平成22年度電気関係学会四国支部連合大会

31318-14

Associative Memory
by Partitioned Hopfield Neural Network
Tomoya SHIMA

Chihiro IKUTA Yoko UWATE(Tokushima University)

Yoshifumi NISHIO

1. Introduction

3. Simulation Results

Memory ability of human is an interesting ability. For
example, human memorizes an image. After that, when human sees the partial image, human could recall the wholeimage. If this memory ability is applied in engineering,much information can be obtained from little information.
Hopfield Neural Network (HNN) is one of the computation
models which simulate memory ability of human [1], and isused for associative memory.
In this study, we propose Partitioned HNN (PHNN) andapply PHNN to image processing (64×64 size image). The
conventional HNN recalls a similar pattern to the input image from some memorized patterns. In our method, PHNN
is disposed on every cell (each cell has 4×4 neurons) on theimage space and recalls a similar pattern to the local input
image only on the cell. Thereby, we can recall the whole
image which has partially same patterns.

We compare PHNN with the conventional HNN. For
HNN, we do not consider the cells, namely every pixel areconnected each other. Two binary images shown in Figs.
2(a) and (b) are memorized into the networks. Figure 2(c)is an input image. The part of slash in Fig. 2(c) has thesame pattern as Fig. 2(a). The part of circle in Fig. 2(c)has similar pattern to Fig. 2(b).

2. Method of Associative Memory
We consider the PHNN composed of 4×4 neurons in one
cell. PHNN is shown in Fig. 1. The memorizing method ofpatterns in a cell is given bynwij =1PPP(p) (p)p=1xi xj

(i 6= j)(i = j),0(1)where P is the number of patterns, x is the input, and w is
the weight parameter. The updating rule and the internal
state of the neuron are given byxi (t + 1) =n 1,ui (t) =−1,nX(ui (t) ≥ 0)
(ui (t) < 0),wij (t)xj (t),(a)

(b)

(c)

Figure 2: (a) Stored image (slash). (b) Stored image (circle).
(c) Input image.

Figure 3(a) is recalled by HNN. Figure 3(b) is recalledby PHNN, which has more cells of the same patterns asFig. 2(a) than Fig. 2(b). Hence, PHNN outputs the slash
image as shown in Fig. 3(c).
From these results, PHNN recalls the whole image frompartially same image.

(2)
(3)

j=1

where u is the internal state of the neuron. We apply thisupdate to all neurons in a cell. PHNN recalls one of thememorized patterns in a cell by repeating this update. We
compare the recalled images with the memorized images forevery cell and count the number of the cells which havethe exactly same patterns. PHNN outputs the whole image
which has more cells of the same patterns from the twomemorized images.

input or output
cellneuron unit(a)(b)(c)Figure 3: (a) Recalled image of HNN. (b) Recalled partial imageof PHNN. (c) Recalled whole image of PHNN.

4. Conclusions
In this study, we have proposed PHNN and applied
PHNN to image processing. In our method, PHNN wasdisposed on every cell and recalled a similar pattern to thelocal input image only on the cell. Computer simulation results showed that PHNN output the image which had moresame patterns.

References[1] J. J. Hopfield, “Neural Networks and Physical Systems
with Emergent Collective Computational Abilities,” Proc.
Natl. Acad. Sci. USA, vol.79, pp. 2554-2558, 1982.

image
PHNN in cell

Figure 1: Composition of PHNN.