Sentence examples for both algorithms we used from inspiring English sources

To evaluate the performance of both algorithms, we used a known set of CFP instances.

For both algorithms, we used a parameter scrambling procedure to give the problem different starting conditions; the pLSA algorithm reads in initial parameter values, which were randomised prior to starting each instance of the program, while the piES algorithm generates its starting conditions according to a random seed, which is itself randomised for each optimisation run.

Because musical scale tones are not always defined by a single frequency ratio (e.g., the ratios of 7∶5 or 10∶7 can both represent a tritone), the algorithm we used allowed tones within a specific frequency distance to represent the same scale tone.

To test this algorithm, we used both simulated and real datasets.

Regardless of which algorithm we used, our results remained unchanged.

For both algorithms, we observe significantly better performance using the FSP over the MSP (p < 0.001).

In these figures, (i) and (ii) are the performance of the algorithm when we use both algorithms together; (iii) and (iv) are when we simply use the k-means algorithm or the k-center algorithm independently.

Algorithms that we use every day, such as Google Instant's predictive search, provide ample illustrations.

Both algorithms were used with default parameters.

In both cases, we use Algorithm 2a with the same equilibrium bifunction, the quadratic regularization function G ( x ) : = ln ( 1 + 2 x ) and parameters θ = 0.7, ρ = 2, α = 0.45.

To compare the performance on equal basis, we allow both algorithms to use the same energy function defined in (6).