/**
	 * Predicts passed attributes using the sigmoid function and returns its chance to fit to the certain label.
	 * @param data
	 * @return
	 */
	float predict(MatrixXf &data){  // Data is basically a vector here, just rows no columns

		// LogisticRegression network graph like calculation
		auto sum = 0.0f;
		for (auto index = 0; index < data.rows(); index++) {

			auto weight = weights(index); // Weights is also a vector
			auto attribute = data(index);

			auto result = weight * attribute;
			sum += result;
		}

		// Sigmoid
		return 1.0f / (1.0f + exp(-sum));
	}


	/**
	 * Learns by a given set of dataSet and trains the perceptron.
	 * @param dataSet
	 */
	void learn(int iterations, MatrixXf &dataSet, MatrixXf &labelSet){  // Data is

		auto difference = MatrixXf(labelSet.rows(), 1); // The vector being used as ( a - y ) ^ T from the formula
		for (auto index = 0; index < iterations; ++index) {

			// Update differences... basically ( prediction - label ) -> ( a - y )^T from the formula
			for (auto col = 0; col < dataSet.cols(); ++col) {

				auto data = dataSet.col(col); // The first data vector
				auto predicted = predict(data.nestedExpression());  // Predicted value
				difference(col) = predicted - labelSet(col);  // Insert into ( a - y ) ^ T vector
			}

			auto gradient = ( 1.0f/(float)dataSet.cols() * ( dataSet * difference)); // 1/m * X * ( A - Y ) ^ T
			weights -= step * gradient;  // Update gradients
		}
	}