In the advanced section of HCR, we concentrate on: 1. the bended ellipse features, 2. the comparison method used in classification and 3. the process of network training.

Bended ellipse features (J.13)

Remember what features do we extract from "characters" in Introduction? Yes, they are , where and means the l^th feature vector of the j^th radical. So the j^th radical is represented as . Similarly, the 1^st handprinted character is represented as where is the m^th feature vector of the handprinted character. For a set of input handprinted characters, each character in the set can be represented by (i means i^th handprinted character, and this set of input has total N of them) and is the n^th feature vector of the i^th character. Now we explain the idea of feature vector in detail.

For characters like "", each vertex (seed) has two connecting sides. For such a seed, it has 1 feature vector. For characters like "", the seed at the center intersection has four connecting sides; therefore it has 6 feature vectors (left&up, left&right, left&down, right&up, right&down, up&down). The way to calculate the number of feature vectors is where a is the number of sides connected to the seed. For each seed, we write all of its feature vectors in a concept feature to simplify further reference and calculation.

Compatibility (J.13)

In the matching process, we compare each handprinted character and standard character with each radical. For example, for the j^th radical R^j, we calculate its compatibility with handprinted character H and let this value be . When all the radicals are compared with the handprinted character, we get . And the compatibility of radicals to each standard characters can be writeen as where is the compatibility of the j^th radical and the i^th standard character. For the recognition task, we would like to minimize the value of and the "standard character" that achieves this minimum value is the classification result we want.

Next we will explain the inter-feature similarity and inter-link similarity mentioned in Introduction. Assume we want to compare the corresponding feature pairs and . When feature vectors l₁ and l₂ are connected and feature vectors m₁ and m₂ are connected (which satisfies inter-link similarity), then , otherwise set the value to be -µ. (We set -µ=10). We define D₁ to be , which is the inter-feature similarity.

Train the network (J.13)

In our network, we write every converged state as a matrix V, each row of V represents the features of a radical and each column represents the features of a handprinted character. When V_lm=1, it means that the l^th feature of the radical and the m^th feature of the handprinted character have correspondence. We can add this pair to the route . To ensure the correctness of the route, V must comply to the following rules:

	Only one 1 in each row(feature-to-feature can not be 1 to many or many to 1)
	At most one 1 in each column
	When network converges, the sum of the compatibility of the route should be maximized

We can write the above restrictions as an function, we call that the energy function:

|These three terms satisfies rule 1 and 2                                 || This term satisfies rule 3                        |

Where A=500, B=500, C=500/N, D=500N/80 and N=L^jM.

The network state changes as the following equation:

where

For initial value of V_lm, if ( is the threshold), then we set V_lm=1.

Our network uses backpropogation (because simple classification is not enough for Chinese characters), and the network structure is as follows:

We use the (where 1<=i<=N, N is the number of standard characters) from above to train the network. Which means if we input then the first neuron of the output layer would be on state, and others be off state. When the network converges, we can use it as the handprinted character classifier.