Fuzzy ART Choice Functions

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP networks synthesize fuzzy logic and ART by exploiting the formal similarity between tile computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic intersection (∩) with the fuzzy intersection(∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric theory in which the fuzzy intersection and the fuzzy union (∨), or component-wise maximum, play complementary roles. A geometric interpretation of fuzzy ART represents each category as a box that increases in size as weights decrease. This paper analyzes fuzzy ART models that employ various choice functions for category selection. One such function minimizes total weight change during learning. Benchmark simulations compare peformance of fuzzy ARTMAP systems that use different choice functions.

3-D Object Recognition by the ART-EMAP Evidence Accumulation Network

ART-EMAP synthesizes adaptive resonance theory (AHT) and spatial and temporal evidence integration for dynamic predictive mapping (EMAP). The network extends the capabilities of fuzzy ARTMAP in four incremental stages. Stage I introduces distributed pattern representation at a view category field. Stage 2 adds a decision criterion to the mapping between view and object categories, delaying identification of ambiguous objects when faced with a low confidence prediction. Stage 3 augments the system with a field where evidence accumulates in medium-term memory (MTM). Stage 4 adds an unsupervised learning process to fine-tune performance after the limited initial period of supervised network training. Simulations of the four ART-EMAP stages demonstrate performance on a difficult 3-D object recognition problem.

The Art of Seeing and Painting

The human urge to represent the three-dimensional world using two-dimensional pictorial representations dates back at least to Paleolithic times. Artists from ancient to modern times have struggled to understand how a few contours or color patches on a flat surface can induce mental representations of a three-dimensional scene. This article summarizes some of the recent breakthroughs in scientifically understanding how the brain sees that shed light on these struggles. These breakthroughs illustrate how various artists have intuitively understand paradoxical properties about how the brain sees, and have used that understanding to create great art. These paradoxical properties arise from how the brain forms the units of conscious visual perception; namely, representations of three-dimensional boundaries and surfaces. Boundaries and surfaces are computed in parallel cortical processing streams that obey computationally complementary properties. These streams interact at multiple levels to overcome their complementary weaknesses and to transform their complementary properties into consistent percepts. The article describes how properties of complementary consistency have guided the creation of many great works of art.

ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network

This article introduces a new neural network architecture, called ARTMAP, that 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^(p)} of input patterns, and ARTb receives a stream {b^(p)} of input patterns, where b^(p) is the correct prediction given a^(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^(p) are presented without b^(p), and their predictions at ARTb are compared with b^(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^(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^(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 pa 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.

Fuzzy ART: An Adaptive Resonance Algorithm for Rapid, Stable Classification of Analog Patterns

The Fuzzy ART system introduced herein incorporates computations from fuzzy set theory into ART 1. For example, the intersection (n) operator used in ART 1 learning is replaced by the MIN operator (A) of fuzzy set theory. Fuzzy ART reduces to ART 1 in response to binary input vectors, but can also learn stable categories in response to analog input vectors. In particular, the MIN operator reduces to the intersection operator in the binary case. Learning is stable because all adaptive weights can only decrease in time. A preprocessing step, called complement coding, uses on-cell and off-cell responses to prevent category proliferation. Complement coding normalizes input vectors while preserving the amplitudes of individual feature activations.

ART 2-A: An Adaptive Resonance Algorithm for Rapid Category Learning and Recognition

This article introduces ART 2-A, an efficient algorithm that emulates the self-organizing pattern recognition and hypothesis testing properties of the ART 2 neural network architecture, but at a speed two to three orders of magnitude faster. Analysis and simulations show how the ART 2-A systems correspond to ART 2 dynamics at both the fast-learn limit and at intermediate learning rates. Intermediate learning rates permit fast commitment of category nodes but slow recoding, analogous to properties of word frequency effects, encoding specificity effects, and episodic memory. Better noise tolerance is hereby achieved without a loss of learning stability. The ART 2 and ART 2-A systems are contrasted with the leader algorithm. The speed of ART 2-A makes practical the use of ART 2 modules in large-scale neural computation.

Working Memory Networks for Learning Temporal Order, with Application to 3-D Visual Object Recognition

Working memory neural networks are characterized which encode the invariant temporal order of sequential events. Inputs to the networks, called Sustained Temporal Order REcurrent (STORE) models, may be presented at widely differing speeds, durations, and interstimulus intervals. The STORE temporal order code is designed to enable all emergent groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed in neural architectures which self-organize learned codes for variable-rate speech perception, sensory-motor planning, or 3-D visual object recognition. Using such a working memory, a self-organizing architecture for invariant 3-D visual object recognition is described. The new model is based on the model of Seibert and Waxman (1990a), which builds a 3-D representation of an object from a temporally ordered sequence of its 2-D aspect graphs. The new model, called an ARTSTORE model, consists of the following cascade of processing modules: Invariant Preprocessor --> ART 2 --> STORE Model --> ART 2 --> Outstar Network.

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.

Adaptive Resonance Associative Map: A Hierarchical ART System for Fast Stable Associative Learning

This paper introduces a new class of predictive ART architectures, called Adaptive Resonance Associative Map (ARAM) which performs rapid, yet stable heteroassociative learning in real time environment. ARAM can be visualized as two ART modules sharing a single recognition code layer. The unit for recruiting a recognition code is a pattern pair. Code stabilization is ensured by restricting coding to states where resonances are reached in both modules. Simulation results have shown that ARAM is capable of self-stabilizing association of arbitrary pattern pairs of arbitrary complexity appearing in arbitrary sequence by fast learning in real time environment. Due to the symmetrical network structure, associative recall can be performed in both directions.

Normal and Amnesis Learning, Recognition, and Memory by a Neural Model of Cortico-Hippocampal Interactions

The processes by which humans and other primates learn to recognize objects have been the subject of many models. Processes such as learning, categorization, attention, memory search, expectation, and novelty detection work together at different stages to realize object recognition. In this article, Gail Carpenter and Stephen Grossberg describe one such model class (Adaptive Resonance Theory, ART) and discuss how its structure and function might relate to known neurological learning and memory processes, such as how inferotemporal cortex can recognize both specialized and abstract information, and how medial temporal amnesia may be caused by lesions in the hippocampal formation. The model also suggests how hippocampal and inferotemporal processing may be linked during recognition learning.

History, revolution and the British popular novel: historical fiction in the romantic age

“History, Revolution and the British Popular Novel” takes as its focus the significant role which historical fiction played within the French Revolution debate and its aftermath. Examining the complex intersection of the genre with the political and historical dialogue generated by the French Revolution crisis, the thesis contends that contemporary fascination with the historical episode of the Revolution, and the fundamental importance of history to the disputes which raged about questions of tradition and change, and the meaning of the British national past, led to the emergence of increasingly complex forms of fictional historical narrative during the “war of ideas.” Considering the varying ways in which novelists such as Charlotte Smith, William Godwin, Mary Robinson, Helen Craik, Clara Reeve, John Moore, Edward Sayer, Mary Charlton, Ann Thomas, George Walker and Jane West engaged with the historical contexts of the Revolution debate, my discussion juxtaposes the manner in which English Jacobin novelists inserted the radical critique of the Jacobin novel into the wider arena of history with anti-Jacobin deployments of the historical to combat the revolutionary threat and internal moves for socio-political restructuring. I argue that the use of imaginative historical narrative to contribute to the ongoing dialogue surrounding the Revolution, and offer political and historical guidance to readers, represented a significant element within the literature of the Revolution crisis. The thesis also identifies the diverse body of historical fiction which materialised amidst the Revolution controversy as a key context within which to understand the emergence of Scott’s national historical novel in 1814, and the broader field of historical fiction in the era of Waterloo. Tracing the continued engagement with revolutionary and political concerns evident in the early Waverley novels, Frances Burney’s The Wanderer (1814), William Godwin’s Mandeville (1816), and Mary Shelley’s Valperga (1823), my discussion concludes by arguing that Godwin’s and Shelley’s extension of the mode of historical fiction initially envisioned by Godwin in the revolutionary decade, and their shared endeavour to retrieve the possibility enshrined within the republican past, appeared as a significant counter to the model of history and fiction developed by Walter Scott in the post-revolutionary epoch.

Invertebrate diversity in Irish and British forests

Ireland and Britain were once covered in natural forest, but extensive anthropogenic deforestation reduced forest cover to less than 1% and 5 %, respectively, by the beginning of the 20th century. Large-scale afforestation has since increased the level of forest cover to 11% in Ireland and 12% in Britain, with the majority of planted forests comprising small monoculture plantations, many of which are of non - native conifer tree species. At present the forest cover of Ireland and Britain generally consists of small areas of remnant semi-natural woodland and pockets of these plantation forests within a predominantly agricultural landscape. Invertebrates comprise a large proportion of the biodiversity found within forested habitats. In particular, spiders and carabid beetles play an important role in food webs as both predators and prey and respond to small-scale changes in habitat structure, meaning they are particularly sensitive to forest management. Hoverflies play an important role in control and pollination and have been successfully used as indicators of habitat disturbance and quality. This research addressed a number of topics pertinent to the forest types present in the contemporary Irish and British landscapes and aimed to investigate the invertebrate diversity of these forests. Spiders and carabid beetles were sampled using pitfall trapping and hoverflies were sampled using Malaise net trapping. Topics included the impacts of afforestation, the importance of open space, the choice of tree species, and the use of indicators for biodiversity assessment, as well as rare native woodlands and the effect of grazing on invertebrate diversity. The results are discussed and evidence-based recommendations are made for forest policy and management to protect and enhance invertebrate biodiversity in order to promote sustainable forest management in Ireland and Britain.

Home, family and society: women of the Irish landed class, 1860-1914. A Munster case study

The thesis analyses the roles and experiences of female members of the Irish landed class (wives, sisters and daughters of gentry and aristocratic landlords with estates over 1,000 acres) using primary personal material generated by twelve sample families over an important period of decline for the class, and growing rights for women. Notably, it analyses the experiences of relatively unknown married and unmarried women, something previously untried in Irish historiography. It demonstrates that women’s roles were more significant than has been assumed in the existing literature, and leads to a more rounded understanding of the entire class. Four chapters focus on themes which emerge from the sources used and which deal with their roles both inside and outside the home. These chapters argue that: Married and unmarried women were more closely bound to the priorities of their class than their sex, and prioritised male-centred values of family and estate. Male and female duties on the property overlapped, as marriage relationships were more equal than the legislation of the time would suggest. London was the cultural centre for this class. Due to close familial links with Britain (60% of sample daughters married English men) their self-perception was British or English, as well as Irish. With the self-confidence of their class, these women enjoyed cultural and political activities and movements outside the home (sport, travel, fashion, art, writing, philanthropy, (anti-)suffrage, and politics). Far from being pawns in arranged marriages, women were deeply conscious of their marriage decisions and chose socially, financially and personally compatible husbands; they also looked for sexual satisfaction. Childbirth sometimes caused lasting health problems, but pregnancy did not confine wealthy women to an invalid state. In opposition to the stereotypical distant aristocratic mother, these women breastfed their children, and were involved mothers. However, motherhood was not permitted to impinge on the more pressing role of wife

The architecture of influence: Paul Rudolph's Art and Architecture Building at Yale

Focussing on Paul Rudolph’s Art & Architecture Building at Yale, this thesis demonstrates how the building synthesises the architect’s attitude to architectural education, urbanism and materiality. It tracks the evolution of the building from its origins – which bear a relationship to Rudolph’s pedagogical ideas – to later moments when its occupants and others reacted to it in a series of ways that could never have been foreseen. The A&A became the epicentre of the university’s counter culture movement before it was ravaged by a fire of undetermined origins. Arguably, it represents the last of its kind in American architecture, a turning point at the threshold of postmodernism. Using an archive that was only made available to researchers in 2009, this is the first study to draw extensively on the research files of the late architectural writer and educator, C. Ray Smith. Smith’s 1981 manuscript about the A&A entitled “The Biography of a Building,” was never published. The associated research files and transcripts of discussions with some thirty interviewees, including Rudolph, provide a previously unavailable wealth of information. Following Smith’s methodology, meetings were recorded with those involved in the A&A including, where possible, some of Smith’s original interviewees. When placed within other significant contexts – the physicality of the building itself as well as the literature which surrounds it – these previously untold accounts provide new perspectives and details, which deepen the understanding of the building and its place within architectural discourse. Issues revealed include the importance of the influence of Louis Kahn’s Yale Art Gallery and Yale’s Collegiate Gothic Campus on the building’s design. Following a tumultuous first fifty years, the A&A remains an integral part of the architectural education of Yale students and, furthermore, constitutes an important didactic tool for all students of architecture.

The demise of the Beothuk as a past still present

This article aims to investigate contemporary cultural representations of the Beothuk Indians in art, literature and museum displays in Newfoundland, Canada, focussing on ways these reimagine the past for the present, offering perspectives on contested histories, such as the circumstances leading to the demise of the Beothuk. Wiped out through the impact of colonialism, the Beothuk are the ‘absent other’ who continue to be remembered and made present through the creative arts, largely at the expense of other indigenous groups on the island. Rather than focussing on the ‘non-absent past, according to Polish scholar Ewa Domańska, ‘instead we turn to a past that is somehow still present, that will not go away or, rather, that of which we cannot rid ourselves’ (2006, 346). Depictions of the last Beothuk are part of a cultural remembering where guilt and reconciliation are played out through media of the imagination