AGMM.py

# Marcus Vinicius Sousa Leite de Carvalho
# marcus.decarvalho@ntu.edu.sg
# ivsucram@gmail.com
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from MyUtil import MyUtil
from MySingletons import MyDevice

import numpy as np
import torch
import math


class GMM:
    weight = 1
    center = None
    variance = None
    win_counter = 1
    inference_sum = 0
    survive_counter = 0
    y_count = None
    dist = None

    _number_features = None

    @property
    def inference(self):
        if self.dist is not None:
            return torch.min(self.dist)
        return torch.tensor(0)

    @property
    def hyper_volume(self):
        if self.dist is not None:
            return self.variance[0][torch.argmin(self.dist)]
        return torch.tensor([[0.01]])

    @property
    def standard_deviation(self):
        return torch.sqrt(self.variance)

    @property
    def std(self):
        return self.standard_deviation

    @property
    def precision(self):
        return 1/self.variance

    @property
    def first_order_moment(self):
        return self.center

    @property
    def second_order_moment(self):
        return self.center ** 2 + self.variance

    @property
    def mode(self):
        return self.center

    @property
    def probX_J(self):
        denumerator = torch.sqrt(2 * math.pi * self.hyper_volume)
        return denumerator * self.inference

    def __init__(self, x):
        self._number_features = x.shape[1]
        self.center = x
        self.variance = 0.01 + torch.zeros(int(self._number_features), dtype=torch.float, device=MyDevice().get())
        self.variance = self.variance.view(1, self.variance.shape[0])

    def compute_inference(self, x, y=None):
        if y is not None:
            if self.y_count is None:
                self.y_count = y
            else:
                self.y_count += y

        c = self.center

        dist = ((x - c) ** 2) / (- 2 * self.variance)
        self.dist = torch.exp(dist)


class AGMM:
    gmm_array = None
    number_samples_feed = 0
    rho = 0.1
    number_features = None

    @property
    def hyper_volume(self):
        hyper_volume = torch.tensor(0, dtype=torch.float, device=MyDevice().get())
        for i in range(len(self.gmm_array)):
            hyper_volume += self.gmm_array[i].hyper_volume
        return hyper_volume

    @property
    def weight_sum(self):
        weight_sum = torch.tensor(0, dtype=torch.float, device=MyDevice().get())
        for i in range(self.M()):
            weight_sum += self.gmm_array[i].weight
        return weight_sum

    def run(self, x, bias2):
        self.number_samples_feed += 1
        if self.gmm_array is None:
            self.gmm_array = [GMM(x)]
            self.number_features = x.shape[1]
        else:
            self.compute_inference(x)
            gmm_winner_idx = np.argmax(self.update_weights())

            if self.M() > 1:
                self.compute_overlap_degree(gmm_winner_idx, 3, 3)

            denominator = 1.25 * torch.exp(-bias2) + 0.75 * self.number_features
            numerator = 4 - 2 * torch.exp(torch.tensor(-self.number_features / 2.0, dtype=torch.float, device=MyDevice().get()))
            threshold = torch.exp(- denominator / numerator)

            condition1 = self.gmm_array[gmm_winner_idx].inference < threshold
            condition2 = self.gmm_array[gmm_winner_idx].hyper_volume > self.rho * (self.hyper_volume - self.gmm_array[gmm_winner_idx].hyper_volume)
            condition3 = self.number_samples_feed > 10
            if condition1 and condition2 and condition3:
                self.create_cluster(x)
                self.gmm_array[-1].variance = (x - self.gmm_array[gmm_winner_idx].center) ** 2
            else:
                self.update_cluster(x, self.gmm_array[gmm_winner_idx])

    def create_cluster(self, x):
        self.gmm_array.append(GMM(x))

        weight_sum = self.weight_sum
        for gmm in self.gmm_array:
            gmm.weight = gmm.weight / weight_sum

    def update_cluster(self, x, gmm):
        gmm.win_counter += 1
        gmm.center += (x - gmm.center) / gmm.win_counter
        gmm.variance += ((x - gmm.center) ** 2 - gmm.variance) / gmm.win_counter

    def delete_cluster(self):
        if self.M() <= 1:
            return

        accumulated_inference = []
        for gmm in self.gmm_array:
            if gmm.survive_counter > 0:
                accumulated_inference.append(gmm.inference_sum / gmm.survive_counter)

        accumulated_inference = torch.stack(accumulated_inference)[torch.isnan(torch.stack(accumulated_inference)) == False]

        delete_list = torch.where(accumulated_inference <= (torch.mean(accumulated_inference) - 0.5 * torch.std(accumulated_inference)))[0]
        if len(delete_list) == len(self.gmm_array):
            raise TypeError('problem')  # FIXME if this happen, it means you have a great problem at your code

        if len(delete_list):
            self.gmm_array = np.delete(self.gmm_array, delete_list.cpu().numpy()).tolist()
            accumulated_inference = torch.tensor(np.delete(accumulated_inference.cpu().numpy(), delete_list.cpu().numpy()).tolist(), dtype=torch.float, device=MyDevice().get())

        sum_weight = 0
        for gmm in self.gmm_array:
            sum_weight += gmm.weight

        if sum_weight == 0:
            max_index = torch.argmax(accumulated_inference)
            self.gmm_array[max_index].weight += 1
            sum_weight = 0
            for gmm in self.gmm_array:
                sum_weight += gmm.weight

        for gmm in self.gmm_array:
            gmm.weight = gmm.weight / sum_weight

    def compute_inference(self, x, y=None):
        for gmm in self.gmm_array:
            gmm.compute_inference(x, y)

    def update_weights(self):
        probX_JprobJ = torch.zeros(len(self.gmm_array))
        weights = torch.zeros(len(self.gmm_array))

        sum_winner_counter = 0
        max_inference = 0
        max_inference_index = 0
        for i in range(self.M()):
            sum_winner_counter += self.gmm_array[i].win_counter
            if self.gmm_array[i].inference > max_inference:
                max_inference = self.gmm_array[i].inference
                max_inference_index = i

        for i in range(self.M()):
            self.gmm_array[i].inference_sum += self.gmm_array[i].inference
            self.gmm_array[i].survive_counter += 1

            probJ = self.gmm_array[i].win_counter / sum_winner_counter
            probX_JprobJ[i] = self.gmm_array[i].probX_J * probJ

        if torch.sum(probX_JprobJ) == 0:
            probX_JprobJ[max_inference_index] += 1

        for i in range(self.M()):
            self.gmm_array[i].weight = float(probX_JprobJ[i] / torch.sum(probX_JprobJ))
            weights[i] = self.gmm_array[i].weight

        return weights

    def compute_overlap_degree(self, gmm_winner_idx, maximum_limit=None, minimum_limit=None):
        if maximum_limit is None:
            maximum_limit = minimum_limit = 3
        elif minimum_limit is None:
            minimum_limit = maximum_limit

        overlap_coefficient = torch.tensor(1 / self.M(), dtype=torch.float, device=MyDevice().get())

        sigma_maximum_winner = maximum_limit * torch.sqrt(self.gmm_array[gmm_winner_idx].variance)
        sigma_minimum_winner = minimum_limit * torch.sqrt(self.gmm_array[gmm_winner_idx].variance)

        winner_center = self.gmm_array[gmm_winner_idx].center

        if maximum_limit == minimum_limit:
            mean_positive_sigma_winner = winner_center + sigma_maximum_winner
            mean_negative_sigma_winner = winner_center - sigma_minimum_winner
        else:
            # FIXME This seems wrong
            mean_positive_sigma_winner = winner_center + sigma_minimum_winner + sigma_maximum_winner
            mean_negative_sigma_winner = winner_center - sigma_minimum_winner - sigma_maximum_winner

        mean_positive_sigma = torch.zeros(int(self.M()), int(self.number_features), dtype=torch.float, device=MyDevice().get())
        mean_negative_sigma = torch.zeros(int(self.M()), int(self.number_features), dtype=torch.float, device=MyDevice().get())
        overlap_mins_mins   = torch.zeros(int(self.M()), int(self.number_features), dtype=torch.float, device=MyDevice().get())
        overlap_mins_plus   = torch.zeros(int(self.M()), int(self.number_features), dtype=torch.float, device=MyDevice().get())
        overlap_plus_mins   = torch.zeros(int(self.M()), int(self.number_features), dtype=torch.float, device=MyDevice().get())
        overlap_plus_plus   = torch.zeros(int(self.M()), int(self.number_features), dtype=torch.float, device=MyDevice().get())

        overlap_score = []

        for i in range(self.M()):
            sigma_maximum = maximum_limit * torch.sqrt(self.gmm_array[i].variance)
            sigma_minimum = minimum_limit * torch.sqrt(self.gmm_array[i].variance)

            if maximum_limit == minimum_limit:
                mean_positive_sigma[i] = self.gmm_array[i].center + sigma_maximum
                mean_negative_sigma[i] = self.gmm_array[i].center - sigma_maximum
            else:
                #FIXME This seems wrong
                mean_positive_sigma[i] = sigma_maximum + sigma_minimum
                mean_negative_sigma[i] = -sigma_minimum - sigma_maximum

            overlap_mins_mins[i] = torch.mean(mean_negative_sigma[i] - mean_negative_sigma_winner)
            overlap_mins_plus[i] = torch.mean(mean_positive_sigma[i] - mean_negative_sigma_winner)
            overlap_plus_mins[i] = torch.mean(mean_negative_sigma[i] - mean_positive_sigma_winner)
            overlap_plus_plus[i] = torch.mean(mean_positive_sigma[i] - mean_positive_sigma_winner)

            condition1 = (overlap_mins_mins[i] >= 0).all() \
                     and (overlap_mins_plus[i] >= 0).all() \
                     and (overlap_plus_mins[i] <= 0).all() \
                     and (overlap_plus_plus[i] <= 0).all()
            condition2 = (overlap_mins_mins[i] <= 0).all() \
                     and (overlap_mins_plus[i] >= 0).all() \
                     and (overlap_plus_mins[i] <= 0).all() \
                     and (overlap_plus_plus[i] >= 0).all()
            condition3 = (overlap_mins_mins[i] > 0).all() \
                     and (overlap_mins_plus[i] > 0).all() \
                     and (overlap_plus_mins[i] < 0).all() \
                     and (overlap_plus_plus[i] > 0).all()
            condition4 = (overlap_mins_mins[i] < 0).all() \
                     and (overlap_mins_plus[i] > 0).all() \
                     and (overlap_plus_mins[i] < 0).all() \
                     and (overlap_plus_plus[i] < 0).all()

            if condition1 or condition2:
                # full overlap, the cluster is inside the winning cluster
                # the score is full score
                overlap_score.append(overlap_coefficient)
            elif condition3 or condition4:
                # partial overlap, the score is the full score multiplied by the overlap degree
                reward = MyUtil.norm_2(self.gmm_array[i].center - self.gmm_array[gmm_winner_idx].center) \
                       / MyUtil.norm_2(self.gmm_array[i].center + self.gmm_array[gmm_winner_idx].center) \
                       + MyUtil.norm_2(self.gmm_array[i].center - torch.sqrt(self.gmm_array[gmm_winner_idx].variance)) \
                       / MyUtil.norm_2(self.gmm_array[i].center + torch.sqrt(self.gmm_array[gmm_winner_idx].variance))
                overlap_score.append(overlap_coefficient * reward)
            else:
                # No overlap, then the score is 0
                overlap_score.append(torch.zeros(1))

        overlap_score.pop(gmm_winner_idx)
        self.rho = torch.sum(torch.stack(overlap_score))
        self.rho = torch.min(self.rho, torch.ones_like(self.rho))
        self.rho = torch.max(self.rho, torch.ones_like(self.rho) * 0.1)  # Do not let rho = zero

    def compute_rho_vigilance_test(self, x, gmm_winner_idx):
        pass

    def compute_rho_containing_rule(self, gmm_winner_idx, maximum_limit, minimum_limit):
        pass

    def compute_number_of_gmms(self):
        if self.gmm_array is None:
            return 0
        else:
            return len(self.gmm_array)

    def M(self):
        return self.compute_number_of_gmms()