Supervised and Unsupervised STratified Adaptive Incremental Network (Love, Medin & Gureckis, 2004)
List of model parameters
Matrix of training items
Boolean specifying whether to include extended information in the output (see below)
Model behaviour where multiple clusters have the same
highest activations. Options are:
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).
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,
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
colskip - Number of optional columns skipped in
PLUS ONE. So, if there are no optional columns, set colskip to 1.
tr must be a matrix, where each row is one trial
presented to the model. Columns are always presented in the order
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
lambda back to the values passed in
Unsupervised learning in
slpSUSTAIN is at an early stage of
testing, as we have not yet established any CIRP for unsupervised
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
ties can be either
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.
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
Returns a list with the following items if
xtdo = FALSE:
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
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
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
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
xtdo = TRUE,
xtdo is returned instead of
A matrix that includes
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.
4. 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).
Lenard Dome, Andy Wills
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.
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