
end
function [y] = symbolize_unit_range(obj,x,t,n)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [y] = symbolize_unit_range(obj,x,t,n)
% PURPOSE: This function returns the symbol sequence obtained from
% normalizing to unit range of data and partitioning
% INPUTS: x = Raw time-series,
% t = Type of partitioning schemes (MEP: 'm', Uniform: 'u',
% K-means: 'k'),
% n = Alphabet size
% OUTPUTS: y = Computed symbol sequence (of same length as 'x')
% MATLAB functions called: length
% Non-MATLAB functions called: normalize
x = normalize_unit_range(PFSA,x);
y = zeros(length(x),1);
switch t
case 'u'
for i = 1:n
y(find(x>=(min(x)+(i-1)/n) & x<(min(x)+i/n))) = i;
end
y(find(y==0)) = n;
case 'm'
x1 = sort(x);
K = max(size(x1));
lim(1) = min(x1);
for i=1:n
lim(i+1) = x1(ceil(i*K/n));
end
for i = 1:n
y(find(x>=lim(i) & x<=lim(i+1))) = i;
end
case 'k'
y = kmeans(x',n,'MaxIter',10000);
end
end
function [states] = generate_states(obj,n,D)
% Code written by Chandrachur Bhattacharya @ Penn State
% Date Last Modified: November 25, 2019
% FORMAT: [states] = generate_states(obj,n,D)
% PURPOSE: This function generates unmerged PFSA states in the D-markov
% setting
% INPUTS: n = Alphabet size,
% D = Markov depth
% OUTPUTS: states = PFSA states (unmerged)
% MATLAB functions called: str2double dec2base
% Non-MATLAB functions called: None
% LIMITATIONS: If D>1, n is restricted to 9