Пример #1
0
def simplified_algo(R, iterations, warp=0):
    S = best_embedding_on_sphere(R, ndim=3)
    R_order = scale_score(R).astype('int16')
    for i in range(iterations):  # @UnusedVariable
        C = np.dot(S.T, S)
        C_sorted = np.sort(C.flat)
        R = C_sorted[R_order]
        S = best_embedding_on_sphere(R, ndim=3)

    if warp > 0:
        base_D = distances_from_directions(S)
        diameter = base_D.max()
        min_ratio = 0.1
        max_ratio = np.pi / diameter
        ratios = np.exp(np.linspace(np.log(min_ratio),
                                    np.log(max_ratio), warp))
        scores = []
        guesses = []
        for ratio in ratios:
            Cwarp = cosines_from_distances(base_D * ratio)
            Sw = best_embedding_on_sphere(Cwarp, ndim=3)
            Cw_order = scale_score(cosines_from_directions(Sw))
            scores.append(correlation_coefficient(Cw_order, R_order))
            guesses.append(Sw)
        best = np.argmax(scores)
        print('Best warp: %d (%f)' % (best, ratios[best]))
        S = guesses[best]
    return S
Пример #2
0
def simplified_algo(R, iterations, warp=0):
    S = best_embedding_on_sphere(R, ndim=3)
    R_order = scale_score(R).astype('int16')
    for i in range(iterations):  # @UnusedVariable
        C = np.dot(S.T, S)
        C_sorted = np.sort(C.flat)
        R = C_sorted[R_order]
        S = best_embedding_on_sphere(R, ndim=3)

    if warp > 0:
        base_D = distances_from_directions(S)
        diameter = base_D.max()
        min_ratio = 0.1
        max_ratio = np.pi / diameter
        ratios = np.exp(np.linspace(np.log(min_ratio), np.log(max_ratio),
                                    warp))
        scores = []
        guesses = []
        for ratio in ratios:
            Cwarp = cosines_from_distances(base_D * ratio)
            Sw = best_embedding_on_sphere(Cwarp, ndim=3)
            Cw_order = scale_score(cosines_from_directions(Sw))
            scores.append(correlation_coefficient(Cw_order, R_order))
            guesses.append(Sw)
        best = np.argmax(scores)
        print('Best warp: %d (%f)' % (best, ratios[best]))
        S = guesses[best]
    return S
Пример #3
0
    def seq():
        N = 180
        iterations = 10
        nradii = 100
        radii = np.linspace(5, 180, nradii)

        K = 1
        for radius_deg, i in itertools.product(radii, range(K)):
            print radius_deg, i
            # Generate a random symmetric matrix
            # x = np.random.rand(N, N)
            S = random_directions_bounded(3, np.radians(radius_deg), N)
            C = np.dot(S.T, S)
            alpha = 1
            f = lambda x: np.exp(-alpha * (1 - x))
            # f = lambda x : x
            R = f(C)
            # Normalize in [0,1]
            R1 = (R - R.min()) / (R.max() - R.min())
            # Normalize in [-1,1]
            R2 = (R1 - 0.5) * 2

            S1 = simplified_algo(R1, iterations)
            S1w = simplified_algo(R1, iterations, warp=50)
            S2 = simplified_algo(R2, iterations)

            s1 = spearman(cosines_from_directions(S1), R1)
            s1w = spearman(cosines_from_directions(S1w), R1)
            s2 = spearman(cosines_from_directions(S2), R2)

            e1 = np.degrees(overlap_error_after_orthogonal_transform(S, S1))
            e1w = np.degrees(overlap_error_after_orthogonal_transform(S, S1w))
            e2 = np.degrees(overlap_error_after_orthogonal_transform(S, S2))
            r0 = np.degrees(distribution_radius(S))
            r1 = np.degrees(distribution_radius(S1))
            r1w = np.degrees(distribution_radius(S1w))
            r2 = np.degrees(distribution_radius(S2))
            yield dict(R0=r0,
                       R1=r1,
                       R1w=r1w,
                       R2=r2,
                       e1=e1,
                       e2=e2,
                       s1=s1,
                       s2=s2,
                       s1w=s1w,
                       e1w=e1w)
Пример #4
0
    def seq():
        N = 180
        iterations = 10
        nradii = 100
        radii = np.linspace(5, 180, nradii)

        K = 1
        for radius_deg, i in itertools.product(radii, range(K)):
            print radius_deg, i
            # Generate a random symmetric matrix
            # x = np.random.rand(N, N)
            S = random_directions_bounded(3, np.radians(radius_deg), N)
            C = np.dot(S.T, S)
            alpha = 1
            f = lambda x: np.exp(-alpha * (1 - x))
            # f = lambda x : x
            R = f(C)
            # Normalize in [0,1]
            R1 = (R - R.min()) / (R.max() - R.min())
            # Normalize in [-1,1]
            R2 = (R1 - 0.5) * 2

            S1 = simplified_algo(R1, iterations)
            S1w = simplified_algo(R1, iterations, warp=50)
            S2 = simplified_algo(R2, iterations)

            s1 = spearman(cosines_from_directions(S1), R1)
            s1w = spearman(cosines_from_directions(S1w), R1)
            s2 = spearman(cosines_from_directions(S2), R2)

            e1 = np.degrees(overlap_error_after_orthogonal_transform(S, S1))
            e1w = np.degrees(overlap_error_after_orthogonal_transform(S, S1w))
            e2 = np.degrees(overlap_error_after_orthogonal_transform(S, S2))
            r0 = np.degrees(distribution_radius(S))
            r1 = np.degrees(distribution_radius(S1))
            r1w = np.degrees(distribution_radius(S1w))
            r2 = np.degrees(distribution_radius(S2))
            yield dict(R0=r0, R1=r1, R1w=r1w, R2=r2, e1=e1, e2=e2,
                       s1=s1, s2=s2,
                       s1w=s1w, e1w=e1w)