B. Kosko (1988), "Bidirectional Associative Memories", IEEE Transaction on Systems, Man and Cybernetics, vol. SMC, no. 18, pp. 49-60.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... called the associative memory model, consists of networks of neuron like elements with discrete activity functions [11] These kinds of models with various restrictions, modifications and generalizations have been studied extensively by various researchers starting with the initial works in [1, 2, 3, 6, 7, 9, 10]. A special type of associative memory, the bidirectional associative memory (BAM) model, was first introduced by Kosko in [2] as an extension of the unidimensional Hopfield autoassociative model; subsequently this model has been investigated extensively. In this paper we generalize the BAM model ....

B. Kosko (1988), "Bidirectional Associative Memories", IEEE Transaction on Systems, Man and Cybernetics, vol. SMC, no. 18, pp. 49-60.

....that achieve good compression need the complete training set in order to operate. Those that can store patterns as they are presented, do not compress much at all. In the following discussion, the algorithms are encoding an arbitrary ########################### . BiAssociative Memories (BAM,[3]) belong to the first family. They are capable of storing ################### patterns . Other algorithms, such as Hamming Associative Memory [5] Flash and Solar systems [6] also belong to the first group. They achieve optimal storage given assumptions of good orthogonality of the input ....

B. Kosko, "Bidirectional associative memories," IEEE Transactions on Systems, Man and Cybernetics, vol. 18, no. 1, pp. 49--60, 1988.

....pattern with their associative memory. The network architecture can be built up with neurones and connectivity on one layer or more layers. i) Algorithms The mathematical formula for the associative memory function is established on the construction of an energy equation E [Hop82] Kos87] [Kos88], called the Steepest Gradient Descent algorithm: Where, 0 i and q j are constants of the energy equation E. The algorithm contains two phases: learning and training. In the learning phase, the associative memory function is used to form the connectivity matrix W for training a set of input ....

Kosko, B., Bidirectional associative memories, IEEE Transactions on Systems, Man, and Cybernetics, 1988, 18(1), pp.49-60.

....recall. This temporal association paradigm is widely used in many neural models. The vast majority of these models are based on either multilayer perceptrons (MLP) with some temporal version of backpropagation training [38] or the Hop eld model of associative memory [21] 33] Also, BAM type [39], 32] and ART type [40] 41] model use the chaining hypothesis to recall temporal sequences. The model proposed in this paper also follows this paradigm; however, in contrast to those models based on MLP and BAM, it learns temporal associations in a self organized manner and the learning process ....

B. Kosko. Bidirectional associative memories. IEEE Transactions on Systems, Man, and Cybernetics, 18(1):49-60, 1988.

....items, we assume that the resulting matrix is given by a linear superposition of all contributions: M = M(0) N l X t=1 a(t)a T (t 1) 13) Note that this matrix is constructed in an incremental and unsupervised way. It cannot be set in advance as in other associative memory models [28] [29], since the activation patterns a(t) are not known beforehand. Consider a trajectory with only three non repeated states and a network with three neurons. For the sake of simplicity, we set K = 1, and assume that neuron j = 1 encoded the rst state of the trajectory at t = 1, neuron 3 encoded the ....

....information is provided to resolve potential ambiguities. The majority of the models for sequence processing are based on either multilayer perceptrons (MLP) with some temporal version of backpropagation training [7] or the Hop eld model of associative memory [6] 28] 41] Also, BAM type [29], 42] and ART type [43] 44] models use the simple associative chaining hypothesis, and have been applied to a variety of complex tasks in natural language processing, time series analysis, and motor control. The model proposed in this paper also follows this paradigm. However, when compared ....

B. Kosko, \Bidirectional associative memories," IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, pp. 49-60, 1988.

....memory. In an associative memory system, related information can be recalled by giving only a part of it as input. For an introduction to the subject one can refer to Kohonen s book [2] Kosko has added a new dimension to the associative memory by introducing bidirectional associative memory (BAM) [4, 3, 5]. In a BAM system, a set of pattern pairs (A i ; B i ) are stored. To recall B i , A i is supplied as input to the system. For recalling A i , system takes B i as input. A BAM is usually implemented using two layer nonlinear neurons. A brief introduction of standard BAM is presented next. 1.1 BAM: ....

....M T ) X 2 i . F (X j i M) Y j i F (Y j i M T ) X j 1 i . F (X f i M) Y f i F (Y f i M T ) X f i The final pair (X f ; Y f ) is one of the training pairs (A i ; B i ) if encoded pairs satisfy some constraints. These constraints were characterized in [4, 3, 5, 8]. An important property of a final state is that it has lower energy value (defined next) than any other neighboring state. Following Kosko [3] the energy function for a pattern pair (A i ; B i ) is defined as, E i = GammaA i MB T i : Thus, for correct recalling of a training pair (A i ; B i ) ....

B. Kosko, Bidirectional associative memories, IEEE Trans. Syst., Man., Cybern., 18(1), 1988.

....for a system with N units in each of two layers is 0:1998N , which can be regarded as BAM s counterpart of the result 0:138N for the autocorrelation associative memory, or the Hopfield model, evaluated by Amit, Gutfreund, and Sompolinsky. 1 Introduction The bidirectional associative memory (BAM) [1] is a variation of associative memory neural networks. The principal function of associative memories is to store and retrieve multiple patterns in a distributed manner. The storage capacity, which represents how many patterns can be stored in a network, is one of the fundamental performance ....

B. Kosko, "Bidirectional associative memories," IEEE Trans. Systems, Man, Cybern, vol. 18, pp. 49--60, 1988.

....transformed to a complex output space[15] Kohonen s self organizing feature maps[16,17] Grossberg s network[18] Hecht Nielson s network[19] and Radial Basis Functions networks[20,21] are some of the different mapping networks which have features of their own. The bidirectional associative memory[22] is a mapping network which is useful for associative information recovery. The Boltzman machine is based on the same principle, but in a probabilistic sense[23] Mapping neural networks find applications in varied fields. They are model free estimation systems[24] which model a system without ....

Kosko, B., "Bidirectional Associative Memories", IEEE tran. Systems, Man and Cyber., SMC-17, 1987

....way as Ising spin systems are used in statistical physics, or Turing machines in theoretical computer science. Although the basic Hop eld model per se is of limited practical applicability, it has inspired such other important neural network architectures as the 2 Binary Associative Memory (BAM) (Kosko, 1988), and Boltzmann machines and their further stochastic variations (Ackley et al. 1985; Haykin, 1999; Rojas, 1996) The accumulated knowledge concerning Hop eld nets has often been an essential prerequisite for understanding the capabilities of these other models. For instance, the convergence ....

....stochastic variations (Ackley et al. 1985; Haykin, 1999; Rojas, 1996) The accumulated knowledge concerning Hop eld nets has often been an essential prerequisite for understanding the capabilities of these other models. For instance, the convergence behavior of the BAM model was analyzed in (Kosko, 1988) along the lines rst established for the Hop eld model in (Hop eld, 1982) In the present paper we investigate a number of issues in the computational analysis of Hop eld networks, complementing the existing literature in this area (Flor een and Orponen, 1994; Parberry, 1994; Siegelmann, 1999; ....

Kosko, B. (1988). Bidirectional associative memories. IEEE Transactions on Systems, Man, and Cybernetics, 18:49-60.

....by GA AS CR Grant B2030007. y Research supported by Academy of Finland Grant No. 37115 96. 1 computer science. Although the basic Hop eld model per se is of limited practical applicability, it has inspired such other important neural network architectures as the Binary Associative Memory (BAM) [27], and Boltzmann machines and their further stochastic variations [2, 19, 37] The accumulated knowledge concerning Hop eld nets has often been an essential prerequisite for understanding the capabilities of these other models. For instance, the convergence behavior of the BAM model was analyzed ....

....and Boltzmann machines and their further stochastic variations [2, 19, 37] The accumulated knowledge concerning Hop eld nets has often been an essential prerequisite for understanding the capabilities of these other models. For instance, the convergence behavior of the BAM model was analyzed in [27] along the lines rst established for the Hop eld model in [20] In the present paper we investigate a number of issues in the computational analysis of Hop eld networks, complementing the existing literature in this area [12, 33, 39, 42, 49] After a brief review of the basic de nitions in ....

B. Kosko. Bidirectional associative memories. IEEE Transactions on Systems, Man, and Cybernetics, 18:49-60, 1988.

....or not the relaxation rate is a sensitive parameter. This paper shows that the relaxation rate has almost no effect on how information flows through the network as long as it is small enough to avoid large discrete steps and or oscillation. 1. Introduction Constraint satisfaction neural networks [1, 2, 3, 4] contain nodes that are connected by excitatory (positive) or inhibitory (negative) weights. Nodes are given initial activation values, after which a relaxation process causes nodes to change their activation value in response to the net input of all of the weighted connections coming into each ....

Kosko, B., (1988). "Bidirectional Associative Memories." IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1.

....for the storage matrix, suggest the auto associative memory with the binary Hebbian learning rule as most suitable for applications. As a consequence, the binary storage with iterative retrieval is highly recommendable in applications. For pattern mapping in bidirectional associative memory models [Kosko, 1988] our treatment should be applicable, allowing a better exploitation of the stored information by iterative retrieval steps. ....

Kosko, B. (1988). Bidirectional associative memories. IEEE Transactions on Systems, man, and Cybernetics, 18:49--60.

....to their relevance to the query. This can be achieved by iterative retrieval: after one item is retrieved, it is used for supression in the retrieval of a second item and so on. Also hetero association could be realized with iterative retrieval, if a bidirectional associative memory model is used [Kosko, 1988]. The first cycle in a bidirectional memory can be analyzed with our methods as described in section 3. A straightforward application of NAMs in information retrieval is the access of words in a large dictionary [H.J. Bentz, 1989] The following results are obtained with a dictionary of ....

Kosko, B. (1988). Bidirectional associative memories. IEEE Transactions on Systems, man, and Cybernetics, 18:49--60.

....set P. Further, it would be beneficial if a smaller representation was possible. To this end, various classical associative memory schemes have been proposed, perhaps the most well known being the Hopfield network [10] Another wellknown example is the bidirectional associative memory (BAM) [11]. These neural approaches to the pattern completion problem allow for associative pattern recall, but suffer severe storage restrictions. Storing patterns of length n requires a network of n neurons, and the number of patterns, m, is then limited by m kn, where typically 0.15 k 0.5. This paper ....

Kosko, Bart, "Bidirectional Associative Memories", IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, pp. 49-60, 1988.

....asymptotic stability I. Introduction I N the early 1980s, Hopfield proposed an auto associative memory model to store and recall information in much the same way as the human brain [1] In the late 1980s, Kosko extended the auto associative memory model to a bidirectional one [2] 3] 4] [5]. This two level, nonlinear memory model is based on earlier studies on associative memories [6] 7] 8] 9] 10] 11] The bidirectional associative memory (BAM) model is more general and powerful than the Hopfield auto associative memory and includes the Hopfield memory as a special case. A ....

....(25) V. Experimental Results The performance of an associative memory is usually measured in terms of its storage capacity, attraction, and spurious memories. In this section, we use several experiments to compare the performance of the proposed GBAM model with that of the Kosko BAM model KBAM [5], the most promising symmetrical BAM model SBAM proposed in [16] and the asymmetrical BAM model ABAM newly proposed in [21] A. A Noisy Pattern Recognition Example Bidirectional associative memories have been demonstrated to be well suited for pattern and object recognition through experiments ....

B. Kosko, "Bidirectional associative memories," IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 49--60, 1988.

....We will investigate the plausibility of several connectivity patterns, starting with the admittedly implausible hypothesis that the brain is wired regularly, and then trying to refine these approximations. Neural network models often assume full connectivity between an input and an output layer (Kosko 1987, 1988; Steinbuch, 1961; Anderson, 1972; Kohonen, 1972; and Nakano, 1972) possibly involving one or more hidden layers (Ackley, Hinton, and Sejnowski, 1985; Rumelhart, Hinton, and Williams, 1986) Some network models assume full, bidirectional (or recurrent) connectivity between all their nodes ....

Kosko, B. (1988). Bidirectional associative memories. IEEE Transactions on Systems, Man, and Cybernetics, SMC-18, 49-60.

....of the pattern set P. Further, it would of course be beneficial if a smaller representation was possible. To this end, various classical associative memory schemes have been proposed, perhaps the most well known being the Hopfield network [Hop82] and the bidirectional associative memory (BAM) [Kos88]. These neural approaches to the pattern completion problem allow for associative pattern recall, but suffer severe storage restrictions. Storing patterns of length n requires a network of n neurons, and the number of patterns, m, is then limited by m kn, where typically .15 k .5. This paper ....

Kosko, Bart, "Bidirectional Associative Memories", IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, pp. 49-60, 1988.

....is equal to 25 when n is Associative memory neural networks presented in 1000. The second problem is that the network is this paper include two types: the Hopfield just as likely to converge to a local solution as to a (Hopfield, 1982) and the bidirectional networks global minimum (Dayhoff, 1990) (Kosko, 1987 1988). The former is an auto On the other hand, the benefit of the bidirectional associative neural network that associates an network is that it can set up a relationship between incomplete pattern with an identical learning two individual patterns. However, the bidirectional pattern. The latter is a ....

Kosko, B. (1988), Bidirectional Associative Memories, IEEE Transactions on Systems, Man, and Cybernetics, 18(1), pp.49-60.

....sequences than the conventional real valued networks, to memorization of melodies. It is shown in computer simulations that the network can memorize some melodies and recall them correctly from any part. 1. Introduction A lot of associative memory models using neural network have been proposed [6, 8, 9, 13, 14]. Most of them are devised to memorize static patterns. Let s think about human s memory. We can memorize not only static patterns like pictures but also temporal sequences like movies, speech, melodies, and so on. For example, when we memorize a melody, we can recall it from a part. Such a ....

Kosko, B.: "Bidirectional Associative Memories", IEEE Trans. Syst. Man. Cybern., Vol.18, No.1, pp. 49-60 (1988).

....units was characterized in section 3 as equal to PSPACE poly, the power of nets with no hidden units (i.e. the basic Hopfield model) is still an open question. An interesting intermediate model in this respect might be the two layer Hopfield net, or Bidirectional Associative Memory model of Kosko [57]. The results in Section 3, which were formulated for fully parallel operation, should be extended to cover also sequential operation. While sequentially updated nets are rather awkward to control (witness the difference between the Goles Mart inez and Haken constructions in Section 2.2) we do ....

B. Kosko. Bidirectional associative memories. IEEE Transactions on Systems. Man, and Cybernetics, 18:49--60, 1988. Reprinted in [6], pp. 165--176.

....e ik = 0. The causal concept C 4 causally increases concepts C 1 and C 5 . It decreases C 3 . Concepts C 1 and C 5 decrease C 4 . Concept C 3 increases C 4 . 1.3.2 FCM Recall FCMs recall as the FCM dynamical system equilibrates. Simple FCM inference thresholds a matrix vector multiplication [7] [20]. State vectors Cn cycle through the FCM adjacency matrix E : C 1 E C 2 E C 3 : The system nonlinearly transforms the weighted input to each node C i C i (t n 1 ) S N X k=1 e ki (t n ) C k (t n ) # (28) Here S(x) is a bounded signal function. For simple FCMs the sigmoid ....

....k=1 e ki (t n ) C k (t n ) # (28) Here S(x) is a bounded signal function. For simple FCMs the sigmoid function S (y) 1 1 e Gammac(y GammaT ) 29) with large c 0 approximates a binary threshold function. Simple threshold FCMs quickly converge to stable limit cycles or fixed points [7] [20]. These limit cycles show hidden patterns in the causal web of the FCM. Technology for Multimedia 13 The FCM in Figure 1.6 gives a three step limit cycle when input state C 1 = 0 0 0 1 0] fires the FCM network. Equation (28) and binary thresholding gives the four step limit cycle C 1 C 2 ....

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B. Kosko, "Bidirectional Associative Memories," IEEE Transactions Systems, Man, and Cybernetics, Vol. 18, No. 1, pp. 49-60, 1988.

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B. Kosko,Bidirectional associative memories,IEEE Transaction on Systems, Man, And Cybernetics, Vol.18, No.1 (1988)49-60.

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B. Kosko, "Bidirectional Associative Memories," IEEE Tr. Syst. Man Cyber., Vol. 18, No. 1, pp. 49-60, 1988.

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Kosko, B. (1988) Bidirectional associative memories, IEEE Transactions on Systems, Man, and Cybernetics, 18, 1, January-February 1988, 141-152.

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B. Kosko, Bidirectional Associative Memories, IEEE Trans. Syst. Man Cybern., vol. 18, no. 1, pp. 49-60, Jan./Feb. 1988.

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