Above are papers related to the following paper: [Paper_ID] Paper #385572. 	[Title] Individual and Collective Prognostic Prediction [Abstract] The prediction of survival time or recurrence time is an important learning problem in medical domains. The Recurrence Surface Approximation (RSA) method is a natural, effective method for predicting recurrence times using censored input data. This paper introduces the Survival Curve RSA (SC-RSA), an extension to the RSA approach which produces accurate predicted rates of recurrence, while maintaining accuracy on individual predicted recurrence times. The method is applied to the problem of breast cancer recurrence using two different datasets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #25184. 	[Title] Feature Selection via Mathematical Programming [Abstract] The problem of discriminating between two finite point sets in n-dimensional feature space by a separating plane that utilizes as few of the features as possible, is formulated as a mathematical program with a parametric objective function and linear constraints. The step function that appears in the objective function can be approximated by a sigmoid or by a concave exponential on the nonnegative real line, or it can be treated exactly by considering the equivalent linear program with equilibrium constraints (LPEC). Computational tests of these three approaches on publicly available real-world databases have been carried out and compared with an adaptation of the optimal brain damage (OBD) method for reducing neural network complexity. One feature selection algorithm via concave minimization (FSV) reduced cross-validation error on a cancer prognosis database by 35.4% while reducing problem features from 32 to 4. Feature selection is an important problem in machine learning [18, 15, 16, 17, 33]. In its basic form the problem consists of eliminating as many of the features in a given problem as possible, while still carrying out a preassigned task with acceptable accuracy. Having a minimal number of features often leads to better generalization and simpler models that can be more easily interpreted. In the present work, our task is to discriminate between two given sets in an n-dimensional feature space by using as few of the given features as possible. We shall formulate this problem as a mathematical program with a parametric objective function that will attempt to achieve this task by generating a separating plane in a feature space of as small a dimension as possible while minimizing the average distance of misclassified points to the plane. One of the computational experiments that we carried out on our feature selection procedure showed its effectiveness, not only in minimizing the number of features selected, but also in quickly recognizing and removing spurious random features that were introduced. Thus, on the Wisconsin Prognosis Breast Cancer WPBC database [36] with a feature space of 32 dimensions and 6 random features added, one of our algorithms FSV (11) immediately removed the 6 random features as well as 28 of the original features resulting in a separating plane in a 4-dimensional reduced feature space. By using tenfold cross-validation [35], separation error in the 4-dimensional space was reduced 35.4% from the corresponding error in the original problem space. (See Section 3 for details.) We note that mathematical programming approaches to the feature selection problem have been recently proposed in [4, 22]. Even though the approach of [4] is based on an LPEC formulation, both the LPEC and its method of solution are different from the ones used here. The polyhedral concave minimization approach of [22] is principally involved with theoretical considerations of one specific algorithm and no cross-validatory results are given. Other effective computational applications of mathematical programming to neural networks are given in [30, 26]. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #27174. 	[Title] Mathematical Programming in Neural Networks [Abstract] This paper highlights the role of mathematical programming, particularly linear programming, in training neural networks. A neural network description is given in terms of separating planes in the input space that suggests the use of linear programming for determining these planes. A more standard description in terms of a mean square error in the output space is also given, which leads to the use of unconstrained minimization techniques for training a neural network. The linear programming approach is demonstrated by a brief description of a system for breast cancer diagnosis that has been in use for the last four years at a major medical facility. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #285675. 	[Title] Parsimonious Least Norm Approximation [Abstract] A theoretically justifiable fast finite successive linear approximation algorithm is proposed for obtaining a parsimonious solution to a corrupted linear system Ax = b + p, where the corruption p is due to noise or error in measurement. The proposed linear-programming-based algorithm finds a solution x by parametrically minimizing the number of nonzero elements in x and the error k Ax b p k 1 . Numerical tests on a signal-processing-based example indicate that the proposed method is comparable to a method that parametrically minimizes the 1-norm of the solution x and the error k Ax b p k 1 , and that both methods are superior, by orders of magnitude, to solutions obtained by least squares as well by combinatorially choosing an optimal solution with a specific number of nonzero elements. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #180399. 	[Title] An Inductive Learning Approach to Prognostic Prediction [Abstract] This paper introduces the Recurrence Surface Approximation, an inductive learning method based on linear programming that predicts recurrence times using censored training examples, that is, examples in which the available training output may be only a lower bound on the "right answer." This approach is augmented with a feature selection method that chooses an appropriate feature set within the context of the linear programming generalizer. Computational results in the field of breast cancer prognosis are shown. A straightforward translation of the prediction method to an artificial neural network model is also proposed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120084. 	[Title] A Neural Network Model for Prognostic Prediction [Abstract] An important and difficult prediction task in many domains, particularly medical decision making, is that of prognosis. Prognosis presents a unique set of problems to a learning system when some of the outputs are unknown. This paper presents a new approach to prognostic prediction, using ideas from nonparametric statistics to fully utilize all of the available information in a neural architecture. The technique is applied to breast cancer prognosis, resulting in flexible, accurate models that may play a role in prevent ing unnecessary surgeries. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #180373. 	[Title] CANCER DIAGNOSIS AND PROGNOSIS VIA LINEAR-PROGRAMMING-BASED MACHINE LEARNING [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #25181. 	[Title] Bilinear Separation of Two Sets in n-Space [Abstract] The NP-complete problem of determining whether two disjoint point sets in the n-dimensional real space R n can be separated by two planes is cast as a bilinear program, that is minimizing the scalar product of two linear functions on a polyhedral set. The bilinear program, which has a vertex solution, is processed by an iterative linear programming algorithm that terminates in a finite number of steps at a point satisfying a necessary optimality condition or at a global minimum. Encouraging computational experience on a number of test problems is reported. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3231. 	[Title] Irrelevant Features and the Subset Selection Problem [Abstract] We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small high-accuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features into useful categories of relevance. We present definitions for irrelevance and for two degrees of relevance. These definitions improve our understanding of the behavior of previous subset selection algorithms, and help define the subset of features that should be sought. The features selected should depend not only on the features and the target concept, but also on the induction algorithm. We describe a method for feature subset selection using cross-validation that is applicable to any induction algorithm, and discuss experiments conducted with ID3 and C4.5 on artificial and real datasets. Please summarise all the given information.

Paper #385572 has the title `Individual and Collective Prognostic Prediction  
` and the abstract `The prediction of survival time or recurrence time is an important learning problem in medical domains. The Recurrence Surface Approximation (RSA) method is a natural, effective method for predicting recurrence times using censored input data. This paper introduces the Survival Curve RSA (SC-RSA), an extension to the RSA approach which produces accurate predicted rates of recurrence, while maintaining accuracy on individual predicted recurrence times. The method is applied to the problem of breast cancer recurrence using two different datasets. 
`.
Question: Which category should Paper #385572 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #385572 has the title `Individual and Collective Prognostic Prediction  
` and the abstract `The prediction of survival time or recurrence time is an important learning problem in medical domains. The Recurrence Surface Approximation (RSA) method is a natural, effective method for predicting recurrence times using censored input data. This paper introduces the Survival Curve RSA (SC-RSA), an extension to the RSA approach which produces accurate predicted rates of recurrence, while maintaining accuracy on individual predicted recurrence times. The method is applied to the problem of breast cancer recurrence using two different datasets. 
`.
Question: Which category should Paper #385572 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks