slpSUSTAIN {catlearn}

SUSTAIN Category Learning Model

Description

Supervised and Unsupervised STratified Adaptive Incremental Network (Love, Medin & Gureckis, 2004)

Usage

slpSUSTAIN(st, tr, xtdo = FALSE, ties = "random")

Arguments

st

List of model parameters

tr

Matrix of training items

xtdo

Boolean specifying whether to include extended information in the output (see below)

ties

Model behaviour where multiple clusters have the same highest activations. Options are: random, first, see below.

Details

This function works as a stateful list processor (slp; see Wills et al., 2017). It takes a matrix (tr) as an argument, where each row represents a single training trial, while each column represents some information required by the model, such as the stimulus representation, indications of supervised/unsupervised learning, etc. (details below).

Argument st must be a list containing the following items:

r - Attentional focus parameter, always non-negative.

beta - Cluster competition parameter, always non-negative.

d - Decision consistency parameter, always non-negative.

eta - Learning rate parameter, see Note 1.

tau - Threshold parameter for cluster recruitment under unsupervised learning conditions (Love et al., 2004, Eq. 11). If every trial is a supervised learning trial, set tau to 0. slpSUSTAIN can accomodate both supervised and unsupervised learning within the same simulation, using the ctrl column in tr (see below).

lambda - Vector containing the initial receptive field tuning value for each stimulus dimension; the order corresponds to the order of dimensions in tr, below. For a stimulus with three dimensions, where all receptive fields are equally tuned, lambda = [1, 1, 1].

cluster - A matrix of the initial positions of each recruited cluster. If set to NA, cluster = NA, then each time the network is reset, a single cluster will be created, centered on the stimulus presented on the current trial.

w - A matrix of initial connection weights. If set to NA as w = NA then, each time the network is reset, zero-strength weights to a single cluster will be created.

dims - Vector containing the length of each dimension (excluding category dimension, see tr, below), i.e. the number of nominal spaces in the representation of each dimension. For Figure 1 of Love et al. (2004), dims = [2, 2, 2].

maxcat - optional. If set, maxcat is an integer specifying the maximum number of clusters to be recruited during unsupervised learning. A similar restriction has been used by Love et al. (2004) to simulate an unsupervised free-sorting task from Experiment 1 in Medin, Wattenmaker, & Hampson (1987). In this experiment, participants needed to sort items into two predefined categories. This parameter will only be used during unsupervised learning. If it is not set, or if it is set to 0, there is no maximum to the number of clusters that can be created.

colskip - Number of optional columns skipped in tr, PLUS ONE. So, if there are no optional columns, set colskip to 1.

Argument tr must be a matrix, where each row is one trial presented to the model. Columns are always presented in the order specified below:

ctrl - A vector of control codes. The control codes are processed prior to the trial and prior to updating cluster's position, lambdas and weights (Love et al., 2004, Eq. 12, 13 and 14, respectively). The available values are:

0 = do supervised learning.

1 = reset network and then do supervised learning.

2 = freeze supervised learning.

3 = do unsupervised learning.

4 = reset network and then do unsupervised learning.

5 = freeze unsupervised learning

'Reset network' means revert w, cluster,and lambda back to the values passed in st.

Unsupervised learning in slpSUSTAIN is at an early stage of testing, as we have not yet established any CIRP for unsupervised learning.

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.

x1, x2, y1, y2, y3, ... - Stimulus representation. The columns represent the kth nominal value for ith dimension. It's a 'padded' way to represent stimulus dimensions and category membership (as category membership in supervised learning is treated as an additional dimension) with varying nominal length, see McDonnell & Gureckis (2011), Fig. 10.2A. All dimensions for the trial are represented in this single row. For example, if for the presented stimulus, dimension 1 is [0 1] and dimension 2 is [0 1 0] with category membership [0 1], then the input representation is [0 1 0 1 0 0 1].

Argument ties can be either random or first. It specifies how the model behaves in the event, when there are multiple winning clusters with the same activations (see Note):

random - The model randomly selects one cluster from the ones that have the same activations. To increase the reproducibility of your simulation, set a specific random seed seed before calling slpSUSTAIN (use e.g.set.seed).

first - The model selects the cluster that was first recruited from the clusters that have the same activations. Up to and including version 0.7.1 of catlearn, this was the default behaviour of slpSUSTAIN.

Value

Returns a list with the following items if xtdo = FALSE:

probs

Matrix of probabilities of making each response within the queried dimension (e.g. column 1 = category A; column 2 = category B), see Love et al. (2004, Eq. 8). Each row is a single trial and columns are in the order presented in tr, see below. In the case of unsupervised learning, probabilities are calculated for all dimensions (as there is no queried dimension for unsupervised learning).

lambda

Vector of the receptive field tunings for each stimulus dimension, after the final trial. The order of dimensions corresponds to the order they are presented in tr, see below.

w

Matrix of connection weights, after the final trial. Each row is a separate cluster, reported in order of recruitment (first row is the first cluster to be recruited). The columns correspond to the columns on the input representation presented (see tr description, below).

cluster

Matrix of recruited clusters, with their positions in stimulus space. Each row is a separate cluster, reported in order of recruitment. The columns correspond to the columns on the input representation presented (see tr description, below).

If xtdo = TRUE, xtdo is returned instead of probs:

xtdo

A matrix that includes probs, and in addition includes the following columns: winning - number of the winning cluster; activation - its output activation after cluster competition, Eq. 6 in Love et al. (2004); recognition_scores - for the current stimulus from Eq. A6 in Love and Gureckis (2007), this measure represents the model's overall familiarity with the stimulus; endorsement - the probability of judging an item as old per Eq. 11 in Love and Gureckis (2007).

Note

1. Love et al. (2004) do not explicitly set a range for the learning rate; we recommend a range of 0-1.

2. The specification of SUSTAIN states that under supervised learning, a new cluster is recruited each time the model predicts category membership incorrectly. This new cluster is centered on the current stimulus. The implementation in slpSUSTAIN adds the stipulation that a new cluster is NOT recruited if it already exists, i.e. if its location in stimulus space is identical to the location on an existing cluster. Instead, it selects the existing cluster and updates as normal. Love et al. (2004) do not specify model behaviour under such conditions, so this is an assumption of our implementation. We'd argue that this is a reasonable implementation - without it SUSTAIN would add clusters indefinitely under conditions where the stimulus -> category associations are proabilistic rather than deterministic.

3. In some cases, two or more clusters can have identical activations because the presented stimulus is equally similar to multiple clusters. Love et al. (2004) does not specify how the model will behave in these cases. In our implementation, we make the assumption that the model picks randomly between the highest activated clusters (given that they have the same activations). This, we felt, was in line with the approximation of lateral inhibition in the SUTAIN specification (Love et al. 2004, Eq. 6).

Author(s)

Lenard Dome, Andy Wills

References

Love, B. C., & Gureckis, T.M. (2007). Models in Search of a Brain. Cognitive, Affective, & Behavioral Neuroscience, 7, 90-108.

Love, B. C., Medin, D. L., & Gureckis, T. M. (2004). SUSTAIN: a network model of category learning. Psychological Review, 111, 309-332.

McDonnell, J. V., & Gureckis, T. M. (2011). Adaptive clustering models of categorization. In E. M. Pothos & A. J. Wills (Eds.), Formal Approaches in Categorization, pp. 220-252.

Medin, D. L., Wattenmaker, W. D., & Hampson, S. E. (1987). Family resemblance, conceptual cohesiveness, and category construction. Cognitive Psychology, 19(2), 242-279.

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.