Source: http://www.google.com/patents/US5214715?ie=ISO-8859-1&dq=6859936
Timestamp: 2014-07-24 01:54:45
Document Index: 135020119

Matched Legal Cases: ['ART 2', 'ART 3', 'ART 1', 'ART 2', 'ART 3', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 2', 'ART 3', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 2', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 2', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 1', 'ART 2', 'ART 3', 'Art 3', 'Art 3']

Patent US5214715 - Predictive self-organizing neural network - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign in<nobr>Advanced Patent Search</nobr>PatentsAn A pattern recognition subsystem responds to an A feature representation input to select A-category-representation and predict a B-category-representation and its associated B feature representation input. During learning trials, a predicted B-category-representation is compared to that obtained through...http://www.google.com/patents/US5214715?utm_source=gb-gplus-sharePatent US5214715 - Predictive self-organizing neural networkAdvanced Patent SearchPublication numberUS5214715 APublication typeGrantApplication numberUS 07/648,653Publication dateMay 25, 1993Filing dateJan 31, 1991Priority dateJan 31, 1991Fee statusPaidAlso published asDE69216077D1, DE69216077T2, EP0569549A1, EP0569549B1, WO1992014200A1Publication number07648653, 648653, US 5214715 A, US 5214715A, US-A-5214715, US5214715 A, US5214715AInventorsGail A. Carpenter, Stephen Grossberg, John W. ReynoldsOriginal AssigneeTrustees Of Boston UniversityExport CitationBiBTeX, EndNote, RefManPatent Citations (6), Non-Patent Citations (6), Referenced by (68), Classifications (10), Legal Events (8) External Links: USPTO, USPTO Assignment, EspacenetPredictive self-organizing neural networkUS 5214715 AAbstract An A pattern recognition subsystem responds to an A feature representation input to select A-category-representation and predict a B-category-representation and its associated B feature representation input. During learning trials, a predicted B-category-representation is compared to that obtained through a B pattern recognition subsystem. With mismatch, a vigilance parameter of the A-pattern-recognition subsystem is increased to cause reset of the first-category-representation selection. Inputs to the pattern recognition subsystems may be preprocessed to complement code the inputs.
We claim: 1. A pattern recognition system comprising:an A pattern recognition subsystem for searching, selecting and learning an A-category-representation in response to an A input pattern; means for predicting a B-category-representation from a selected A-category-representation; means for providing a control B-category-representation; means for detecting a mismatch between a predicted B-category-representation and a control B-category representation; and means responsive to a mismatch between a predicted B-category-representation and a control B-category-representation to cause selection of a new A-category-representation. 2. A system as claimed in claim 1 wherein the A pattern recognition subsystem comprises:a feature representation field of nodes for receiving input signals, defining an A input pattern, and template signals; means for selecting an A-category-representation in an A-category-representation field of nodes based on a pattern from the feature representation field; means for generating the template signals based on the selected A-category-representation; means for adapting A-category-representation selection and the template signals to the input signals; and first reset means for resetting A-category-representation selection with an insufficient match between the input pattern and the template signal. 3. A system as claimed in claim 2 further comprising a B pattern recognition subsystem for providing the control B-category-representation from a B input pattern.
GOVERNMENT SUPPORT The United States Government has rights to the claimed invention under one or more of the following contracts:
BACKGROUND OF THE INVENTION Adaptive resonance architectures are neural networks that self-organize stable recognition categories in real time in response to arbitrary sequences of input patterns. The basic principles of adaptive resonance theory (ART) were introduced in Grossberg, "Adaptive pattern classification and universal recoding, II: Feedback, expectation, olfaction, and illusions." Biological Cybernetics, 23 (1976) 187-202. A class of adaptive resonance architectures has since been characterized as a system of ordinary differential equations by Carpenter and Grossberg, "Category learning and adaptive pattern recognition: A neural network model", Proceedings of the Third Army Conference on Applied Mathematics and Computing, ARO Report 86-1 (1985) 37-56, and "A massively parallel architecture for a self-organizing neural pattern recognition machine." Computer Vision, Graphics, and Image Processing, 37 (1987) 54-115. One implementation of an ART system is presented in U.S. application Ser. No. PCT/US86/02553, filed Nov. 26, 1986 by Carpenter and Grossberg for "Pattern Recognition System." A network known as ART 2 is presented in U.S. Pat. No. 4,914,708 to Carpenter and Grossberg. A further network known as ART 3 is presented in U.S. patent application Ser. No. 07/464,247 filed by Carpenter and Grossberg on Jan. 12, 1990.
SUMMARY OF THE INVENTION The present invention allows for the association of a first feature representation input pattern, such as the visual representation of an object, with a predicted consequence, such as taste. In the system disclosed and claimed, a first pattern recognition subsystem is associated with the first feature representation and a second subsystem is associated with the predicted consequence. However, to avoid confusion with first and second patterns in time, the first and second subsystems and their components and patterns are identified by the letters A and B (and a and b) rather than the terms first and second.
Preferably, predicted B-category-representations and control B-category-representations are associated through a mapping field. A one-to-one correspondence is maintained between nodes of the mapping field and nodes of a B-category-representation field. Adaptive mapping is maintained from nodes of the A-category-representation field to nodes of the mapping field. The predicted B category representation associated with the selected A category representation may be learned as the control B category representation selected by the B pattern recognition subsystem. In operation, one or both of the pattern recognition systems may receive an input and either input may precede the other. Where an A input pattern is received before a B input pattern, the predicted B-category-representation associated with the selected A-category-representation may prime the B pattern recognition subsystem. The B subsystem would then initially select the predicted B-category-representation as the control B-category-representation, subject to reset with mismatch in the B feature representation field.
In general operation, A and B inputs may be applied to respective pattern recognition subsystems. Each subsystem allows for searching, selection and learning of a category representation. However, learning in the A subsystem is inhibited by reset with mismatch between a B-category-representation predicted by the A subsystem and the actual B-category-representation determined by the B subsystem. With reset of the A subsystem, it again searches and selects. A subsystem learning is allowed only after a match is obtained at the present level of vigilance within the A subsystem and a match is obtained between the subsystems.
Preferably, input signals to the feature representation fields comprise vectors of feature representations and complements of the feature representations.
More specifically, a new neural network architecture, called ARTMAP, autonomously learns to classify arbitrarily many, arbitrarily ordered vectors into recognition categories based on predictive success. This supervised learning system is built up from a pair of Adaptive Resonance Theory modules (ARTa and ARTb) that are capable of self-organizing stable recognition categories in response to arbitrary sequences of input patterns. During training trials, the ARTa module receives a stream {a.sup.(p) } of input patterns, and ARTb receives a stream {b.sup.(p) } of input patterns, where b.sup.(p) is the correct prediction given a.sup.(p). These ART modules are linked by an associative learning network and an internal controller that ensures autonomous system operation in real time. During test trials, the remaining patterns a.sup.(p) are presented without b.sup.(p), and their predictions at ARTb are compared with b.sup.(p). Tested on a benchmark machine learning database in both on-line and off-line simulations, the ARTMAP system learns orders of magnitude more quickly, efficiently, and accurately than alternative algorithms, and achieves 100% accuracy after training on less than half the input patterns in the database. It achieves these properties by using an internal controller that conjointly maximizes predictive generalization and minimizes predictive error by linking predictive success to category size on a trial-by-trial basis, using only local operations. This computation increases the vigilance parameter ρa of ARTa by the minimal amount needed to correct a predictive error at ARTb. Parameter ρa calibrates the minimum confidence that ARTa must have in a category, or hypothesis, activated by an input a.sup.(p) in order for ARTa to accept that category, rather than search for a better one through an automatically controlled process of hypothesis testing. Parameter ρa is compared with the degree of match between a.sup.(p) and the top-down learned expectation, or prototype, that is read-out subsequent to activation of an ARTa category. Search occurs if the degree of match is less than ρa. ARTMAP is hereby a type of self-organizing expert system that calibrates the selectivity of its hypotheses based upon predictive success. As a result, rare but important events can be quickly and sharply distinguished even if they are similar to frequent events with different consequences. Between input trials ρa relaxes to a baseline vigilance ρa. When ρa is large, the system runs in a conservative mode, wherein predictions are made only if the system is confident of the outcome. Very few false-alarm errors then occur at any stage of learning, yet the system reaches asymptote with no loss of speed. Because ARTMAP learning is self-stabilizing, it can continue learning one or more databases, without degrading its corpus of memories, until its full memory capacity is utilized.
FIG. 2 is a block diagram of a system embodying the present invention.
FIG. 3 is a detailed schematic illustration which can be applied to each of the ARTa and ARTb modules of FIG. 2.
FIG. 4 is a schematic illustration of the associative memory and the F2 fields of FIG. 2 with the associated internal control.
FIG. 5 is a schematic illustration of the ARTa subsystem with match tracking internal control responsive to a reset signal from FIG. 4.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT As we move freely through the world, we can attend to both familiar and novel objects, and can rapidly learn to recognize, test hypotheses about, and learn to name novel objects without unselectively disrupting our memories of familiar objects. A new self-organizing neural network architecture--called a predictive ART or ARTMAP architecture--is capable of fast, yet stable, on-line recognition learning, hypothesis testing, and adaptive naming in response to an arbitrary stream of input patterns.
The possibility of stable learning in response to an arbitrary stream of inputs is required by an autonomous learning agent that needs to cope with unexpected events in an uncontrolled environment. One cannot restrict the agent's ability to process input sequences if one cannot predict the environment in which the agent must function successfully. The ability of humans to vividly remember exciting adventure movies is a familiar example of fast learning in an unfamiliar environment.
A successful autonomous agent must be able to learn about rare events that have important consequences, even if these rare events are similar to frequent events with very different consequences. Survival may hereby depend on fast learning in a nonstationary environment. Many learning schemes are, in contrast, slow learning models that average over individual event occurrences and are degraded by learning instabilities in a nonstationary environment.
An efficient recognition system needs to be capable of many-to-one learning. For example, each of the different exemplars of the font for a prescribed letter may generate a single compressed representation that serves as a visual recognition category. This exemplar-to-category transformation is a case of many-to-one learning. In addition, many different fonts--including lower case and upper case printed fonts and scripts of various kinds--can all lead to the same verbal name for the letter. This is a second sense in which learning may be many-to-one.
Learning may also be one-to-many, so that a single object can generate many different predictions or names. For example, upon looking at a banana, one may classify it as an oblong object, a fruit, a banana, a yellow banana, and so on. A flexible knowledge system may thus need to represent in its memory many predictions for each object, and to make the best prediction for each different context in which the object is embedded.
Why does not an autonomous recognition system get trapped into learning only that interpretation of an object which is most salient given the system's initial biases? One factor is the ability of that system to reorganize its recognition, hypothesis testing, and naming operations based upon its predictive success or failure. For example, a person may learn a visual recognition category based upon seeing bananas of various colors and associate that category with a certain taste. Due to the variability of color features compared with those of visual form, this learned recognition category may incorporate form features more strongly than color features. However, the color green may suddenly, and unexpectedly, become an important differential predictor of a banana's taste.
The different taste of a green banana triggers hypothesis testing that shifts the focus of visual attention to give greater weight, or salience, to the banana's color features without negating the importance of the other features that define a banana's form. A new visual recognition category can hereby form for green bananas, and this category can be used to accurately predict the different taste of green bananas. The new, finer category can form, moreover, without recoding either the previously learned generic representation of bananas or their taste association.
Future representations may also form that incorporate new knowledge about bananas, without disrupting the representations that are used to predict their different tastes. In this way, predictive feedback provides one means whereby one-to-many recognition and prediction codes can form through time, by using hypothesis testing and attention shifts that support new recognition learning without forcing unselective forgetting of previous knowledge.
The architecture described herein forms part of Adaptive Resonance Theory, or ART, which was introduced in 19763,4 in order to analyze how brain networks can autonomously learn in real time about a changing world in a rapid but stable fashion. Since that time, ART has steadily developed as physical theory to explain and predict ever larger data bases about cognitive information processing and its neural substrates5-8. A parallel development has described a series of rigorously characterized neural architectures--called ART 1, ART 2, and ART 3 --with increasingly powerful learning, pattern recognition, and hypothesis testing capabilities1,9-11.
The present class of architectures are called Predictive ART architectures because they incorporate ART modules into systems that can learn to predict a prescribed m-dimensional output vector b given a prescribed n-dimensional input vector a (FIG. 2). The present example of Predictive ART is called ARTMAP because its transformation from vectors in n to vectors in m defines a map that is learned by example from the correlated pairs {a.sup.(p), b.sup.(p) } of sequentially presented vectors, p=1, 2, . . . 12. For example, the vectors a.sup.(p) may encode visual representations of objects, and the vectors b.sup.(p) may encode their predictive consequences, such as different tastes in the banana example above. The degree of code compression in memory is an index of the system's ability to generalize from examples.
ARTMAP is a supervised learning system. With supervised learning, an input vector a.sup.(p) is associated with another input vector b.sup.(p) on each training trial. On a test trial, a new input a is presented that has never been experienced before. This input predicts an output vector b. System performance is evaluated by comparing b with the correct answer. This property of generalization is the system's ability to correctly predict answers to a test set of novel inputs a.
An overview of the system is presented in FIG. 2. It includes two ART modules ARTa and ARTb. Each module includes the usual feature representation short term memory field F1 and category representation short term memory field F2. Thus, ARTa includes short term fields F1 a and F2 a, while ARTb includes short term memory fields F1 b and F2 b. Thus, a pattern represented by the Vector a selects, through a long term memory adaptive filter 22a, a category representation in field F2 a. That category representation may itself be a pattern within F2 a, but typically a single category is chosen. In the adaptive filter 22a, each element of the vector in F1 a is weighted toward each category node of F2 a. However, for clarification only a few weighted connections 22a of the bottom-up adaptive filter are illustrated. A template from the selected category which defines an expected pattern is generated by a top-down adaptive filter 24a. Top-down weights are provided from all nodes of F2 a to all nodes of F1 a but for clarification only a few weighted connections 24a are illustrated.
As in a conventional ART system, the top-down template is compared with the input vector a in F1 a against a vigilance parameter. If the match is sufficient, as determined by an internal control system 24, the initial selection is maintained. If the match is insufficient, the previously selected category is no longer considered and another category is selected by the bottom-up adaptive filter. In this respect, ARTa is conventional.
In accordance with the present invention, ARTa is associated with another ART module ARTb. ARTb operates in the same fashion as ARTa but receives different inputs. For example, ARTa may receive a visual representation vector while ARTb receives a taste representation vector. The internal control systems of the two ART systems are linked by control system 25 in a manner described below. The categories which are selected by the ARTa and ARTb modules from associated inputs a and b are associated in an associative memory 26. Operation of this memory as a map field is described below.
The ARTMAP system is designed to conjointly maximize generalization and minimize predictive error under fast learning conditions in real time in response to an arbitrary ordering of input patterns. Remarkably, the network can achieve 100% test set accuracy on the machine learning benchmark database described below. Each ARTMAP system learns to make accurate predictions quickly, in the sense of using relatively little computer time; efficiently, in the sense of using relatively few training trials; and flexibly, in the sense that its stable learning permits continuous new learning, on one or more databases, without eroding prior knowledge, until the full memory capacity of the network is exhausted. In an ARTMAP network, the memory capacity is chosen arbitrarily large without sacrificing the stability of fast learning or accurate generalization.
An essential feature of the ARTMAP design is its ability to conjointly maximize generalization and minimize predictive error on a trial-by-trial basis using only local operations. It is this property which enables the system to learn rapidly about rare events that have important consequences even if they are very similar to frequent events with different consequences. The property builds upon a key design feature of all ART systems; namely, the existence of an orienting subsystem that responds to the unexpectedness, or novelty, of an input exemplar a by driving a hypothesis testing cycle, or parallel memory search, for a better, or totally new, recognition category for a. Hypothesis testing is triggered by the orienting subsystem if a activates a recognition category that reads out a learned expectation, or prototype, which does not match a well enough. The degree of match provides an analog measure of the predictive confidence that the chosen recognition category represents a, or of the novelty of a with respect to the hypothesis that is symbolically represented by the recognition category. This analog match value is computed at the orienting subsystem where it is compared with a dimensionless parameter that is called vigilance. A cycle of hypothesis testing is triggered if the degree of match is less than vigilance. Conjoint maximization of generalization and minimization of predictive error is achieved on a trial-by-trial basis by increasing the vigilance parameter in response to a predictive error on a training trial. The minimum change is made that is consistent with correction of the error. In fact, the predictive error causes the vigilance to increase rapidly until it just exceeds the analog match value, in a process called match tracking.
Before each new input arrives, vigilance relaxes to a baseline vigilance value. Setting baseline vigilance to 0 maximizes code compression. The system accomplishes this by allowing an "educated guess" on every trial, even if the match between input and learned code is poor. Search ensues, and a new category is established, only if the prediction made in this forced-choice situation proves wrong. When predictive error carries a cost, however, baseline vigilance can be set at some higher value, thereby decreasing the "false alarm" rate. With positive baseline vigilance, the system responds "I don't know" to an input that fails to meet the minimum matching criterion. Predictive error rate can hereby be made very small, but with a reduction in code compression. Search ends when the internal control system 24 determines that a global consensus has been reached.
ARTMAP achieves its combination of desirable properties by acting as a type of self-organizing expert system. It incorporates the basic properties of all ART systems to carry out autonomous hypothesis testing and parallel memory search for appropriate recognition codes. Hypothesis testing terminates in a sustained state of resonance that persists as long as an input remains approximately constant. The resonance generates a focus of attention that selects the bundle of critical features common to the bottom-up input and the top-down expectation, or prototype, that is read-out by the resonating recognition category. Learning of the critical feature pattern occurs in this resonant and attentive state, hence the term adaptive resonance.
The resonant focus of attention is a consequence of a matching rule called the 2/3 Rule9. This rule clarifies how a bottom-up input pattern can supraliminally activate its feature detectors at the level F1 of an ART network, yet a top-down expectation can only subliminally sensitize, or prime, the level F1. Supraliminal activation means that F1 can automatically generate output signals that initiate further processing of the input. Subliminal activation means that F1 cannot generate output signals that initiate further processing of the input. Subliminal activation means that F1 cannot generate output signals, but its primed cells can more easily be activated by bottom-up inputs. For example, the verbal command "Look for the yellow banana" can prime visual feature detectors to respond more sensitively to visual inputs that represent a yellow banana, without forcing these cells to be fully activated, which would have caused a visual hallucination.
Carpenter and Grossberg6 have shown that the 2/3 Rule is realized by a kind of analog spatial logic. This logical operation computes the spatial intersection of bottom-up and top-down information. The spatial intersection is the focus of attention. It is of interest that sublimal top-down priming, which instantiates a type of "intentionality" in an ART system implies a type of matching law, which instatiates a type of "logic." Searle17 and others have criticized some AI models because they sacrifice intentionality for logic. In ART, intentionality implies logic.
As discussed above, the main elements of an ARTMAP system are shown in FIG. 2. Two modules, ARTa and ARTb read vector inputs a and b. If ARTa and ARTb were disconnected, each module would self-organize category groupings for the separate input sets. In the application described below, ARTa and ARTb are fast-learn ART 1 modules coding binary input vectors. ARTa and ARTb are here connected by an inter-ART module that in many ways resembles ART 1. This inter-ART module includes a Map Field 26 that controls the learning of an associative map from ARTa recognition categories to ARTb recognition categories. This map does not directly associate exemplars a and b, but rather associates the compressed and symbolic representations of families of exemplars a and b. The Map Field also controls match tracking of the ARTa vigilance parameter. A mismatch at the Map Field between the ARTa category activated by an input a and the ARTb category activated by the input b increases ARTa vigilance by the minimum amount needed for the system to search for and, if necessary, learn a new ARTa category whose prediction matches the ARTb category.
This inter-ART vigilance resetting signal is a form of "back propagation" of information, but one that differs from the back propagation that occurs in the Back Propagation network. For example, the search initiated by the inter-ART reset can shift attention to a novel cluster of visual features that can be incorporated through learning into a new ARTa recognition category. This process is analogous to learning a category for "green bananas" based on "taste" feedback. However, these events do not "back propagate" taste features into the visual representation of the bananas, as can occur using the Back Propagation network. Rather, match tracking reorganizes the way in which visual features are grouped, attended, learned, and recognized for purposes of predicting an expected taste.
ART modules ARTa and ARTb Each ART module in FIG. 2 establishes compressed recognition codes in response to sequences of input patterns a and b. Associative learning at the Map Field 26 links pairs of pattern classes via these compressed codes. One type of generalization follows immediately from this learning strategy: If one vector a is associated with a vector b, then any other input that activates a's category node will predict the category of pattern b. Any ART module can be used to self-organize the ARTa and ARTb categories. In the poison mushroom application below, a and b are binary vectors, so ARTa and ARTb can be ART 1 modules. The main computations of the ART 1 module will here be outlined. A full definition of ART 1 modules, as systems of differential equations, along with an analysis of their network dynamics, can be found in Carpenter and Grossberg9. For other applications ART 2 and ART 3 modules may be more appropriate.
In an ART 1 module, an input pattern I is represented in field F1 and the recognition category for I is represented in field F2. We consider the case where the competitive field F2 makes a choice and where the system is operating in a fast-learn mode, as defined below. An algorithm for simulations is given below.
FIG. 3 illustrates the main components of an ART 1 module. The binary vector I forms the bottom-up input to the field F1 whose activity vector is denoted x. The competitive field F2 is designed to make a choice. Adaptive pathways 22 lead from each F1 node to all F2 nodes, and pathways 24 lead from each F2 node to all F1 nodes. Only sample pathways are shown. Reset occurs when the match between x and I fails to meet the criterion established by the vigilance parameter ρ. All paths are excitatory unless marked with a minus sign. A field of M nodes F1 with output vector x≡(x1, . . . , xM) registers the F0 →F1 input vector I≡(I1, . . . , IM). Each F1 node can receive input from three sources: the F0 →F1 bottom-up input; nonspecific gain controls 25 and 30; and top-down signals 24 from the N nodes of F2, via an F2 → F1 adaptive filter. A node is said to be active if it generates an output signal equal to 1. Output from inactive nodes equals 0. In ART 1 an F1 node is active if at least 2 of the 3 input signals are large. This rule for F1 activation is called the 2/3 Rule. The 2/3 Rule is realized in its simplest, dimensionless form as follows.
The ith F1 node is active if its net input exceeds a fixed threshold. Specifically, ##EQU1## where term Ii is the binary F0 →F1 input, term g1 is the binary nonspecific F1 gain control signal, term Σyj zji is the sum of F2 →F1 signals yj via pathways with adaptive weights zji and z is a constant such that
0&lt;z&lt;1.                                                     (2)
The signal g1 from the F1 gain control 30 is defined by ##EQU2## Note that F2 activity inhibits F1 gain, as shown in FIG. 3. These laws for F1 activation imply that, if F2 is inactive, ##EQU3## If exactly one F2 node J is active, the sum Σyj zji in (1) reduces to the single term zJi, so ##EQU4##
Let Tj denote the total input from F1 to jth F2 node, given by ##EQU5## where the Zij denote the F1 →F2 adaptive weights. If some Tj >0, define the F2 choice index J by
TJ =max{Tj :j=1 . . . N}.                        (7)
In the typical case, J is uniquely defined. Then the F2 output vector y=(y1, . . . , yN) obeys ##EQU6## If two or more indices j share maximal input, then they equally share the total activity. This case is not considered here.
In fast-learn ART 1, adaptive weights reach their new asymptote on each input presentation. The learning laws, as well as the rules for choice and search, are conveniently described using the following notation. If a is a binary M-vector, define the norm of a by ##EQU7## If a and b are two binary vectors, define a third binary vector by ∩ b by
(a&#8745;b)i =1 ai =1 and bi =1.          (10)
Finally, let a be a subset of b (a b) if a ∩ b =a.
All ART 1 learning is gated by F2 activity; that is, the adaptive weights zJi and ZiJ can change only when the Jth F2 node is active. Then both F2 →F1 and F1 →F2 weights are functions of the F1 vector x, as follows.
Top-down F2 →F1 weights in active paths learn x; that is, when the Jth F2 node is active
ZJi &#8594;Xi.                                  (11)
All other Zji remain unchanged. Stated as a differential equation, this learning rule is ##EQU8## In (12), learning by Zji is gated by yj. When the yj gate opens--that is, when yj >0--then learning begins and Zji is attracted to Xi. In vector terms, if yj >0, then Zj ≡(Zj1, Zj2, . . . , ZjM) approaches x. Such a law is therefore sometimes called learning by gated steepest descent. It is also called the outstar learning rule, and was introduced into the neural modelling literature in 196923.
Initially all Zji are maximal:
Zji (0)=1.                                            (13)
Thus with fast learning, the top-down weight vector Zj is a binary vector at the start and end of each input presentation. By (4), (5), (10), (11), and (13), the F1 activity vector can be described as ##EQU9## By (5) and (12), when node J is active, learning causes
ZJ &#8594;I&#8745;Zj.sup.(old)                (15)
where ZJ.sup.(old) denotes ZJ at the start of the input presentation. By (11) and (14), x remains constant during learning, even though |Zj | may decrease.
The first time an F2 node J becomes active, it is said to be uncommitted. Then, by (13)-(15),
ZJ &#8594;I                                          (16)
during learning. Thereafter node J is said to be committed.
In simulations it is convenient to assign initial values to the bottom-up F1 →F2 adaptive weights Zij in such a way that F2 nodes first become active in the order j=1,2, . . . . This can be accomplished by letting
Zij (0)=aj                                       (17)
a1 &gt;a2. . . &gt;aN.                            (18)
Like the top-down weight vector ZJ, the bottom-up F1 →F2 weight vector ZJ ≡(Z1J . . . ZiJ . . . ZMJ) also becomes proportional to the F1 output vector x when the F2 node J is active. In addition, however, the bottom-up weights are scaled inversely to |x|, so that ##EQU10## where β>0. This F1 →F2 learning law, called the Weber Law Rule9, realizes a type of competition among the weights ZJ adjacent to a given F2 node J. This competitive computation could alternatively be transferred to the F1 field, as it is in ART 2. By (14), (15), and (19), during learning ##EQU11##
The Zij initial values are required to be small enough so that an input I that perfectly matches a previously learned vector ZJ will select the F2 node J rather than an uncommitted node. This is accomplished by assuming that ##EQU12## for all F0 →F1 inputs I. When I is first presented, x=I, so by (6), (15), (17), and (20), the F1 →F2 input vector T≡(T1,T2, . . . , TN) is given by ##EQU13## In the simulations below, β is taken to be so small that, among committed nodes, Tj is determined by the size of |I∩zj | relative to |zj |. If β were large, Tj would depend primarily on |I∩zj |. In addition, aj values are taken to be so small that an uncommitted node will generate the maximum Tj value in (22) only if |I∩zj |=0 for all committed nodes. Larger values of aj and β bias the system toward earlier selection of uncommitted nodes when only poor matches are to be found among the committed nodes. A more complete discussion of this aspect of ART 1 system design is given by Carpenter and Grossberg9.
By (7), (21), and (22), a committed F2 node J may be chosen even if the match between I and zj is poor; the match need only be the best one available. If the match is too poor, then the ART 1 system can autonomously carry out hypothesis testing, or search, for a better F2 recognition code. This search process is mediated by the orienting subsystem, which can reset F2 nodes in response to poor matches at F1 (FIG. 3). The orienting subsystem is a type of novelty detector that measures system confidence. If the degree of match between bottom-up input I and top-down weight vector zj is too poor, the system's confidence in the recognition code labelled by J is inadequate. Otherwise expressed, the input I is too unexpected relative to the top-down vector zj, which plays the role of a learned top-down expectation.
An unexpected input triggers a novelty burst at the orienting subsystem, which sends a nonspecific reset wave r from the orienting subsystem to F2. The reset wave enduringly shuts off node j so long as input I remains on. With J off and its top-down F2 →F1 signals silent, F1 can again instate vector x=I, which leads to selection of another F2 node through the bottom-up F2 →F1 adaptive filter. This hypothesis testing process leads to activation of a sequence of F2 nodes until one is chosen whose vector of adaptive weights forms an adequate match with I, or until an uncommitted node is selected. The search takes place so rapidly that essentially no learning occurs on that time scale. Learned weights are hereby buffered against recoding by poorly matched inputs that activate unacceptable F2 recognition codes. Thus, during search, previously learned weights actively control the search for a better recognition code without being changed by the signals that they process.
As noted above, the degree of match between bottom-up input I and top-down expectation zj is evaluated at the orienting subsystem, which measures system confidence that category J adequately represents input I. A reset wave is triggered only if this confidence measure falls below a dimensionless parameter P that is called the vigilance parameter. The vigilance parameter calibrates the system's sensitivity to disconfirmed expectations.
One of the main reasons for the successful classification of nonstationary data sequences by ARTMAP is its ability to recalibrate the vigilance parameter based on predictive success. How this works will be described below. For now, we characterize the ART 1 search process given a constant level of vigilance.
In fast-learn ART 1 with choice at F2, the search process occurs as follows:
Step 1--Select one F2 node J that maximizes Tj in (22), and read-out its top-down weight vector zJ.
Step 2--With J active, compare the F1 output vector x=I∩zJ with the F0 →F1 input vector I at the orienting subsystem 26, 28 (FIG. 3).
Step 3A--Suppose that I∩zJ fails to match I at the level required by the vigilance criterion, i.e., that ##EQU14## Then F2 reset occurs: node J is shut off for the duration of the input interval during which I remains on. The index of the chosen F2 node is reset to the value corresponding to the next highest F1 →F2 input Tj. With the new node active, Steps 2 and 3A are repeated until the chosen nodes satisfies the resonance criterion in Step 3B. Note that reset never occurs if
&#961;&#8806;0.                                            (24)
When (24) holds, an ART system acts as if there were no orienting subsystem.
Step 3B--Suppose that I∩zJ meets the criterion for resonance; i.e., that
|x|=|I&#8745;zJ |&#8807;&#961;|I|.             (25)
Then the search ceases and the last chosen F2 node J remains active until input I shuts off (or until ρ increases). In this state, called resonance, both the F1 →F2 and the F2 →F1 adaptive weights approach new values if I∩zJ.sup.(old) ≠zJ.sup.(old). Note that resonance cannot occur if ρ>1.
If ρ≦1, search ceases whenever I J, as is the case if an uncommitted node J is chosen. If vigilance is close to 1, then reset occurs if F2 →F1 input alters the F1 activity pattern at all; resonance requires that I be a subset of zJ. If vigilance is near 0, reset never occurs. The top-down expectation zJ of the first chosen F2 node J is then recoded from zJ.sup.(old) to I∩zJ.sup.(old), even if I and zJ.sup.(old) are very different vectors.
For simplicity, ART 1 is exposed to discrete presentation intervals during which an input is constant and after which F1 and F2 activities are set to zero. Discrete presentation intervals are implemented in ART 1 by means of the F1 and F2 gain control signals g1 and g2 (FIG. 5). The F2 gain signal g2 is assumed, like g1 in (3), to be 0 if F0 is inactive. Then, when F0 becomes active., g2 and F2 signal thresholds are assumed to lie in a range where the F2 node that receives the largest input signal can become active. When an ART 1 system is embedded in a hierarchy, F2 may receive signals from sources other than F1. This occurs in the ARTMAP system described below. In such a system, F2 still makes a choice and gain signals from F0 are still required to generate both F1 and F2 output signals. In the simulations, F2 nodes that are reset during search remain off until the input shuts off. A real-time ART search mechanism that can cope with continuously fluctuating analog or binary inputs of variable duration, fast or slow learning, and compressed or distributed F2 codes is described by Carpenter and Grossberg11.
The Map Field A Map Field module 26 links the F2 fields of the ARTa and ARTb modules. FIG. 4 illustrates the main components of the Map Field. We will describe one such system in the fast-learn mode with choice at the fields F2 a and F2 b. As with the ART 1 and ART 2 architectures themselves9,10, many variations of the network architecture lead to similar computations. In the ARTMAP hierarchy, ARTa, ARTb and Map Field modules are all described in terms of ART 1 variables and parameters. Indices a and b identify terms in the ARTa and ARTb modules, while Map Field variables and parameters have no such index. Thus, for example, ρa, ρb, and ρ denote the ARTa, ARTb, and Map Field vigilance parameters, respectively.
Both ARTa and ARTb are fast-learn ART 1 modules. With one optional addition, they duplicate the design described above. That addition, called complement coding, represents both the on-response to an input vector and the off-response to that vector. This ART coding strategy has been shown to play a useful role in searching for appropriate recognition codes in response to predictive feedback 24,25. To represent such a code in its simplest form, let the input vector a itself represent the on-response, and the complement of a, denoted by ac, represent the off-response, for each ARTa input vector a. If a is the binary vector (a1, . . . ,aMa), the input to ARTa in the 2Ma -dimensional binary vector.
(a,ac)&#8801;(a1, . . . , aMa,a1 c, . . . , aMa c)                                           (26)
ai c =1-ai.                                  (27)
The utility of complement coding for searching an ARTMAP system will be described below. Conditions will also be given where complement coding is not needed. In fact, complement coding was not needed for any of the simulations described below, and the ARTa input was simply the vector a.
In the discussion of the Map Field module below, F2 a nodes, indexed by j=1 . . . Na, have binary output signals yj a ; and F2 b nodes indexed by k=1 . . . Nb, have binary output signals yk b. Correspondingly, the index of the active F2 a node is denoted by J, and the index of the active F2 b node is denoted by K. Because the Map Field is the interface where signals from F2 a and F2 b interact, it is denoted by Fab. The nodes of Fab have the same index k, k=1,2, . . . , Nb as the nodes of F2 b because there is a one-to-one correspondence between these sets of nodes.
The output signals of Fab nodes are denoted by Xk.
Each node of Fab can receive input from three sources: F2 a, F2 b, and Map Field gain control 32 (signal G). The Fab output vector x obeys the 2/3 Rule of ART 1; namely, ##EQU15## where term yk b is the F2 b output signal, term G is a binary gain control signal, term Σyj a wjk is the sum of F2 a →Fab signals yj a via pathways with adaptive weights wjk, and w is a constant such that
0&lt;w&lt;1.                                                     (29)
Values of the gain control signal G and the F2 a →Fab weight vectors wj ≡(wj1, . . . , wjNb), j=1 . . . Na, are specified below.
Comparison of (1) and (28) indicates an analogy between fields F2 b, Fab, and F2 a in a Map Field module and fields F0, F1, and F2, respectively, in an ART 1 module. Differences between these modules include the bidirectional non-adaptive connections between F2 b and Fab in the Map Field module (FIG. 4) compared to the bidirectional adaptive connections between fields F1 and F2 in the ART 1 module (FIG. 3). These different connectivity schemes require different rules for the gain control signals G and g1.
The Map Field gain control signal G obeys the equation ##EQU16## Note that G is a persistently active, or tonic, signal that is turned off only when both ARTa and ARTb are active.
If an active F2 a node J has not yet learned a prediction, the ARTMAP system is designed so that J can learn to predict any ARTb pattern if one is active or becomes active while J is active. This design constraint is satisfied using the assumption, analogous to (13), that F2 a →Fab initial values
wjk (0)=1                                             (31)
for j =1 . . . Na and k=1 . . . Nb.
Rules governing G and wj (0) enable the following Map Field properties to obtain. If both ARTa and ARTb are active, then learning of ARTa →ARTb associations can take place at Fab. If ARTa is active but ARTb is not, then any previously learned ARTa →ARTb prediction is read out at Fab. If ARTb is active but ARTa is not, then the selected ARTb category is represented at Fab. If neither ARTa nor ARTb is active, then Fab is not active. By (28)-(31), the 2/3 Rule realizes these properties in the following four cases.
1.) F2 a active and F2 b active--If both the F2 a category node J and the F2 b category node K are active, then G=0 by (30). Thus by (28), ##EQU17## All xk =0 for k≠K. Moreover xK =1 only if an association has previously been learned in the pathway from node J to node K, or if J has not yet learned to predict any ARTb category. If J predicts any category other than K, then all xk 32 0.
2.) F2 a active and F2 b inactive--If the F2 a node J is active and F2 b is inactive, then G=1. Thus ##EQU18## By (31) and (33), if an input a has activated node J in F2 a but F2 b is not yet active, J activates all nodes k in Fab if J has learned no predictions. If prior learning has occurred, all nodes k are activated whose adaptive weights wJk are still large.
3.) F2 b active and F2 a inactive--If the F2 b node K is active and F2 a is inactive, then G=1. Thus ##EQU19## In this case, the Fab output vector x is the same as the F2 a output vector yb.
4.) F2 a inactive and F2 b inctive--If neither F2 a nor F2 b is active, the total input to each Fab node is G=1, so all xk =0 by (28).
F2 b choice and priming is as follows. If ARTb receives an input b while ARTa has no input, then F2 b chooses the node K with the largest F1 b →F2 b input. Field F2 b then activates the Kth Fab node, and Fab →F2 b feedback signals support the original F1 b →F2 b choice. If ARTa receives an input a while ARTb has no input, F2 a chooses a node J. If, due to prior learning, some wJK =1 while all other wJk =0, we say that a predicts the ARTb category K, as Fab sends its signal vector x to F2 b. Field F2 b is hereby attentionally primed, or sensitized, but the field remains inactive so long as ARTb has no input from F0 b. If then an F0 b →F1 b input b arrives, the F2 b choice depends upon network parameters and timing. It is natural to assume, however, that b simultaneously activates the F1 b and F2 b gain control signals g1 b and g2 b (FIG. 3). Then F2 b processes the Fab prime x as soon as F1 2 processes the input b, and F2 b chooses the primed node K. Field F1 b then receives F2 b →F1 b expectation input zK b as well as F0 b →F1 b input b, leading either to match or reset.
F2 a →Fab learning laws are as follows. The F2 a →Fab adaptive weights wjk obey an outstar learning law similar to that governing the F2 →F1 weights zji in (12); namely, ##EQU20## According to (35), the F2 a →Fab weight vector wj approaches the Fab activity vector x if the Jth F2 a node is active. Otherwise wj remains constant. If node J has not yet learned to make a prediction, all weights wJk equal 1, by (31). In this case, if ARTb receives no input b, then all xk values equal 1 by (33). Thus, by (35), all wjk values remain equal to 1. As a result, category choices in F2 a do not alter the adaptive weights wjk until these choices are associated with category choices in F2 b.
Map Field Reset And Match Tracking
The Map Field provides the control that allows the ARTMAP system to establish different categories for very similar ARTa inputs that make different predictions, while also allowing very different ARTa inputs to form categories that make the same prediction. In particular, the Map Field orienting subsystem 34, 36 becomes active only when ARTa makes a prediction that is incompatible with the actual ARTb input. This mismatch event activates the control strategy, called match tracking, that modulates the ARTa vigilance parameter ρa in such a way as to keep the system from making repeated errors. As illustrated in FIG. 4, a mismatch at Fab while F2 b is active triggers an inter-ART reset signal R to the ARTa orienting subsystem. This occurs whenever ##EQU21## where ρ denotes the Map Field vigilance parameter. The entire cycle of ρa adjustment proceeds as follows through time. At the start of each input presentation, ρa equals a fixed baseline vigilance ρa. When an input a activates an F2 a category node J and resonance is established, ##EQU22## as in (25). Thus, there is no reset ra generated by the ARTa orienting subsystem 38, 39 (FIG. 5). An inter-ART reset signal R is sent to ARTa if the ARTb category predicted by a fails to match the active ARTb category, by (36). The inter-ART reset signal R raises ρa to a value that is just high enough to cause (37) to fail, so that ##EQU23## Node J is therefore reset and an ARTa search ensues. Match tracking continues until an active ARTa category satisfies both the ARTa matching criterion (37) and the analogous Map Field matching criterion. Match tracking increases the ARTa vigilance by the minimum amount needed to abort an incorrect ARTa →ARTb prediction and to drive a search for a new ARTa category that can establish a correct prediction. As shown by example below, match tracking allows a to make a correct prediction on subsequent trials, without repeating the initial sequence of errors. Match tracking hereby conjointly maximizes predictive generalization and minimizes predictive error on a trial-by-trial basis, using only local computations.
The operation of match tracking can be implemented in several different ways. One way is to use a variation on the Vector Integration to Endpoint, or VITE, circuit26 as follows. Let an ARTa binary reset signal ra (FIG. 5) obey the equation ##EQU24## as in (23). The complementary ARTa resonance signal ra c =1-ra. Signal R equals 1 during inter-ART rest; that is, when inequality (36) holds. The size of the ARTa vigilance parameter ρa at 38 is determined by the match tracking equation ##EQU25## where γ>1. During inter-ART reset, R=ra =1, causing ρa to increase until ra c =0. Then ρa |a|>|xa |, as required for match tracking (38). When ra c =0, ρa relaxes to ρa. This is assumed to occur at a rate slower than node activation, also called short term memory (STM), and faster than learning, also called long term memory (LTM). Such an intermediate rate is called medium term memory (MTM)11. Thus the higher vigilance with continued input to F0 a will be maintained for subsequent search.
An ARTa search that is triggered by increasing ρa according to (40) ceases if some active F2 a node J satisfies
|a&#8745;zJ a |&#8807;&#961;a |a|.                                    (41)
If no such node exists, F2 a shuts down for the rest of the input presentation. In particular, if a zJ a, match tracking makes ρa >1, so a cannot activate another category in order to learn the new prediction. The following anomalous case can thus arise. Suppose that a=zJ a but the ARTb input b mismatches the ARTb expectation zK b previously associated with J. Then match tracking will prevent the recoding that would have associated a with b. That is, the ARTMAP system with fast learning and choice will not learn the prediction of an exemplar that exactly matches a learned prototype when the new prediction contradicts the previous predictions of the exemplars that created the prototype. This situation does not arise when all ARTa inputs a have the same number of 1's, as follows.
Consider the case in which all ARTa inputs have the same norm:
|a|&#8801;constant.                      (42)
When an ARTa category node J becomes committed to input a, then |zJ a |=|a|. Thereafter, by the 2/3 Rule (15), zJ a can be recoded only by decreasing its number of 1 entries, and thus its norm. Once this occurs, no input a can ever be a subset of zJ a, by (42). In particular, the situation described in the previous section cannot arise.
In the simulations reported below, all ARTa inputs have norm 22. Equation (42) can also be satisfied by using complement coding, since |(a,ac)|=Ma. Preprocessing ARTa inputs by complement coding thus ensures that the system will avoid the case where some input a is a proper subset of the active ARTa prototype zJ a and the learned prediction of category J mismatches the correct ARTb pattern.
Finally, note that with ARTMAP fast learning and choice, an ARTa category node J is permanently committed to the first ARTb category node K to which it is associated. However, the set of input exemplars that access either category may change through time, as in the banana example described in the introduction.
The role of match tracking is illustrated by the following example. The input pairs shown in Table 1 are presented in order a.sup.(1), b.sup.(1)), (a.sup.(2), b.sup.(2)), (a.sup.(3), b.sup.(3)). The problem solved by match tracking is created by vector a.sup.(2) lying "between" a.sup.(1) and a.sup.(3), with a.sup.(1) a.sup.(2) a.sup.(3), while a.sup.(1) and a.sup.(3) are mapped to the same ARTb vector. Suppose that, instead of match tracking, the Map Field orienting subsystem merely activated the ARTa reset system. Coding would then proceed as follows.
TABLE 1______________________________________ARTa inputs          ARTb inputs______________________________________a.sup.(1) (111000)          b.sup.(1) (1010)a.sup.(2) (111100)          b.sup.(2) (0101)a.sup.(3) (111110)          b.sup.(3) (1010)______________________________________ Table 1: Nested ARTa inputs and their associated ARTb inputs.
Choose ρa ≦0.6 and ρb >0. Vectors a.sup.(1) then b.sup.(1) are presented, activate ARTa and ARTb categories J=1 and K =1, and the category J=1 learns to predict category K =1, thus associating a.sup.(1) with b.sup.(1). Next a.sup.(2) then b.sup.(2) are presented. Vector a.sup.(2) first activates J=1 without reset, since ##EQU26## However, node J=1 predicts node K=1. Since ##EQU27## ARTb search leads to activation (selection) of a different F2 b node, K=2. Because of the conflict between the prediction (K=1) made by the active F2 a node and the currently active F2 b node (K=2), the Map Field orienting subsystem resets F2 a, but without match tracking. Thereafter a new F2 a node (J=2) learns to predict the correct F2 b node (K=2), associating a.sup.(2) with b.sup.(2).
Vector a.sup.(3) first activates J=2 without ARTa reset, thus predicting K=2, with z2 b =b.sup.(2). However, b.sup.(3) mismatches z2 b, leading to activation of the F2 b node K=1, since b.sup.(3) =b.sup.(1). Since the predicted node (K=2) then differs from the active node (K=1), the Map Field orienting subsystem again resets R2 a. At this point, still without match tracking, the F2 a node J=1 would become active, without subsequent ARTa reset, since z1 a =a.sup.(1) and ##EQU28## Since node J=1 correctly predicts the active node K=1, no further reset or new learning would occur. On subsequent prediction trials, vector a.sup.(3) would once again activate J=2 and then K=2. When vector b.sup.(3) is not presented, on a test trial, vector a.sup.(3) would not have learned its correct prediction; rather, b.sup.(2) would be incorrectly predicted.
With match tracking, when a.sup.(3) is presented, the Map Field orienting subsystem causes ρa to increase to a value slightly greater than |a.sup.(3) ∩a.sup.(2) ||a.sup.(3) |-1 =0.8 while node J=2 is active. Thus after node J=2 is reset, node J=1 will also be reset because ##EQU29## The reset of node J=1 permits a.sup.(3) to choose an uncommitted F2 a node (J=3) that is then associated with the active F2 b node (K=1). Because vector a.sup.(3) is exactly learned at the new J=3 node, subsequent a.sup.(3) inputs will select J=3 directly at any vigilance; J=2 will not first be selected. Thereafter each ARTa input predicts the correct ARTb output without search or error unaffected by the lower base level of vigilance.
If a high level of vigilance had been initially set as the baseline vigilance, a.sup.(1), a.sup.(2), and a.sup.(3) would have been learned at nodes J=1, 2 and 3 with reset at the baseline vigilance and without the need for reset from the mapping field. However, in a typical system the high baseline vigilance would result in smaller categories, that is more precisely defined categories for all input patterns. Thus there would be an unnecessary loss in generalization. By providing a lower level of vigilance which is tracked where necessary with mismatch at the mapping field, the system is able to maximize generalization at the lower vigilance levels while minimizing predictive error by tracking to higher vigilance where required. In choosing baseline vigilance, one must balance the need for generalization against the risk of early predictive errors in the learning process.
The utility of ARTa complement coding is illustrated by the following example. Assume that the nested input pairs in Table 7 are presented to an ARTMAP system in order (a.sup.(3), b.sup.(3)), (a.sup.(2), b.sup.(2)), (a.sup.(1), b.sup.(1)), with match tracking but without complement coding. Choose ρa <0.5 and ρb >0.
Vectors a.sup.(3) and b.sup.(3) are presented and activate ARTa and ARTb categories J=1 and K=1. The system learns to predict b.sup.(3) given a.sup.(3) by associating the F2 a node J=1 with the F2 b node K=1.
Next a.sup.(2) and b.sup.(2) are presented. Vector a.sup.(2) first activates J=1 without reset, since |a.sup.(2) ∩z1 a ||a.sup.(2) |-1 =1 ≧ρa =ρa. However, node J=1 predicts node K=1. As in the previous example, after b.sup.(2) is presented, the F2 b node K=2 becomes active and leads to an inter-ART reset. Match tracking makes ρa >1, so F2 a shuts down until the pair (a.sup.(2), b.sup.(2)) shuts off. Pattern b.sup.(2) is coded in ARTb as z2 b, but no learning occurs in the ARTa and Fab modules.
Next a.sup.(1) activates J=1 without reset, since |a.sup.(1) ∩z1 a ||a.sup.(1) |-1 =1≧ρa =ρa. Since node J=1 predicts the correct pattern b.sup.(1) =z1 b, no reset ensues. Learning does occur, however, since za a shrinks to a.sup.(1). If each input can be presented only once, a.sup.(2) does not learn to predict b.sup.(2). However if the input pairs are presented repeatedly, match tracking allows ARTa to establish 3 category nodes and an accurate mapping.
With complement coding, the correct map can be learned on-line for any ρa >0. The critical difference is due to the fact that |a.sup.(2) ∩z1 a ||a.sup.(2) |-1 now equals 5/6 when a.sup.(2) is first presented, rather than equaling 1 as before. Thus either ARTa reset (if ρa >5/6) or match tracking (if ρa ≦5/6) establishes a new ARTa node rather than shutting down on that trial. On the next trial, a.sup.(1) also establishes a new ARTa category that maps to b.sup.(1).
SIMULATION ALGORITHMS ART 1 Algorithm Fast-learn ART 1 with binary F0 →F1 input vector I and choice at F2 can be simulated by following the rules below. Fields F0 and F1 have M nodes and field F2 has N nodes.
Initially all F2 nodes are said to be uncommitted. Weights Zij in F1 →F2 paths initially satisfy
Zij (0)=&#945;j,                                (A1)
where Zj ≡(Z1j, . . . , ZMj) denotes the bottom-up F1 →F2 weight vector. Parameters αj are ordered according to
&#945;1 &gt;&#945;2 &gt;. . . &gt;&#945;N,        (A2)
where ##EQU30## for β>0 and for any admissible F0 →F1 input I. In the simulations in this article, aj and β are small.
Weights zji in F2 →F1 paths initially satisfy
zji (0)=1                                             (A4)
The top-down, F2 →F1 weight vector (zj1, . . . , zjM) is denoted zj.
The binary F1 output vector x≡(x1, . . . , xM) is given by ##EQU31## The input Tj from F1 to the jth F2 node obeys ##EQU32## The set of committed F2 nodes and update rules for vectors zj and Zj are defined iteratively below.
If F0 is active (|I|>0), the initial choice at F2 is one node with index J satisfying ##EQU33## If more than one node is maximal, one of these is chosen at random. After an input presentation on which node J is chosen, J becomes committed. The F2 output vector is denoted by y≡(y1, . . . , yN).
ART 1 search ends upon activation of an F2 category with index j=J that has the largest Tj value and that also satisfies the inequality
|I&#8745;zJ |&#8807;&#961;|I|(A8)
where ρ is the ART 1 vigilance parameter. If such a node J exists, that node remains active, or in resonance, for the remainder of the input presentation. If no node satisfies (A8), F2 remains inactive after search, until I shuts off.
At the end of an input presentation the F2 →F1 weight vector ZJ satisfies
ZJ =I&#8745;zJ.sup.(old)                       (A 9)
where zJ.sup.(old) denotes zJ at the start of the current input presentation. The F1 →F2 weight vector ZJ satisfies ##EQU34##
ARTMAP algorithm The ARTMAP system incorporates two ART modules and an inter-ART module linked by the following rules.
ARTa and ARTb are fast-learn ART 1 modules. Inputs to ARTa may, optionally, be in the complement code form. Embedded in an ARTMAP system, these modules operate as outlined above, with the following additions. First, the ARTa vigilance parameter ρa can increase during inter-ART reset according to the match tracking rule. Second, the Map Field Fab can prime ARTb. That is, if Fab sends nonuniform input to F2 b in the absence of an F0 b →F1 b input b, then F2 b remains inactive. However, as soon as an input b arrives, F2 b chooses the node K receiving the largest Fab →F2 b input. Node K, in turn, sends to F1 b the top-down input zK b. Rules for match tracking and complement coding are specified below.
Let xa ≡(x1 a. . . xMa a) denote the F1 a output vector; let ya ≡(y1 a. . . yNa a) denote the F2 a output vector; let xb ≡(x1 b. . . xMb b) denote the F1 b output vector; and let yb ≡(y1 b. . . yNb b) denote the F2 b output vector. The Map Field Fab has Nb nodes and binary output vector x. Vectors xa, ya, xb, yb, and x are set to 0 between input presentations.
Map Field learning is as follows. Weights wjk, where j=1 . . . Na and k=1 . . . Nb, in F2 a →Fab paths initially satisfy
wjk (0)=1.                                            (A11)
Each vector (wj1, . . . wjNb) is denoted wj. During resonance with the ARTa category J active, wj →x. In fast learning, once J learns to predict the ARTb category K, that association is permanent; i.e., wJK =1 for all times.
Map Field activation is as follows. The Fab output vector x obeys ##EQU35##
Match tracking is as follows. At the start of each input presentation the ARTa vigilance parameter ρa equals a baseline vigilance ρa. The Map Field vigilance parameter is ρ. If
|x|&lt;&#961;|yb |,   (A13)
then ρa is increased until it is slightly larger than |a∩zJ a ||a|-1. Then
|xa |=|a&#8745;zJ a |&lt;&#961;a |a|,             (A14)
where a is the current ARTa input vector and J is the index of the active F2 a node. When this occurs, ARTa search leads either to activation of a new F2 a node J with
|xa |=|a&#8745;zJ a |&#8807;&#961;a |a|       (A15)
|x|=|yb &#8745;wJ |&#8807;&#961;|yb |;      (A16)
or, if no such node exists, to the shut-down of F2 a for the remainder of the input presentation.
The optional feature of a complement coding arranges ARTa inputs as vectors
(a,ac)&#8801;(a1. . . aMa,a1 c. . . aMa a),(A17)
ai c &#8801;1- ai.                           (A18)
Complement coding may be useful if the following set of circumstances could arise: an ARTa input vector a activates an F2 a node J previously associated with an F2 b node K; the current ARTb input b mismatches zK b ; and a is a subset of zJ a. These circumstances never arise if all |a|≡ constant. For the simulations in this article, |a|≡22. With complement coding, |(a,ac)|≡Ma.
ARTMAP processing The following nine cases summarize fast-learn ARTMAP system processing with choice at F2 a and F2 b and with Map Field vigilance ρ>0. Inputs a and b could appear alone, or one before the other. Input a could make a prediction based on prior learning or make no prediction. If a does make a prediction, that prediction may be confirmed or disconfirmed by b. The system follows the rules outlined in the previous section assuming, as in the simulations, that all |a|≡ constant and that complement coding is not used. For each case, changing weight vectors zJ a, zK b, and wK are listed. Weight vectors ZJ a and ZK b change accordingly, by (A11). All other weights remain constant.
Case 1: a only, no prediction. Input a activates a matching F2 a node J, possibly following ARTa search. All F2 a →Fab weights WJk =1, so all xk =1. ARTb remains inactive. With learning zJ a →zJ a(old) ∩a.
Case 2: a only, with prediction. Input a activates a matching F2 a node J. Weight wJK =1 while all other wJk =0, and x=wJ. F2 b is primed, but remains inactive. With learning, ZJ a →zJ a(old) ∩a.
Case 3: b only. Input b activates a matching F2 b node K, possibly following ARTb search. At the Map Field, x=yb. ARTa remains inactive. With learning, zK b →zK b(old) ∩b.
Case 4: a then b, no prediction. Input a activates a matching F2 a node J. All xk become 1 and ARTb is inactive, as in Case 1. Input b then activates a matching F2 b node K, as in Case 3. At the Map Field x→yb ; that is, xK =1 and other xk =0. With learning ZJ a →zJ a(old) ∩a, zK b →zK b(old) ∩b, and wJ →yb ; i.e., J learns to predict K.
Case 5: a then b, with prediction confirmed. Input a activates a matching F2 a node J, which in turn activates a single Map Field node K and primes F2 b, as in Case 2. When input b arrives, the Kth F2 b node becomes active and the prediction is confirmed; that is,
|b&#8745;zK b |&#8807;&#961;b |b|                                     (A19)
Note that K may not be the F2 b node b would have selected without the Fab →F2 b prime. With learning, zJ a →zJ a(old) ∩a and zK b →aK b(old) ∩b.
Case 6. a then b, prediction not confirmed. Input a activates a matching F2 a node, which in turn activates a single Map Field node and primes F2 b, as in Case 5. When input b arrives, (A19) fails, leading to reset of the F2 b node via ARTb reset. A new F2 b node K that matches b becomes active. The mismatch between the F2 a →Fab weight vector and the new F2 b vector yb sends Map Field activity x to 0, by (A12), leading to Map Field reset, by (A13). By match tracking, ρa grows until (A14) holds. This triggers an ARTa search that will continue until, for an active F2 a node J, wJK =1, and (A15) holds. If such an F2 a node does become active, learning will follow, setting zJ a →zJ a(old) ∩a and zK b →zK.sup. b(old) ∩b. If the F2 a node J is uncommitted, learning sets wJ →yb. If no F2 a node J that becomes active satisfies (A15) and (A16), F2 a shuts down until the inputs go off. In that case, with learning, zK b →zK b(old) ∩b.
Case 7: b then a, no prediction. Input b activates a matching F2 b node K, then X=yb, as in Case 3. Input a then activates a matching F2 a node J with all wJk =1. At the Map Field, x remains equal to yb. With learning, zJ a →zJ a (old) ∩a, wJ →yb, and zK b →zK b(old) ∩b.
Case 8: b then a, with prediction confirmed. Input b activates a matching F2 b node K, then x=yb, as in Case 7. Input a then activates a matching F2 a node J with wJK =1 and all other wJk =0. With learning zJ a →zJ a(old) ∩a and zK b →zK b(old) ∩b.
Case 9: b then a, with prediction not confirmed. Input b activates a matching F2 b node K, then x=yb and input a activates a matching F2 a node, as in Case 8. However (A16) fails and x→0, leading to a Map Field reset. Match tracking resets ρa as in Case 6, ARTa search leads to activation of an F2 a node (J) that either predicts K or makes no prediction, or F2 a shuts down. With learning zK b →zK b(old) ∩b. If J exists, zJ a →zJ a(old) ∩a; and if J initially makes no prediction, wj →yb, i.e., J learns to predict K.
ARTMAP Simulations: Distinguishing Edible And Poisonous Mushrooms The ARTMAP system was tested on a benchmark machine learning database that partitions a set of vectors a into two classes. Each vector a characterizes observable features of a mushroom as a binary vector, and each mushroom is classified as edible or poisonous. The database represents the 11 species of genus Agaricus and the 12 species of the genus Lepiota described in The Audubon Society Field Guide to North American Mushrooms19. These two genera constitute most of the mushrooms described in the Field Guide from the family Agaricaceae (order Agaricales, class Hymenomycetes, subdivision Basidiomycetes, division Eumycota). All the mushrooms represented in the database are similar to one another: "These mushrooms are placed in a single family on the basis of a correlation of characteristics that include microscopic and chemical features . . ."19 (p.500). The Field Guide warns that poisonous and edible species can be difficult to distinguish on the basis of their observable features. For example, the poisonous species Agaricus californicus is described as a "dead ringer" for the Meadow Mushroom, Agaricus campestris, that "may be known better and gathered more than any other wild mushroom in North America" (p. 505). This database thus provides a test of how ARTMAP and other machine learning systems distinguish rare but important events from frequently occurring collections of similar events that lead to different consequences.
The database of 8124 exemplars describes each of 22 observable features of a mushroom, along with its classification as poisonous (48.2%) or edible (51.8%). The 8124 "hypothetical examples" represent ranges of characteristics within each species; for example, both Agaricus californicus and Agaricus campestris are described as having a "white to brownish cap," so in the database each species has corresponding sets of exemplar vectors representing their range of cap colors. There are 126 different values of the 22 different observable features. A list of the observable features and their possible values is given in Table 2. For example, the observable feature of "cap-shape" has six possible values. Consequently, the vector inputs to ARTa are 126-element binary vectors, each vector having 22 1's and 104 0's, to denote the values of an exemplar's 22 observable features. The ARTb input vectors are (1,0) for poisonous exemplars and (0,1) for edible exemplars.
The ARTMAP system learned to classify test vectors rapidly and accurately, and system performance compares favorably with results of other machine learning algorithms applied to the same database. The STAGGER algorithm reached its maximum performance level of 95% accuracy after exposure to 1000 training inputs20. The HILLARY algorithm achieved similar results21. The ARTMAP system consistently achieved over 99% accuracy with 1000 exemplars, even counting "I don't know" responses as errors. Accuracy of 95% was usually achieved with on-line training on 300-400 exemplars and with off-line training on 100-200 exemplars. In this sense, ARTMAP was an order of magnitude more efficient than the alternative systems. In addition, with continued training, ARTMAP predictive accuracy always improved to 100%. These results are elaborated below.
Almost every ARTMAP simulation was completed in under two minutes on an IRIS�4D computer, with total time ranging from about one minute for small training sets to two minutes for large training sets. This is comparable to 2-5 minutes on a SUN�4 computer. Each timed simulation included a total of 8124 training and test samples, run on a time-sharing system with non-optimized code. Each 1-2 minute computation included data read-in and read-out, training, testing, and calculation of multiple simulation indices.
On-line learning imitates the conditions of a human or machine operating in a natural environment. An input a arrives, possibly leading to a prediction. If made, the prediction may or may not be confirmed. Learning ensues, depending on the accuracy of the prediction. Information about past inputs is available only through the present state of the system. Simulations of on-line learning by the ARTMAP system use each sample pair (a,b) as both a test item and a training item. Input a first makes a prediction that is compared with b. Learning follows as dictated by the internal rules of the ARTMAP architecture.
Four types of on-line simulations were carried out, using two different baseline settings of the ARTa vigilance parameter ρa : ρa =0 (forced choice condition) and ρa =0.7 (conservative condition); and using sample replacement or no sample replacement. With sample replacement, any one of the 8124 input samples was selected at random for each input presentation. A given sample might thus be repeatedly encountered while others were still unused. With no sample replacement, a sample was removed from the input pool after it was first encountered. The replacement condition had the advantage that repeated encounters tended to boost predictive accuracy. The no-replacement condition had the advantage of having learned from a somewhat larger set of inputs at each point in the simulation. The replacement and no-replacement conditions had similar performance indices, all other things being equal. Each of the 4 conditions was run on 10 independent simulations. With ρa =0, the system made a prediction in response to every input. Setting ρa =0.7 increased the number of "I don't know" responses, increased the number of ARTa categories, and decreased the rate of incorrect predictions to nearly 0%, even early in training. The ρa =0.7 condition generally outperformed the ρa =0 condition, even when incorrect predictions and "I don't know" responses were both counted as errors. The primary exception occurred very early in training, when a conservative system gives the large majority of its no-prediction responses.
Results are summarized in Table 3. Each entry gives the number of correct predictions over the previous 100 trials (input presentations), averaged over 10 simulations. For example, with ρa =0 in the no-replacement condition, the system made, on the average, 94.9 correct predictions and 5.1 incorrect predictions on trials 201-300. In all cases a 95% correct-prediction rate was achieved before trial 400. With ρa =0, a consistent correct-prediction rate of over 99% was achieved by trial 1400, while with ρa =0.7 the 99% consistent correct-prediction rate was achieved earlier, by trial 800. Each simulation was continued for 8100 trials. In all four cases, the minimum correct-prediction rate always exceeded 99.5% by trial 1800 and always exceeded 99.8% by trial 2800. In all cases, across the total of 40 simulations summarized in Table 2, 100% correct prediction was achieved on the last 1300 trials of each run.
Note the relatively low correct-prediction rate for ρa =0.7 on the first 100 trials. In the conservative mode, a large number of inputs initially make no prediction. With ρa =0.7 an average total of only 2 incorrect predictions were made on each run of 8100 trials. Note too that Table 3 underestimates prediction accuracy at any given time, since performance almost always improves during the 100 trials over which errors are tabulated.
In off-line learning, a fixed training set is repeatedly presented to the system until 100% accuracy is achieved on that set. For training sets ranging in size from 1 to 4000 samples, 100% accuracy was almost always achieved after one or two presentations of each training set. System performance was then measured on the test set, which consisted of all 8124 samples not included in the training set. During testing no further learning occurred.
The role of repeated training set presentations was examined by comparing simulations that used the 100% training set accuracy criterion with simulations that used only a single presentation of each input during training. With only a few exceptions, performance was similar. In fact for ρa =0.7, and for small training sets with ρa =0, 100% training-set accuracy was achieved with single input presentations, so results were identical. Performance differences were greatest for ρa =0 simulations with mid-sized training sets (60-500 samples), when 2-3 training set presentations tended to add a few more ARTa learned category nodes. Thus, even a single presentation of training-then-testing inputs, carried out on-line, can be made to work almost as well as off-line training that uses repeated presentations of the training set. This is an important benefit of fast learning controlled by a match tracked search.
The simulations summarized in Table 4 illustrate off-line learning with ρhd a=0. In this forced choice case, each ARTa input led to a prediction of poisonous or edible. The number of test set errors with small training sets was relatively large, due to the forced choice. The table illustrates system performance after training on input sets ranging in size from 3 to 4000 exemplars. Each line shows average correct and incorrect test set predictions over 10 independent simulations, plus the range of learned ARTa category numbers.
Table 4 summarizes the average results over 10 simulations at each size training set. For example, with very small, 5-sample training sets, the system established between 1 and 5 ARTa categories, and averaged 73.1% correct responses on the remaining 8119 test patterns. Success rates ranged from chance (51.8%, one category) in one instance where all five training set exemplars happened to be edible, to surprisingly good (94.2%, 2 categories). The range of success rates for fast-learn training on very small training sets illustrates the statistical nature of the learning process. Intelligent sampling of the training set or, as here, good luck in the selection of representative samples, can dramatically alter early success rates. In addition, the evolution of internal category memory structure, represented by a set of ARTa category nodes and their top-down learned expectations, is influenced by the selection of early exemplars. Nevertheless, despite the individual nature of learning rates and internal representations, all the systems eventually converge to 100% accuracy on test set exemplars using only approximately) 1/600 as many ARTa categories as there are inputs to classify.
As in the case of poisonous mushroom identification, it may be important for a system to be able to respond "I don't know" to a novel input, even if the total number of correct classifications thereby decreases early in learning. For higher values of the baseline vigilance ρa, the ARTMAP system creates more ARTa categories during learning and becomes less able to generalize from prior experience than when ρa equals 0. During testing, a conservative coding system with ρa =0.7 makes no prediction in response to inputs that are too novel, and thus initially has a lower proportion of correct responses. However, the number of incorrect responses is always low with ρa =0.7, even with very few training samples, and the 99% correct-response rate is achieved for both forced choice (ρa =0) and conservative (ρa =0.7) systems with training sets smaller than 1000 exemplars.
Table 5 summarizes simulation results that repeat the conditions of Table 4 except that ρa =0.7. Here, a test input that does not make a 70% match with any learned expectation makes an "I don't know" prediction. Compared with the ρa =0 case of Table 4, Table 5 shows that larger training sets are required to achieve a correct prediction rate of over 95%. However, because of the option to make no prediction, the average test set error rate is almost always less than 1%, even when the training set is very small, and is less than 0.1% after only 500 training trials. Moreover, 100% accuracy is achieved using only (approximately) 1/130 as many ARTa categories as there are inputs to classify.
Each ARTMAP category code can be described as a set of ARTa feature values on 1 to 22 observable features, chosen from 126 feature values, that are associated with the ARTb identification as poisonous or edible. During learning, the number of feature values that characterize a given category is monotone decreasing, so that generalization within a given category tends to increase. The total number of classes can, however, also increase, which tends to decrease generalization. Increasing the number of training patterns hereby tends to increase the number of categories and decrease the number of critical feature values of each established category. The balance between these opposing tendencies leads to the final net level of generalization.
Table 6 illustrates the long term memory structure underlying the 125-sample forced-choice simulation ρa =0. Of the nine categories established at the end of the training phase, 4 are identified as poisonous (P) and 5 are identified as edible (E). Categories 1, 5, 7 and 8 are identified as poisonous (P) and categories 2, 3, 4, 6, and 9 are identified as edible (E). Each ARTa category assigns a feature value to a subset of the 22 observable features. For example, Category 1 (poisonous) specifies values for 5 features, and leaves the remaining 17 features unspecified. The corresponding ARTa weight vector has 5 ones and 121 zeros. Note that the features that characterize category 5 (poisonous) form a subset of the features that characterize category 6 (edible). This category structure gave 96.4% correct responses on the 7999 test set samples, which are partitioned as shown in the last line of Table 5. When 100% accuracy is achieved, a few categories with a small number of specified features typically code large clusters, while a few categories with many specified features code small clusters of rare samples.
Table 7 illustrates the statistical nature of the coding process, which leads to a variety of category structures when fast learning is used. Test set prediction accuracy of the simulation that generated Table 7 was similar to that of Table 6, and each simulation had a 125-sample training set. However, the simulation of Table 7 produced only 4 ARTa categories, only one of which (category 1) has the same long term memory representation as category 2 in Table 6. Note that, at this stage of coding, certain features are uninformative. For example, no values are specified for features 1, 2, 3, or 22 in Table 6 or Table 7; and feature 16 (veil-type) always has the value "partial." However, performance is still only around 96%. As rare instances from small categories later in the coding process, some of these features may become critical in identifying exemplars of small categories.
While the invention has been particularly shown and described with reference to a preferred embodiment thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. For example, with only two choices of poisonous or nonpoisonous as the second-category-representation in the simulation, a full ART pattern recognition system ARTb would not be required. In that simple case, ARTa could be reset as described in response to a simple comparison. However, the use of the second pattern recognition system ARTb allows for a much more complex comparison. Further, any of the ART systems may be utilized in the present invention, and the invention may even be applied to other neural network systems.
TABLE 2______________________________________22 Observable Features and their 126 ValuesNumber Feature         Possible Values______________________________________ 1     cap-shape       bell, conical, convex, flat,                  knobbed, sunken 2     cap-surface     fibrous, grooves, scaly,                  smooth 3     cap-color       brown, buff, gray, green,                  pink, purple, red, white,                  yellow, cinnamon 4     bruises         bruises, no bruises 5     odor            none, almond, anise, creosote,                  fishy, foul, musty, pungent,                  spicy 6     gill-attachment attached, descending,                  free, notched 7     gill-spacing    close, crowded, distant 8     gill-size       broad, narrow 9     gill-color      brown, buff, orange, gray,                  green, pink, purple, red,                  white, yellow, chocolate,                  black10     stalk-shape     enlarging, tapering11     stalk-root      bulbous, club, cup, equal,                  rhizomorphs, rooted, missing12     stalk-surface-above-ring                  fibrous, silky, scaly, smooth13     stalk-surface-below-ring                  fibrous, silky, scaly, smooth14     stalk-color-above-ring                  brown, buff, orange, gray,                  pink, red, white, yellow,                  cinnamon15     stalk-color-below-ring                  brown, buff, orange, gray,                  pink, red, white, yellow,                  cinnamon16     veil-type       partial, universal17     veil-color      brown, orange, white,                  yellow18     ring-number     none, one, two19     ring-type       none, cobwebby, evanescent,                  flaring, large, pendant,                  sheathing, zone20     spore-print-color                  brown, buff, orange, green,                  purple, white, yellow,                  chocolate, black21     population      abundant, clustered,                  numerous, scattered, several,                  solitary22     habitat         grasses, leaves, meadows,                  paths, urban, waste, woods______________________________________
TABLE 3______________________________________On-Line LearningAverage number of correct predictions onprevious 100 trials   --&#961;a = 0             --&#961;a = 0                       --&#961;a = 0.7                               --&#961;a = 0.7Trial   no replace             replace   no replace                               replace______________________________________ 100    82.9      81.9      66.4    67.3 200    89.8      89.6      87.8    87.4 300    94.9      92.6      94.1    93.2 400    95.7      95.9      96.8    95.8 500    97.8      97.1      97.5    97.8 600    98.4      98.2      98.1    98.2 700    97.7      97.9      98.1    99.0 800    98.1      97.7      99.0    99.0 900    98.3      98.6      99.2    99.01000    98.9      98.5      99.4    99.01100    98.7      98.9      99.2    99.71200    99.6      99.1      99.5    99.51300    99.3      98.8      99.8    99.81400    99.7      99.4      99.5    99.81500    99.5      99.0      99.7    99.61600    99.4      99.6      99.7    99.81700    98.9      99.3      99.8    99.81800    99.5      99.2      99.8    99.91900    99.8      99.9      99.9    99.92000    99.8      99.8      99.8    99.8______________________________________
TABLE 4______________________________________Off-Line Forced-Choice Learning    Average     Average    NumberTraining % Correct   % Incorrect                           of ARTaSet Size (Test Set)  (Test Set) Categories______________________________________  3      65.8        34.2       1-3  5      73.1        26.9       1-5 15      81.6        18.4       2-4 30      87.6        12.4       4-6 60      89.4        10.6        4-10 125     95.6         4.4        5-14 250     97.8         2.2        8-14 500     98.4         1.6        9-221000     99.8         0.2        7-182000      99.96       0.04      10-164000     100         0          11-22______________________________________
TABLE 5______________________________________Off-Line Conservative Learning  Average % Average % Average %                               NumberTraining  Correct   Incorrect No-Response                               of ARTaSet Size  (Test Set)            (Test Set)                      (Test Set)                               Categories______________________________________  3    25.6      0.6       73.8     2-3  5    41.1      0.4       58.5     3-5 15    57.6      1.1       41.3      8-10 30    62.3      0.9       36.8     14-18 60    78.5      0.8       20.8     21-27 125   83.1      0.7       16.1     33-37 250   92.7      0.3        7.0     42-51 500   97.7      0.1        2.1     48-641000   99.4       0.04      0.5     53-662000   100.0      0.00      0.05    54-694000   100.0      0.00      0.02    61-73______________________________________
TABLE 6__________________________________________________________________________# Feature     1 = P              2 = E                   3 = E 4 = E                              5 = P                                   6 = E                                        7 = P 8 = P  9__________________________________________________________________________                                                     = E 1  cap-shape 2  cap-surface 3  cap-color 4  bruises?                                   yes   no     yes 5  odor             none                 none 6  gill-attachment         free free       free free free free  free   free 7  gill-spacing         close           close                              close                                   close                                        close close  close 8  gill-size        broad                           narrow broad 9  gill-color                                       buff10  stalk-shape                                      tapering                                                     enlarged11  stalk-root                                       missing                                                     club12  stalk-surface-above-ring                   smooth                         smooth                              smooth                                   smooth                                        smooth                                              smooth smooth13  stalk-surface-below-ring                   smooth                            smooth14  stalk-color-above-ring           white                                   white                                        white pink   white15  stalk-color-below-ring                     white        white16  veil-type   partial              partial                   partial                         partial                              partial                                   partial                                        partial                                              partial                                                     partial17  veil-color  white              white      white                              white                                   white                                        white white  white18  ring-number one       one   one       one  one   one    one19  ring-type             pendant              pendant                                              evanescent                                                     pendant20  spore-print-color                                white21  population                       several                                   several                                        scattered                                              several                                                     scattered22  habitat  # coded/category:         2367 1257 387   1889 756  373  292   427    251__________________________________________________________________________
TABLE 7______________________________________#   Feature         1 = E   2 = P 3 = P 4 = E______________________________________ 1  cap-shape 2  cap-surface 3  cap-color 4  bruises?                      no 5  odor            none 6  gill-attachment free    free 7  gill-spacing                  close close 8  gill-size       broad               broad 9  gill-color10  stalk-shape                         enlarging11  stalk-root12  stalk-surface-above-ring            smooth13  stalk-surface-below-ring14  stalk-color-above-ring15  stalk-color-below-ring  white16  veil-type       partial partial                             partial                                   partial17  veil-color      white   white white18  ring-number             one         one19  ring-type                           pendant20  spore-print-color21  population22  habitat    # coded/category:               3099    1820  2197  883______________________________________
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