MFD-SOM算法：颜色特征提取的创新应用

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"这篇研究论文探讨了改进的自组织映射（SOM）算法及其在颜色特征提取中的应用。文章作者包括Li-Ping Chen、Yi-Guang Liu、Zeng-Xi Huang和Yong-Tao Shi，发表于2013年。该研究主要关注在图像分析和压缩等应用中如何减少主导颜色特征的冗余，同时保持提取颜色的多样性和质量。" 在图像处理领域，自组织映射（Self-Organization Map, SOM）是一种常用的数据降维和可视化方法，尤其适用于高维数据的聚类和特征提取。传统的SOM算法基于“胜者为王”（Winner-Takes-All）的竞争原则，即在训练过程中，最接近输入数据的神经元会更新其权重，而其他神经元则不作更新或更新较少。这种策略可能导致非主成分特征在学习过程中被削弱或丢失，从而影响特征的多样性。论文提出了一种改进的SOM算法，称为MFD-SOM（可能是Multi-Factor Dimensionality SOM的缩写，但原文未提供全称）。MFD-SOM旨在通过一定程度上防止非主成分特征在训练过程中的损失，来保持所提取特征的多样性。这可能通过调整竞争机制或采用更复杂的权值更新策略实现，以确保非主导特征在映射中得到适当的表示。此外，MFD-SOM采用了新的方式更新神经元的权值向量，这有助于减少从主要特征中提取的特征的冗余。这可能涉及到更精细的权重调整策略，如考虑多个因素或多尺度的信息，以更有效地捕获数据的复杂性。通过这种方式，MFD-SOM不仅减少了特征的冗余，还可能提高了特征提取的效率和准确性。颜色特征在图像分析和压缩中扮演着关键角色。有效的颜色特征提取可以提高识别、分类和压缩的效果。MFD-SOM在颜色特征提取中的应用可能涉及从图像中选择最具代表性的颜色，或者创建一个紧凑的颜色码书，用于表示和压缩图像数据。这篇研究论文提出了MFD-SOM这一创新算法，以解决传统SOM算法在颜色特征提取时存在的问题，并通过实例应用证明了其在保留特征多样性及降低冗余方面的优势，这对于图像处理领域的理论研究和实际应用具有重要意义。

signiﬁcantly. However, such approach not only reduces

the effectiveness of features due to achieving many more

redundant features, but also further deteriorates the per-

formance of conventional SOM algorithm because more

iterations are required.

2.2 Dynamic neighborhood radius and learning rate

Within the t-th training epoch in the conventional SOM,

both values of a(t) and r(t) are ﬁxed for different winners

in competition, namely all winners are treated equally

within a training epoch. While in our algorithm, the

learning rate and neighborhood size for a winner of com-

petition are dynamic, which can be calculated by

tðÞ¼a tðÞ1 e exp K

c;j



ð6Þ

and

tðÞ¼r tðÞ1  e exp K

c;j



; ð7Þ

where a(t) and r(t) can be calculated by Eqs. (4) and (5),

respectively, e ðe 2½0; 1Þ and K

are user-deﬁned constant

values used to tune the learning rate and neighborhood

radius for a winner. d

c,j

is the distance between x

and w

which can be represented as

c;j

 x



: ð8Þ

It can be seen from Eqs. (6) and (7) that the learning

rates [a

(t)] and neighborhood radiuses [r

(t)] for winners

of competition are dynamic within each training epoch,

which partly depends on the value of d

c,j

.Ifd

c,j

? 0,

then r

(t) & r(t)(1 - e) and a

(t) & a(t)(1 - e), a

weakened learning for the input x

occurs. On the

contrary, if d

? 1 and K

is a big constant, then

(t) & r(t) and a

(t) & a(t), a learning for x

will be

normal. Compared with the weakened learning, within a

training epoch, if a normal learning occurs, the winner of

competition can be given a larger neighborhood radius

and a greater learning rate.

Being of greater ratios in the training data, features of

the principal components in the training data will be ahead

of non-principal components to be trained well. Thus, the

normal learning is mainly triggered by non-principal

components in the training data. Compared with the con-

ventional SOM, features of non-principal components are

given more chance to compete, and thereby better repre-

sentations of their features can be achieved by the proposed

algorithm. What is more, with the decrease of training

error, the number of neurons needed to update will also

decrease, which is beneﬁt to improve the performance of

the proposed algorithm.

Figure 1 demonstrates the different competitive behav-

iors of both algorithms. In Fig. 1a, coordinates (x

)of

the eleven red points are used to train both networks.

Figure 1b presents a possible distribution of points (x

)

trained by the conventional SOM. It can be seen that there

exists a large distance between the sixth sample point

(marked with a red circle in Fig. 1b) and the closest trained

point (the sixth blue point in Fig. 1b). As to our algorithm,

when it learns the position vector of the sixth sample point

(red circle in Fig. 1b), due to the large training error, the

learning will be normal. Thus, a possible intermediate

result trained by our algorithm is demonstrated in Fig. 1c.

When the training ﬁnishes, a possible distribution of points

can be demonstrated by Fig. 1d. From Fig. 1d, it can be

seen that the maximum distance or training error is greatly

less than that achieved by the conventional SOM.

2.3 New way to update weight vectors of neurons

To reduce redundancy of features extracted from the

principal components and to avoid the problem of over-

ﬁtting, we present a new way to update weight vectors of

neurons.

As shown in Fig. 2a, in the traditional way, not only the

winner (marked with red ball) but also its neighbors

(marked with blue balls) will be directly affected by the

training vector (marked with purple triangle). As to the

new way, as illustrated in Fig. 2b, each neighbor of a

winner will only be directly affected by the neuron closest

to both the winner and itself (not including itself) in the

lattice.

The weight vector (w

) of the current winner c can be

directly updated by

t þ 1ðÞ¼w

tðÞþa

tðÞx

 w

tðÞ



: ð9Þ

For each neighbor of the winner c, its learning rate

(t)] is determined by

tðÞ¼a tðÞ1  e exp K

i;t



; ð10Þ

where d

i,t

is the Euclidean distance between both weight

vectors of the neighbor and the training data.

Then, new weight vector for each neighbor of the win-

ner can be represented as

t þ 1ðÞ¼w

tðÞþa

tðÞw

tðÞw

tðÞðÞ; ð11Þ

where w

(t) is the weight vector of the training data, and it

should be updated before its output. By tuning the learning

rate a

(t), the distance between weight vectors of the

training data and its output will be neither too close nor too

far. Thus, features extracted from the principal components

in the training data by our algorithm will be of lower

redundancy.

Neural Comput & Applic (2014) 24:1759–1770 1761

123

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