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Roelof K Brouwer

Publications and source records attributed to Roelof K Brouwer.

2 recordsLinked to original sources

A feed-forward network for input that is both categorical and quantitative.

The data on which a multi-layer perceptron (MLP) is to be trained to approximate a continuous function may have inputs that are categorical rather than numeric or quantitative such as color, gender, race, etc. A categorical variable causes a discontinuous relationship between an input variable and the output. A MLP, with connection matrices that multiply input values and sigmoid functions that further transform values, represents a continuous mapping in all input variables. A MLP therefore requires that all inputs correspond to numeric, continuously valued variables and represents a continuous function in all input variables. The way that this problem is usually dealt with is to replace the categorical values by numeric ones and treat them as if they were continuously valued. However, there is no meaningful correspondence between the continuous quantities generated this way and the original categorical values. Another approach is to encode the categorical portion of the input using 1-out-of-n encoding and include this code as input to the MLP. The approach in this paper is to segregate categorical variables from the continuous independent variables completely. The MLP is trained with multiple outputs; a separate output unit for each of the allowed combination of values of the categorical independent variables. During training the categorical value or combination of categorical values determines which of the output units should have the target value on it, with the remaining outputs being 'do not care'. Three data sets were used for comparison of methods. Results show that this approach is much more effective than the conventional approach of assigning continuous variables to the categorical features. In case of the data set where there were several categorical variables the method proposed here is also more effective than the 1-out-of-n input method.

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A discrete fully recurrent network of max product units for associative memory and classification.

This paper defines the truncated normalized max product operation for the transformation of states of a network and provides a method for solving a set of equations based on this operation. The operation serves as the transformation for the set of fully connected units in a recurrent network that otherwise might consist of linear threshold units. Component values of the state vector and outputs of the units take on the values in the set [0, 0.1,..., 0.9, 1]. The result is a much larger state space given a particular number of units and size of connection matrix than for a network based on threshold units. Since the operation defined here can form the basis of transformations in a recurrent network with a finite number of states, fixed points or cycles are possible and the network based on this operation for transformations can be used as an associative memory or pattern classifier with fixed points taking on the role of prototypes. Discrete fully recurrent networks have proven themselves to be very useful as associative memories and as classifiers. However they are often based on units that have binary states. The effect of this is that the data to be processed consisting of vectors in R(n) have to be converted to vectors in [0, 1]m with m much larger than n since binary encoding based on positional notation is not feasible. This implies a large increase in the number of components. The effect can be lessened by allowing more states for each unit in our network. The network proposed demonstrates those properties that are desirable in an associative memory very well as the simulations show.

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