Steven Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6(3):251--276, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....contribution of less relevant, including redundant, attributes. We look now at one way of learning such a weight vector. 3 Learning a Weight Vector There are many weight learning algorithms. We choose to use an online optimizer [9] An early example of such a learner is Salzberg s EACH algorithm [8]. This in uenced Aha s IB4 [1] And this, in turn, in uenced Kira s and Rendell s RELIEF algorithm [5] which removed IB4 s assumption of a uniform distribution of irrelevant attribute values. Kononenko experimented with variants of the RELIEF algorithm [6] A minor variant of Kononenko s RELIEF F ....

Salzberg, S.L.: A Nearest Hyperrectangle Learning Method, Machine Learning, vol.6, pp.251-276, 1991

....selection method is that it treats features as completely relevant or irrelevant. In reality, the degree of relevance may not be just 0 or 1, but any value between them. Knowledge representation in exemplar based learning models are either representative instances [2, 5] or hyperrectangles [58, 59]. For example, instancebased learning model retains examples in memory as points, and never changes them. The only decisions that are made are what points to store and how to measure similarity. Several variants of this model have been developed [2, 3, 4, 5] Nested generalized exemplars model ....

....examples in memory as points, and never changes them. The only decisions that are made are what points to store and how to measure similarity. Several variants of this model have been developed [2, 3, 4, 5] Nested generalized exemplars model represents the learned knowledge as hyperrectangles [58, 59]. This model changes the point storage model of the instance based learning and retains examples in the memory as axisparallel hyperrectangles. The Classification by Feature Partitioning [27, 28, 65] and Classification with Overlapping Feature Intervals [67] algorithms are also exemplar based ....

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S. Salzberg, A Nearest Hyperrectangle Learning Method, Machine Learning, 6:251-276, 1991.

....memory verbatim, with no change of representation. An example is defined as a vector of feature values along with a label which represents the category (class) of the example. Knowledge representation of exemplar based models can be maintained as representative instances [2, 5] hyperrectangles [62, 63], or feature projection based representations [7, 8, 22, 32, 73] Unlike Explanation Based Generalization (EBG) 19, 50] little or no domain specific knowledge is required in exemplar based learning. Figure 2.1 presents a hierarchical classification of exemplar based learning models. ....

....exemplar is an axis parallel hyperrectangle that may cover several training examples. These hyperrectangles may overlap or nest. Hyperrectangles are grown during training in an incremental manner. Salzberg implemented NGE in a program called EACH (Exemplar Aided Constructor of Hyperrectangles) [63]. In EACH, the learner compares new examples to those it has seen before and finds the most similar generalized exemplar in memory. NGE theory makes several significant modifications to the exemplar based model. It retains the notion that examples should be stored verbatim in memory, but once it ....

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S. Salzberg, A Nearest Hyperrectangle Learning Method, Machine Learning, 6:251--276, 1991.

....of IBL s similarity function [AHA91b] The two metrics are equivalent when a purely instance based learning algorithms is used, and DHET extends IBL s similarity function to inductive learning algorithms that use and or create general rules. DHET is also similar to the distance metric used by NGE [SAL91]. It is somewhat simpler since rules containing don t cares represent hyperplanes rather than hyperrectangles. It is also 69 inherently heterogeneous whereas NGE s distance is designed for purely continuous domains. Extensions to heterogeneous spaces have been proposed (see for example [WET93] ....

....to heterogeneous spaces have been proposed (see for example [WET93] NGE s distance is also a weighted sum, where each attributewise distance is assigned its own weight in the computation of the final distance. Mechanisms to assign weights to attributes in distance computation may be found in [SAL91, STA86, WET93]. DHET could be similarly extended. 5. Evaluation In this section, we give empirical evidence of the adequacy of DHET. The results were obtained by executing the same algorithm, only varying the metric it uses. ILA (Incremental Learning Algorithm) was chosen because of its simplicity, execution ....

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Salzberg, S. (1991). A Nearest Hyperrectangle Learning Method. Machine Learning, 6, 277-309. 137

.... AI, the concept has appeared in several disciplines (from computer vision to robotics) using terminology such as similarity based, example based, memory based, exemplar based, case based, analogical, nearest neighbour, and instance based (Stan ll and Waltz, 1986; Kolodner, 1993; Aha et al. 1991; Salzberg, 1990). Ideas about this type of analogical reasoning can be found also in non mainstream linguistics and pyscholinguistics (Skousen, 1989; Derwing Skousen, 1989; Chandler, 1992; Scha, 1992) In computational linguistics (apart from incidental computational work of the linguists referred to earlier) ....

Salzberg, S. (1990) `A nearest hyperrectangle learning method'. Machine Learning 6, 251-276.

....J classes and l training observations. The training observations consist of n feature measurements x = x 1 ; Delta Delta Delta ; x n ) 2 n and the known class labels j = 1; J . The goal is to predict the class label of a given query q. The K nearest neighbor classification method [6, 12, 15, 16, 19, 20] is a simple and appealing approach to this problem: it finds the K nearest neighbors of q in the training set, and then predicts the class label of q as the most frequent one occurring in the K neighbors. Such a method produces continuous and overlapping, rather than fixed, neighborhoods and uses ....

S. Salzberg, A Nearest Hyperrectangle Learning Method. Machine Learning 6:251-276, 1991.

....patterns, borders, knowledge discovery, classification. 1 1 Introduction Instance based learning (lazy learning) Aha, 1997) as exemplified by k nearest neighbor (k NN) Cover Hart, 1967) is an extensively and thoroughly studied topic in machine learning (Aha et al. 1991; Dasarathy, 1991; Salzberg, 1991; Zhang, 1992; Langley Iba, 1993; Wettscherech, 1994; Datta Kibler, 1995; Wettschereck Dietterich, 1995; Devroye et al. 1996; Domingos, 1996; Datta Kibler, 1997; Wilson Martinez, 1997; Keung Lam, 2000; Kubat Cooperson, 2000; Wilson Martinez, 2000) The intuition behind the k NN ....

Salzberg, S. (1991). A nearest hyperrectangle learning method. Machine Learning, 6, 251--276.

....and N training observations. The training observations consist of q feature measurements x = x 1 ; Delta Delta Delta ; x q ) 2 q and the known class labels, L j , j = 1; J . The goal is to predict the class label of a given query x 0 . The K nearest neighbor classification method [6, 11, 12, 13, 16, 17] is a simple and appealing approach to this problem: it finds the K nearest neighbors of x 0 in the training set, and 1 then predicts the class label of x 0 as the most frequent one occurring in the K neighbors. Such a method produces continuous and overlapping, rather than fixed, neighborhoods ....

S. Salzberg, A Nearest Hyperrectangle Learning Method. Machine Learning 6:251-276, 1991.

....with each instance, and uses only those instances with good records during prediction. Instances with very poor prediction records are deleted from the set of stored exemplars. IB4 is an extension of the IB3 algorithm that also learns feature weights in a manner similar to that used by Salzberg [Sal91] see also Chapter 4, Section 5.7) Aha [Aha90] reports substantially superior performance for IB4 over IB1 in the presence of many irrelevant features. However, this superior performance was only obtained when k was kept fixed at k = 1 for IB1. This confirms the results from Section 3 where we ....

....by constructing hyperrectangles that represent a collection of training examples that belong to the same class. More compact representations of the training data lead to faster classification times and may increase the ability of the user to understand decisions made by the classifier. Salzberg [Sal91] describes a family of learning algorithms based on nested generalized exemplars (NGE) In NGE, an exemplar is a single training example, and a generalized exemplar is an axis parallel hyperrectangle that may cover several training examples. These hyperrectangles may overlap or nest. The NGE ....

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S. Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:277--309, 1991.

....resulting class. To approximate a PR drawn by the ICR, GEM uses orthogonal hyperrectangles under the form of intervals defined over the instance space. This approach is widely used by Symbolic Learning systems (see for example ID3 [Quinlan, 1986] AQ [Michalski, 1983] or Nearest Hyperrectangles [Salzberg, 1991]) because of their natural understanding: an orthogonal box can be easily represented by a conjunctive rule where each term tests a cut point value of an attribute. Interpretation Biases Each PR of the ICR is approximated by a set of closed geometrical figures. There are two basic biases used ....

Salzberg Steven (1991) A Nearest Hyperrectangle Learning Method. Machine Learning vol. 6, n 3, May 1991, Kluwer Academic Publishers.

....was correct or incorrect. Considering each training instance once, weight adjustment has the purpose of decreasing the distance similarity metric among instances of the same class and increasing the distance among instances of different classes. These types of algorithms can be seen in Salzberg [27] (in a Nearest Hyperrectangle framework) Aha [28] and Kira and Rendell [29] Lowe [2] and Scherf and Brauer [30] have proposed another local search mechanism as gradient descent optimization to optimize a set of continuous weights. Lowe applies the gradient descent over the distance similarity ....

S.L. Salzberg, A nearest hyperrectangle learning method, Machine Learning 6 (1991) 251-276.

....from the data initially, it is assumed that each feature is useful for induction; its degree of usefulness is reflected in the magnitude of its weight. Using continuous weights for 47 features involves searching a much larger space and involves a greater chance of overfitting [KLY97] Salzberg [Sal91] incorporates incremental feature weighting in an instance based learner called EACH. For each correct classification made, the weight for each matching feature is incremented by f (the global feature adjustment rate) Mismatching features have their weights decremented by this same amount. For ....

S. Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:251--276, 1991.

....ed well or possibly better without the pair. The new exemplar has double the weight of the previous two examples. The score for each exemplar, Q i can be computed as follows: score i = jQ i Q i (s i ; a i )j 1 K X j 6=i jQ(s j ; a j ) Q i (s j ; a j )j A similar approach was proposed in (Salzberg 1991) where instead of averaging instances, he generalizes instances into nested hyperrectangles. While partitioning the space into hyperrectangles can work well for discrete classi cation tasks, it has aws for regression. Most importantly, all of the points within a region almost never have the exact ....

Salzberg, S. 1991. A nearest hyperrectangle learning method. Machine Learning 6(3):251-276.

.... neural networks are usually timeconsuming and hard to apply (see for example [1] 2] 3] or for a method that extracts fuzzy rules [4] Extracting rules directly from the data is usually complicated, especially in the case of noisy data examples, due to the crisp nature of the underlying rules [5], 6] Decision trees offer an alternative, but are usually harder to understand [7] 8] 9] Directly learning fuzzy rule bases offers an interesting alternative. Algorithms that adjust an apriori defined rule set have been proposed before, but the structure of the rule base has to be defined ....

S. Salzberg, "A nearest hyperrectangle learning method", in Machine Learning, 1991, 6, pp. 251--276.

.... vision to robotics, bearing such diverse labels as similarity based learning, example (or exemplar ) based learning, analogical reasoning, lazy learning, nearest neighbor classifiers, instance based learning, and case based reasoning (Stanfill and Waltz, 1986; Kolodner, 1992; Aha et al. 1991; Salzberg, 1990). Examples are represented as vectors of attribute values with an associated class label. Those attributes define a pattern space. During training, a set of examples (the training set) is presented in an incremental fashion to the learning algorithm, and added to memory. During processing, an ....

Salzberg, S.: 1990, `A nearest hyperrectangle learning method". Machine Learning 6, 251--276.

....cant time. IPs usually span a design space because they are descriptions of exible designs that have to be synthesized to hardware before they actually can be used. The idea of generalizing cases was already implicitly present since the very beginning of CBR and instance based learning research [10,1,16]. For the purpose of adaptation, recent CBR systems in the area of design and planning [9,13,3] use complex case representations that realize generalized cases. 2 In this paper we will present a general (and partially a more formal) view on the concept of generalized cases that also partially ....

.... of IP reuse, but we observed that this is also true for all kinds of parameterizable products in electronic commerce applications [19] Of course, the idea of generalizing cases (or examples) was implicitly present already since the very beginning of CBR and instance based learning research [10,1,16]. However, these approaches are limited to hyperrectangular representations of generalized cases that cannot deal with dependencies between attributes as required, e.g. for IP reuse. We introduced the idea of using constraints as a very exible means for representing generalized cases. ....

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S Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:277{ 309, 1991.

....drift, but it is somewhat reluctant to adjust quickly to radical changes. Also, instance based algorithms are known to be sensitive to attribute relevance: irrelevant attributes have a detrimental effect on predictive accuracy, though some approaches to improve on this have recently been suggested (Salzberg, 1991; Cost Salzberg, 1993) In recent years, some authors have begun to explicitly address the problem of concept drift and context dependence. Probably the first system to attack the CONCEPT DRIFT AND HIDDEN CONTEXTS 29 problem of drift was STAGGER (Schlimmer Granger, 1986) which learns ....

Salzberg, S. (1991). A Nearest Hyperrectangle Learning Method. Machine Learning, 6(3), 251-- 276.

....stored in the memory are called exemplars. The basic idea in exemplar based learning is to use past experiences or cases to understand, plan, or learn from novel situations [7, 10, 15] The learning paradigm used in this paper is referred as Exemplar Based Generalization (coined by Salzbeg [17]) where exemplars are not only simple examples, but templates that are obtained by generalizing appropriate components of examples [5] y Recommended by Arun Sen 353 354 H. A. G UVEN IR and I. CICEKLI EBMT has been proposed by Nagao [14] as translation by analogy which is in parallel with ....

Steven Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:251-276 (1991).

....lower dimensional sub space. To compare the bene ts (in terms of predictive accuracy) of this approach with other attribute selection techniques, a suitable learning paradigm is required. Learning algorithms based on the Instance Based Learning paradigm (IBL) Aha, Kibler, Albert 1991; Aha 1992; Salzberg 1991; Wettschereck Dietterich 1995; Wilson Martinez 1997) are ideal, as the accuracy of these techniques degrades in the presence of irrelevant or redundant data (Payne 1999) and they can be applied to problems where the domain contains numeric data. Instance based learning algorithms, which are ....

Salzberg, S. (1991). A Nearest Hyperrectangle Learning Method. Machine Learning 6, 251-276.

....Science, King s College, University of Aberdeen, Aberdeen, Scotland, AB24 3UE. 2 Department of Computing Science, King s College, University of Aberdeen, Aberdeen, Scotland, AB24 3UE. nearest neighbour theme have also been proposed that represent the induced hypothesis as hyper rectangles [15], as a set of prototype points or selected instances [2, 4] or as feature projections [3] Nearest Neighbour learning algorithms determine the class label of an unclassified instance by comparing it to a set of stored, classified instances, and identifying the class label of the nearest ....

....in the test instance is irrelevant) then the resulting attribute distance will also be small and have little impact on the choice of nearest neighbour. Many Nearest Neighbour learning algorithms employ weights to modify the effect a specific component has in the resulting classification process [1, 8, 15, 18]. For example, PEBLS [5] and EACH [15] assign a weight to each of the instances (or hyper rectangles in the case of EACH) and modify this weight according to whether the instances result in correct or incorrect class predictions. The weight is used to measure the reliability of an instance, and ....

[Article contains additional citation context not shown here]

S. Salzberg, `A Nearest Hyperrectangle Learning Method', Machine Learning, 6, 251--276, (1991).

....time. IPs usually span a design space because they are descriptions of flexible designs that have to be synthesized to hardware before they actually can be used. The idea of generalizing cases was already implicitly present since the very beginning of CBR and instance based learning research [10, 1, 16]. For the purpose of adaptation, recent CBR systems in the area of design and planning [9, 13, 3] use complex case representations that realize generalized cases. 2 In this paper we will present a general (and partially a more formal) view on the concept of generalized cases that also partially ....

.... domain of IP reuse, but we observed that this is also true for all kinds of parameterizable products in electronic commerce applications [19] Of course, the idea of generalizing cases (or examples) was implicitly present already since the very beginning of CBR and instance based learning research [10, 1, 16]. However, these approaches are limited to hyperrectangular representations of generalized cases that cannot deal with dependencies between attributes. We introduced the idea of using constraints as a flexible means for representing generalized cases. We also provided a general framework for ....

[Article contains additional citation context not shown here]

S Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:277-- 309, 1991.

....for noisy data, but has to be carefully controlled to avoid over generalization. The third kind of algorithm is based on the idea to build a classifier directly by constructing n di mensional rectangles (assuming n attributes) Each rectangle specifies a region that belongs to one class (see [15], 18] and can be easily transformed into one if then rule. These approaches are primarily designed to build good classifiers, which makes it hard to minimize the number of rectangles or number of attributes that are used to describe one rectangle. As a consequence the resulting rule base can ....

S. Salzberg. A nearest hyperrectangle learning method. In Machine Learning, 6, pages 251-- 276, 1991.

.... Intelligence, the concept has appeared in several disciplines (from computer vision to robotics) using terminology such as similarity based, example based, memorybased, case based, analogical, lazy, nearest neighbour, and instance based (Stanfill and Waltz, 1986; Kolodner, 1993; Aha et al. 1991; Salzberg, 1990). Ideas about this type of analogical reasoning are rare in linguistics and pyscholinguistics (Skousen, 1989; Derwing Skousen, 1989; Chandler, 1992; Scha, 1992 are salient examples) In computational linguistics (apart from incidental computational work of the linguists referred to earlier) ....

Salzberg, S. (1990) `A nearest hyperrectangle learning method'. Machine Learning 6, 251--276.

....which the same k NN based classification can be performed as in the pure memory based case. The abstraction occurring in this approach is that after a merge, the merged cases incorporated in the new generalized case cannot be reconstructed individually. Example approaches to merging cases are nge [14] and rise [9] The experiments reported here are performed with fambl, which features roughly the same functionality as nge and rise, but is optimized for learning speed (see [17] for more details) 2.3.5. A comparison of memory requirements and generalization accuracy All mentioned learning ....

S. Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:277--309, 1991.

....is necessary. If we observe the arena at the reactive level and, as a situation repeats itself, collect the best and the worst agents in handling such situation, then the genetic material in these agents can be used as examples and counterexamples in an Inductive Learning mechanism (e.g. [Sal91]) The results of this inductive mechanism are general descriptions of populations, that can be associated with appropriate fitness function values. The complexity of these descriptions is proportional to the generality of the inductive learning mechanism and its underlying representation ....

S.L. Salzberg. A nearest hyperrectangle learning method. In Machine Intelligence 6, pages 251--276. 1991.

....in comparison with pure memory based learning. We use the term abstraction here as denoting the forgetting of learning material during learning. This material notion of abstraction is not to be confused with the informational abstraction from learning material exhibited by weighting metrics (Salzberg, 1991; Cost and Salzberg, 1993; Wettschereck, Aha, and Mohri, 1997) and, more generally, by the abstraction bias in all memory based learning approaches that high similarity between instances is to be preferred over lower similarity, and that only the most similar items are to be used as information ....

....Finally, Section 5 identifies future research. 2 Careful abstraction in memory based learning Memory based learning, also known as instance based, example based, lazy, case based, exemplar based, locally weighted, and analogical learning (Stanfill and Waltz, 1986; Aha, Kibler, and Albert, 1991; Salzberg, 1991; Kolodner, 1993; Aha, 1997; Atkeson, Moore, and Schaal, 1997) is a class of supervised inductive learning algorithms for learning classification tasks (Shavlik and Dietterich, 1990) Memory based learning treats a set of labeled (pre classified) training instances as points in a ....

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Salzberg, S. 1991. A nearest hyperrectangle learning method. Machine Learning, 6:277--309.

....Machine Learning A Hybrid Nearest Neighbor and Nearest Hyperrectangle Algorithm Dietrich Wettschereck Dearborn Hall 303 Department of Computer Science Oregon State University Corvallis, OR 97331 3202 USA wettscd cs.orst.edu Abstract. Algorithms based on Nested Generalized Exemplar (NGE) theory [10] classify new data points by computing their distance to the nearest generalized exemplar (i.e. an axis parallel multidimensional rectangle) An improved version of NGE, called BNGE, was previously shown to perform comparably to the Nearest Neighbor algorithm. Advantages of the NGE approach ....

....Neighbor algorithm at improved classification speed. KBNGE is a fast and easy to use inductive learning algorithm that gives very accurate predictions in a variety of domains and represents the learned knowledge in a manner that can be easily interpreted by the user. 1 Introduction Salzberg [10] describes a family of learning algorithms based on nested generalized exemplars (NGE) In NGE, an exemplar is a single training example and a generalized exemplar is an axis parallel hyperrectangle that may cover several training examples. These hyperrectangles may overlap or nest. The NGE ....

[Article contains additional citation context not shown here]

Salzberg, S.: A Nearest Hyperrectangle Learning Method. Machine Learning 6 (1991) 277--309

.... Almuallim and Dietterich, 1991, Kira and Rendell, 1992, Cardie, 1993, Schlimmer, 1993, Vafaie and DeJong, 1993, Caruana and Freitag, 1994, John et al. 1994, Langley and Sage, 1994, Skalak, 1994] A related field is that of feature weighting [Aha, 1989, Cain et al. 1991, Kelly and Davis, 1991, Salzberg, 1991, Creecy et al. 1992, Skalak, 1992, Mohri and Tanaka, 1994] Feature selection can be seen as a special case of feature weighting where each weight is either 0 or 1, and thus weighting methods are potentially more powerful. However, because they have more degrees of freedom, they can also be ....

....are few training examples. Feature weighting methods also vary in what the weights can depend on, and thus in their degree of context sensitivity. In the representationally simplest schemes, there is one weight per feature, and they are therefore completely context free [Kelly and Davis, 1991, Salzberg, 1991, Lee, 1994, Mohri and Tanaka, 1994] More flexible approaches employ one weight per feature value [Nosofsky et al. 1989, Stanfill and Waltz, 1986] one weight per feature per class [Aha, 1989] or a combination of the two [Creecy et al. 1992] and thus exhibit a moderate degree of context ....

S. Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:251--276, 1991.

....or malignant. The data set currently has 683 entries and is available from the UC Irvine machine learning repository [346] Heath et al. 204] reported 94.9 accuracy on a subset of this data set (it then had only 470 instances) with an average decision tree size of 4.6 nodes, using SADT. Salzberg [421] reported 96.0 accuracy using 1 NN on the same (smaller) data set. Herman and Yeung [207] reported 99.0 accuracy using piece wise linear classification, again using a somewhat smaller data set. Bennett and Mangasarian [25] reported 97.4 accuracy using their MSM1 algorithm, using a different ....

Steven Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:251--276, 1991.

.... AI, the concept has appeared in several disciplines (from computer vision to robotics) using terminology such as similarity based, example based, memory based, exemplar based, case based, analogical, nearest neighbour, and instance based (Stanfill and Waltz, 1986; Kolodner, 1993; Aha et al. 1991; Salzberg, 1990). Ideas about this type of analogical reasoning can be found also in non mainstream linguistics and pyscholinguistics (Skousen, 1989; Derwing Skousen, 1989; Chandler, 1992; Scha, 1992) In computational linguistics (apart from incidental computational work of the linguists referred to ....

Salzberg, S. (1990) `A nearest hyperrectangle learning method'. Machine Learning 6, 251--276.

....IBL technique while SE Learn is a rule based one. As mentioned in Section 3.2, the computational complexity of SE Learn makes it impractical for problems with many attributes and examples. 4. 3 Other related works Several approaches combine instance based and rule based learning, including NGE [ Salzberg, 1991 ] BNGE [ Wettschereck and Dietterich, 1995 ] and RISE [ Domingos, 1996 ] These approaches generalize the examples from the training set into rules in a learning phase, then classify every object according to its closest rule (w.r.t. some distance) Thus, the rules used to classify an object ....

....according to its closest rule (w.r.t. some distance) Thus, the rules used to classify an object o do not depend on the object itself (they are fixed during the learning phase) In any case, only one rule is elected to classify o; for instance, the most specific rule among the closest to o [ Salzberg, 1991 ] or the one with the best Laplace accuracy [ Domingos, 1996 ] Clearly enough, these approaches are very different from scope classification. First, they use rules as instances, while no rules have to be generated within the scope approach (no learning phase is mandatory) Second, they are ....

Steven Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:251--276, 1991.

....we have investigated all use as their basis a form of k nearest neighbor learning. This family of algorithms has been accorded several names in the machine learning and related literatures, including instance based learning (Bradshaw, 1987; Aha, Kibler, Albert, 1991) exemplar based learning (Salzberg, 1991), memory based reasoning learning (Stanfill Waltz, 1986; Atkeson, 1989) and case based learning (Aha, 1991) We include in this family of algorithms more sophisticated methods that first extract a set of neighbors, and then attempt relatively expensive function estimation methods using, for ....

Salzberg, S. L. (1991). A nearest hyperrectangle learning method. Machine Learning, 6, 251-- 276.

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Steven Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6(3):251--276, 1991.

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Steven Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6(3):251--276, 1991.

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S. Salzberg, A nearest hyperrectangle learning method., volume 6, 277--309, 1991.

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S Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:277--309, 1991.

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S. Salzberg, A Nearest Hyperrectangle Learning Method. Machine Learning 6:251-276, 1991.

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Steven Salzberg. A nearest hyperrectangle learning method. In Proc. 6th International Conference on Machine Learning, pages 251--276, 1991.

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Salzberg, S. (1991). A nearest hyperrectangle learning method. Machine Learning, 2, 229-246.

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S Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:251--276, 1991.

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, pp. 318--362. Salzberg, Steven (1991). A Nearest Hyperrectangle Learning Method. Machine Learning, 6, pp.

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S. Salzberg, A Nearest Hyperrectangle Learning Method, Machine Learning, 6:251-276, 1991.

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