In this study, five cultivars (Ceres, Zorro, Falcon, Express, and Samourai) of winter rapeseed were classified by using the common vector approach (CVA). For this purpose, seven yield characters (plant height, number of branches per plant, number of pods per plant, number of pods on main stem, number of seeds per pod, pod length and thousand seed weight) of each cultivar were used. The seven and six yield characters taken from five cultivars were classified by using CVA. 100% classification rate is guaranteed for the training set of both studies. For the test set, the classification of five cultivars has low performance, but the classification of seven and six yield characters gave satisfactory results. It is concluded that the CVA method was successful in the classification of different varieties belonging to any plant and/or of different characters belonging to any variety.
1 Introduction
Rapeseed is an important oilseed crop in the agricultural systems of many arid and
semiarid areas. Agronomic and quality advantages of new varieties have enlarged
their production areas worldwide (Gül et al. 2007). Rapeseed in Turkey is mostly
cultivated as a winter annual for oil production and rarely livestock feed. If planted in
spring, they can be grown as summer crop but the seed yield would be decreased due
to short growing season and lack of enough water at the end of growing season, thus,
winter cropping is preferred. The canola cultivars are slow growing especially in
winter and most of them will complete their life cycle in 210 to 270 days
Computer-based algorithms have been extensively used in agriculture in order to
classify various plants and their characters or samples. Classification of plant
varieties with computer algorithms has been become popular in recent years. The
common vectors representing the invariant features of the plants can be extracted by
eliminating the differences in each class of plants (Gülmezoglu 1999). Then these
common vectors are used for the classification of varieties and characters of plants.
Different methods were used in order to derive features or parameters from plant
varieties
In this study, we considered five cultivars (Ceres, Zorro, Falcon, Express, and Samourai) of winter rapeseed. Initially, these cultivars were classified by using the common vector approach (CVA). Secondly, seven yield characters (plant height, number of branches per plant, number of pods per plant, number of pods on main stem, number of seeds per pod, pod length and thousand seed weight) and six yield characters excepting number of branches per plant were classified by using CVA. 2
This research was carried out over three years during 2005 at the Faculty of Agriculture of Eskisehir Osmangazi University, Eskisehir (39o 48′ N; 30o 31′ E; 789 m in elevation). The field experiments included five winter rapeseed cultivars (Ceres, Zorro, Falcon, Express, Synergy and Samourai). The experiment was planned in a Randomized Complete Block Design with four replications. The individual plots were 3 m long and consisted of five rows. The cultivars were sown on the first week of September, using a seed rate of 10 kg ha -1 in 40 cm spaced lines on a well prepared seed bed. The experiment was fertilized respectively with 150 kg N ha -1 as ammonium nitrate: 33-0-0 and 50 kg P2O5 ha -1 as di-ammonium phosphate: 18-460. The plants were irrigated once during emergence and thinned at the rosette stage. The weeds were controlled by hand weeding.
Each cultivar was represented with seven yield characters which are plant height, number of branches per plant, number of pods per plant, number of pods on main stem, number of seeds per pod, pod length and thousand seed weight. Each character includes 20 plant samples which were taken from field study conducted during growing year.
As in all classification methods, CVA has training and testing stages. In the training stage, a common vector which represents common or invariant properties of each class is calculated and an in difference subspace for each class is constructed. Let the vectors a1c,ac2,...,acm Є Rn be the feature vectors for a variety-class C in the training set where m ≤ n. Then each of these feature vectors which are assumed to be linearly independent can be written as aic = aic,dif + accom +ε ic for i=1,2, …, m (1) c where the vector ai,dif indicates the differences resulting from climatic effects and c alien-pollination, and the vector acom is the common vector of the variety or c character class C, and ε i represents the error vector (Gülmezoğlu et al. 2001). The common vector can be obtained from the subspace method. Let us define the covariance matrix of the feature vectors belonging to a variety or character class as m i=1 Φ = ∑ (aic − aave )(aic − aave ) c c
T c where aave is the average feature vector of Cth class whose covariance matrix is to be calculated and T indicates the transpose of a matrix.
The eigenvalues of the covariance matrix Ф are non-negative and they can be written in decreasing order: λ1 ≥ λ2 ≥ K ≥ λn. Let u1c, uc2,..., ucn be the orthonormal eigenvectors corresponding to these eigenvalues. The first (m-1) eigenvectors of the covariance matrix corresponding to the nonzero eigenvalues form an orthonormal basis for the difference subspace B (Gülmezoğlu et al. 2001). The orthogonal complement, B┴, is spanned by all the eigenvectors corresponding to the zero eigenvalues. This subspace is called the indifference subspace and has a dimension of (n-m+1). The direct sum of two subspaces B and B┴ is the whole space, and the intersection of them is the null space. The common vector can be shown as the linear combination of the eigenvectors corresponding to the zero eigenvalues of Ф (Gülmezoğlu et al. 2001), that is,
accom = aic , ucm ucm +L + aic , ucn ucn ∀ i=1,2,…,m (3) From here, the common vector acom is the projection of any feature vector onto the indifference subspace B┴. The common vector represents the common properties or invariant features of the variety or character class C. The common vector is independent from index i. Therefore, the common vector is unique for each class and c all the error vectors ε i would be zero.
During the classification stage, the following decision criterion is used: 2 dis tan ce = argmin 1≤C≤S n
⎧⎪⎡ c ⎤ c ⎪⎫ ∑ ⎨⎢(ax - aic )T u j ⎥ u j ⎬ j=m ⎩⎪⎣ ⎦ ⎭⎪ (2) (4) where ax is an unknown or test vector and S indicates the total number of classes. If the distance is minimum for any class C, the feature vector ax is assigned to class C.
Classification algorithm given above can be summarized as follows: Step 1: Construct feature vectors by using samples taken for each character belonging to any cultivar. Be sure that number of samples in each feature vector (or dimension of each feature vector) is greater than number of feature vectors (or characters) for each cultivar.
Step 2: Find the covariance matrix (Eq. (2)) for each cultivar by using feature vectors belonging to that cultivar.
Step 3: Find the eigenvalues λi and corresponding eigenvectors ui for each covariance matrix.
Step 4: Find the common vector (Eq. (3)) for each cultivar by using the (n-m+1) eigenvectors corresponding to zero eigenvalues.
Step 5: When an unknown feature vector ax is given, classify this vector by using Eq. (4). 3
In the first study, each of five cultivars forms one class in the CVA method. Seven characters each of which includes 20 samples for each cultivar or class form seven feature vectors of that class. Therefore, there are five classes and each class has seven feature vectors. When the feature vectors (characters) used in the training stage were tested, all classes (cultivars) were correctly classified, i.e., 100% correct recognition rate was obtained. When the “leave-one-out” strategy was used in the testing stage, that is, when six feature characters were used in the training stage and remaining one character was tested, 25.7% correct recognition rate was obtained as average of “leave-one-out” steps. The results obtained from this study are given in Table 1. The average score obtained in the test set is very low because samples included in the characters representing different cultivars are very close to each other.
In the second study, the characters were classified by using CVA. First of all, seven characters were considered and each of seven characters forms one class in the CVA method. Twenty samples taken from each cultivar for any character form one feature vector of that character. Therefore, there are seven classes and each class has five feature vectors. When the feature vectors, each of them includes 20 samples, used in the training stage were tested, all classes (characters) were correctly classified, i.e., 100% correct recognition rate was obtained. When the “leave-oneout” strategy was used in the testing stage, that is, when six feature characters were used in the training stage and remaining one character was tested, 77.1% correct recognition rate was obtained as average of “leave-one-out” steps. The results obtained for this study are given in Table 2. Varieties Samourai Zorro Falcon Ceres Express Average Yield Characters Plant Height Number of Branches per Plant Number of Pods per Plant Number of Pods on Main Stem Number of Seeds per Pod Pod Length Thousand Seed Weight Average
Secondly, six characters excepting number of branches per plant were classified. All characters were correctly classified (100% correct recognition rate was obtained) in the training set and 90% recognition rate was obtained for the test set. These scores are remarkable because samples taken from cultivars for each character are close to each other and well represent that character. These results are given in Table 3.
It is known that varieties of different plants have been successfully classified by
using various computer-based algorithms. Especially, classification of wheat
varieties with computer algorithms has been become popular in recent years (Zayas
et al. 1996, Utku and Köksel 1998, Neuman and Bushuk 198
Additionally, characters were classified by using CVA method. Initially, seven characters are applied to the classification process and 100% and 77.1% recognition rates were obtained for the training and test sets respectively. The reason of low score for the test set is that the samples belonging to number of branches per plant character are similar to samples belonging to other characters. When the number of branches per plant character is discarded, that is, when the remaining six characters are classified, 90% recognition rate is obtained for the test set.
It is concluded that the CVA method was very successful in the classification of different varieties belonging to any plant and/or of different characters belonging to any variety. Such classifications can be very helpful in assignment of unknown varieties or unknown characters to identify plant. When more specific characters are extracted for each variety of plants, good performance can be achieved from the classification process.
As a future work, number of varieties for any plant and the number of characters will be increased. Satisfactory results are also expected from this work.