slpALCOVE: ALCOVE category learning model

In catlearn: Formal Psychological Models of Categorization and Learning

ALCOVE category learning model

Description

Kruschke's (1992) category learning model.

Usage

slpALCOVE(st, tr, dec = 'ER', humble = TRUE, attcon = FALSE, absval = -1,
          xtdo = FALSE)

Arguments

st	List of model parameters
tr	R-by-C matrix of training items
dec	String defining decision rule to be used
humble	Boolean specifying whether a humble or strict teacher is to be used
attcon	Boolean specifying whether attention is constrained
absval	Real number specifying teaching value for category absence
xtdo	Boolean specifying whether to write extended information to the console (see below).

Details

The coverage in this help file is relatively brief; Catlearn Research Group (2016) provides an introduction to the mathematics of the ALCOVE model, whilst a more extensive tutorial on using slpALCOVE can be found in Wills et al. (2016).

The functions works as a stateful list processor. Specifically, it takes a matrix as an argument, where each row is one trial for the network, and the columns specify the input representation, teaching signals, and other control signals. It returns a matrix where each row is a trial, and the columns are the response probabilities at the output units. It also returns the final state of the network (attention and connection weights), hence its description as a 'stateful' list processor.

Argument st must be a list containing the following items:

colskip - skip the first N columns of the tr array, where N = colskip. colskip should be set to the number of optional columns you have added to matrix tr, PLUS ONE. So, if you have added no optional columns, colskip = 1. This is because the first (non-optional) column contains the control values, below.

c - specificity constant (Kruschke, 1992, Eq. 1). Positive real number. Scales psychological space.

r - distance metric (Kruschke, 1992, Eq. 1). Set to 1 (city-block) or 2 (Euclidean).

q - similarity gradient (Kruschke, 1992, Eq. 1). Set to 1 (exponential) or 2 (Gaussian).

phi - decision constant. For decision rule ER, it is referred to as mapping constant phi, see Kruschke (1992, Eq. 3). For decision rule BN, it is referred to as the background noise constant b, see Nosofsky et al. (1994, Eq. 3).

lw - associative learning rate (Kruschke, 1992, Eq. 5) . Real number between 0 and 1.

la - attentional learning rate (Kruschke, 1992, Eq. 6). Real number between 0 and 1.

h - R by C matrix of hidden node locations in psychological space, where R = number of input dimensions and C = number of hidden nodes.

alpha - vector of length N giving initial attention weights for each input dimension, where N = number of input dimensions. If you are not sure what to use here, set all values to 1.

w - R by C matrix of initial associative strengths, where R = number of output units and C = number of hidden units. If you are not sure what to use here, set all values to zero.

Argument tr must be a matrix, where each row is one trial presented to the network. Trials are always presented in the order specified. The columns must be as described below, in the order described below:

ctrl - vector of control codes. Available codes are: 0 = normal trial, 1 = reset network (i.e. set attention weights and associative strengths back to their initial values as specified in h and w (see below)), 2 = Freeze learning. Control codes are actioned before the trial is processed.

opt1, opt2, ... - optional columns, which may have any names you wish, and you may have as many as you like, but they must be placed after the ctrl column, and before the remaining columns (see below). These optional columns are ignored by this function, but you may wish to use them for readability. For example, you might include columns for block number, trial number, and stimulus ID number. The argument colskip (see above) must be set to the number of optional columns plus 1.

x1, x2, ... - input to the model, there must be one column for each input unit. Each row is one trial.

t1, t2, ... - teaching signal to model, there must be one column for each output unit. Each row is one trial. If the stimulus is a member of category X, then the teaching signal for output unit X must be set to +1, and the teaching signal for all other output units must be set to absval.

m1, m2, ... - missing dimension flags, there must be one column for each input unit. Each row is one trial. Where m = 1, that input unit does not contribute to the activation of the hidden units on that trial. This permits modelling of stimuli where some dimensions are missing on some trials (e.g. where modelling base-rate negelct, Kruschke, 1992, p. 29–32). Where m = 0, that input unit contributes as normal. If you are not sure what to use here, set to zero.

Argument dec, if specified, must take one of the following values:

ER specifies an exponential ratio rule (Kruschke, 1992, Eq. 3).

BN specifies a background noise ratio rule (Nosofsky et al., 1994, Eq. 3). Any output activation lower than zero is set to zero before entering into this rule.

Argument humble specifies whether a humble or strict teacher is to be used. The function of a humble teacher is specified in Kruschke (1992, Eq. 4b). In this implementation, the value -1 in Equation 4b is replaced by absval.

Argument attcon specifies whether attention should be constrained or not. If you are not sure what to use here, set to FALSE. Some implementations of ALCOVE (e.g. Nosofsky et al., 1994) constrain the sum of the attentional weights to always be 1 (personal communication, R. Nosofsky, June 2015). The implementation of attentional constraint in alcovelp is the same as that used by Nosofsky et al. (1994), and present as an option in the source code available from Kruschke's website (Kruschke, 1991).

Argument xtdo (eXTenDed Output), if set to TRUE, will output to the console the following information on every trial: (1) trial number, (2) attention weights at the end of that trial, (3) connection weights at the end of that trial, one row for each output unit. This output can be quite lengthy, so diverting the output to a file with the sink command prior to running alcovelp with extended output is advised.

Value

Returns a list containing three components: (1) matrix of response probabilities for each output unit on each trial, (2) attentional weights after final trial, (3) connection weights after final trial.

Author(s)

Andy Wills

References

Catlearn Research Group (2016). Description of ALCOVE. http://catlearn.r-forge.r-project.org/desc-alcove.pdf

Kruschke, J. (1991). ALCOVE.c. Retrieved 2015-07-20, page since removed, but archival copy here: https://web.archive.org/web/20150605210526/http://www.indiana.edu/~kruschke/articles/ALCOVE.c

Kruschke, J. (1992). ALCOVE: an exemplar-based connectionist model of category learning. Psychological Review, 99, 22-44

Nosofsky, R.M., Gluck, M.A., Plameri, T.J., McKinley, S.C. and Glauthier, P. (1994). Comparing models of rule-based classification learning: A replication and extension of Shepaard, Hovland, and Jenkins (1961). Memory and Cognition, 22, 352-369.

Wills, A.J., O'Connell, G., Edmunds, C.E.R., & Inkster, A.B.(2017). Progress in modeling through distributed collaboration: Concepts, tools, and category-learning examples. Psychology of Learning and Motivation, 66, 79-115.

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