Neuroscience 2007, the 37th annual meeting of the Society for Neuroscience
2007.11.3-7

Program#/Poster#: 396.22/MM1

Title: Learning IT-like topographically organized parts-based representation
by topographic non-negative matrix factorization

Location: San Diego Convention Center: Halls B-H

Presentation Start/End Time: Monday, Nov 05, 2007, 9:00 AM -10:00 AM

Authors: *K. HOSODA1, M. WATANABE2, H. WERSING3, E. KOERNER3, H. TSUJINO4,
H. TAMURA5, I. FUJITA5;

2Dept. of Quantum Engin. and Systems Sci., 1Univ. of Tokyo, Tokyo, Japan; 3HONDA
Res. Inst. Europe GmbH, Offenbach, Germany; 4HONDA Res. Inst. Japan Co., Ltd,
Saitama, Japan; 5Grad. Sch. of Frontier Biosci., Osaka Univ., Osaka, Japan

Visual processing for shape recognition is achieved by the ventral visual stream,
where neurons show preference to visual features such as edges, curvatures,
and T-junctions. The geometrical complexity of optimal stimulus features increases
gradually with the cortical level. In the inferotemporal (IT) cortex, a majority
of individual neurons respond optimally to fairly complex features. On a greater
spatial scale, optical imaging studies have indicated two interesting features
of IT population activity. First, a single object elicits multiple patches
of activity across the cortex, which appears to represent component features
of the object (Tsunoda et al. 2001). Second, patches of activity continuously
shift their position when an object is systematically transformed (Wang et
al. 1998).

In this study, we attempted to construct a theoretical model which explains
the above mentioned features of IT neural representation, parts-based coding
and topographic organization. In our model, we extended the non-negative matrix
factorization (NMF) method developed by Lee & Seung, (1999), a basis decomposition
method which represents input patterns by additive combinations of non-negative
basis functions. Our extension was to incorporate a neighborhood function as
follows. While the original NMF is formulated as V~=WH where V, W, and H are
input, basis function, and coefficient matrices respectively, the extended
model is formulated as V~=WMH where the matrix M represents neighborhood relations
among basis functions, such as Gaussian function. Hereafter we refer to our
model as the topographic non-negative matrix factorization (TNMF) model.

To investigate the properties of TNMF, we incorporated a hierarchical model
which mimicked the early levels of the ventral pathway extracting visual features
with increasing specificity and invariance based on alternating feature detection
and integration processes (Wersing & K¨orner, 2003). After training the
hierarchical model using real objects, the representation of the final layer
was used as inputs to the TNMF model. Simulation results showed that the TNMF
model attained the two goal properties, topographic organization and parts-based
representation. We then compared responses of model neurons in various layers
and monkey IT neurons to 64 semi-complex objects. Similarity of stimulus preference
with actual IT neurons (pairwise activity correlation of 64 objects for the
IT neuron and the best-fit model neuron) is higher for the output of the TNMF
model than for the earlier layers of the model.

Support: MEXT grant of Japan 17022015

MEXT grant of Japan 1702205

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