Status.hpp

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/*
 *
 * Copyright (c) 2014, Laurens van der Maaten (Delft University of Technology)
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    This product includes software developed by the Delft University of Technology.
 * 4. Neither the name of the Delft University of Technology nor the names of
 *    its contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY LAURENS VAN DER MAATEN ''AS IS'' AND ANY EXPRESS
 * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
 * EVENT SHALL LAURENS VAN DER MAATEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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 */
 
#ifndef QDTSNE_STATUS_HPP
#define QDTSNE_STATUS_HPP
 
#include <vector>
#include <array>
#include <algorithm>
#include <cstddef>
 
#include "sanisizer/sanisizer.hpp"
 
#include "SPTree.hpp"
#include "Options.hpp"
#include "utils.hpp"
 
namespace qdtsne {
 
template<std::size_t num_dim_, typename Index_, typename Float_> 
class Status {
public:
    Status(NeighborList<Index_, Float_> neighbors, Options options) :
        my_neighbors(std::move(neighbors)),
        my_tree(sanisizer::cast<internal::SPTreeIndex>(my_neighbors.size()), options.max_depth),
        my_options(std::move(options))
    {
        const auto nobs = sanisizer::cast<Index_>(my_neighbors.size()); // use Index_ to check safety of cast in num_observations().
        const std::size_t buffer_size = sanisizer::product<std::size_t>(nobs, num_dim_);
 
        sanisizer::resize(my_dY, buffer_size);
        sanisizer::resize(my_uY, buffer_size);
        sanisizer::resize(my_gains, buffer_size, static_cast<Float_>(1));
        sanisizer::resize(my_pos_f, buffer_size);
        sanisizer::resize(my_neg_f, buffer_size);
 
        if (options.num_threads > 1) {
            sanisizer::resize(my_parallel_buffer, nobs);
        }
    }
private:
    NeighborList<Index_, Float_> my_neighbors; 
    std::vector<Float_> my_dY, my_uY, my_gains, my_pos_f, my_neg_f;
    Float_ my_non_edge_sum = 0;
 
    internal::SPTree<num_dim_, Float_> my_tree;
    std::vector<Float_> my_parallel_buffer; // Buffer to hold parallel-computed results prior to reduction.
 
    Options my_options;
    int my_iter = 0;
 
    typename decltype(I(my_tree))::LeafApproxWorkspace my_leaf_workspace;
 
public:
    int iteration() const {
        return my_iter;
    }
 
    int max_iterations() const {
        return my_options.max_iterations;
    }
 
    Index_ num_observations() const {
        return my_neighbors.size(); // safety of the cast to Index_ is already checked in the constructor.
    }
 
#ifndef NDEBUG
    const auto& get_neighbors() const {
        return my_neighbors;
    }
#endif
 
public:
    void run(Float_* const Y, const int limit) {
        Float_ multiplier = (my_iter < my_options.early_exaggeration_iterations ? my_options.exaggeration_factor : 1);
        Float_ momentum = (my_iter < my_options.momentum_switch_iterations ? my_options.start_momentum : my_options.final_momentum);
 
        for(; my_iter < limit; ++my_iter) {
            if (my_iter == my_options.early_exaggeration_iterations) {
                multiplier = 1;
            }
            if (my_iter == my_options.momentum_switch_iterations) {
                momentum = my_options.final_momentum;
            }
            iterate(Y, multiplier, momentum);
        }
    }
 
    void run(Float_* const Y) {
        run(Y, my_options.max_iterations);
    }
 
private:
    static Float_ sign(const Float_ x) { 
        constexpr Float_ zero = 0;
        constexpr Float_ one = 1;
        return (x == zero ? zero : (x < zero ? -one : one));
    }
 
    void iterate(Float_* const Y, const Float_ multiplier, const Float_ momentum) {
        compute_gradient(Y, multiplier);
 
        // Update gains
        const auto buffer_size = my_gains.size(); 
        for (decltype(I(buffer_size)) i = 0; i < buffer_size; ++i) {
            Float_& g = my_gains[i];
            constexpr Float_ lower_bound = 0.01;
            constexpr Float_ to_add = 0.2;
            constexpr Float_ to_mult = 0.8;
            g = std::max(lower_bound, sign(my_dY[i]) != sign(my_uY[i]) ? (g + to_add) : (g * to_mult));
        }
 
        // Perform gradient update (with momentum and gains)
        for (decltype(I(buffer_size)) i = 0; i < buffer_size; ++i) {
            my_uY[i] = momentum * my_uY[i] - my_options.eta * my_gains[i] * my_dY[i];
            Y[i] += my_uY[i];
        }
 
        // Make solution zero-mean for each dimension
        std::array<Float_, num_dim_> means{};
        const Index_ num_obs = num_observations();
        for (Index_ i = 0; i < num_obs; ++i) {
            for (std::size_t d = 0; d < num_dim_; ++d) {
                means[d] += Y[sanisizer::nd_offset<std::size_t>(d, num_dim_, i)];
            }
        }
        for (std::size_t d = 0; d < num_dim_; ++d) {
            means[d] /= num_obs;
        }
        for (Index_ i = 0; i < num_obs; ++i) {
            for (std::size_t d = 0; d < num_dim_; ++d) {
                Y[sanisizer::nd_offset<std::size_t>(d, num_dim_, i)] -= means[d];
            }
        }
 
        return;
    }
 
private:
    void compute_gradient(const Float_* const Y, const Float_ multiplier) {
        my_tree.set(Y);
        compute_edge_forces(Y, multiplier);
 
        std::fill(my_neg_f.begin(), my_neg_f.end(), 0);
        compute_non_edge_forces();
 
        const auto buffer_size = my_dY.size();
        for (decltype(I(buffer_size)) i = 0; i < buffer_size; ++i) {
            my_dY[i] = my_pos_f[i] - (my_neg_f[i] / my_non_edge_sum);
        }
    }
 
    void compute_edge_forces(const Float_* const Y, Float_ multiplier) {
        std::fill(my_pos_f.begin(), my_pos_f.end(), 0);
        const Index_ num_obs = num_observations();
 
        parallelize(my_options.num_threads, num_obs, [&](const int, const Index_ start, const Index_ length) -> void {
            for (Index_ i = start, end = start + length; i < end; ++i) {
                const auto& current = my_neighbors[i];
                const auto offset = sanisizer::product_unsafe<std::size_t>(i, num_dim_);
                const auto self = Y + offset;
                const auto pos_out = my_pos_f.data() + offset;
 
                for (const auto& x : current) {
                    Float_ sqdist = 0; 
                    const auto neighbor = Y + sanisizer::product_unsafe<std::size_t>(x.first, num_dim_);
                    for (std::size_t d = 0; d < num_dim_; ++d) {
                        const Float_ delta = self[d] - neighbor[d];
                        sqdist += delta * delta;
                    }
 
                    const Float_ mult = multiplier * x.second / (static_cast<Float_>(1) + sqdist);
                    for (std::size_t d = 0; d < num_dim_; ++d) {
                        pos_out[d] += mult * (self[d] - neighbor[d]);
                    }
                }
            }
        });
 
        return;
    }
 
    void compute_non_edge_forces() {
        if (my_options.leaf_approximation) {
            my_tree.compute_non_edge_forces_for_leaves(my_options.theta, my_leaf_workspace, my_options.num_threads);
        }
 
        const Index_ num_obs = num_observations();
        if (my_options.num_threads > 1) {
            // Don't use reduction methods, otherwise we get numeric imprecision
            // issues (and stochastic results) based on the order of summation.
            parallelize(my_options.num_threads, num_obs, [&](const int, const Index_ start, const Index_ length) -> void {
                for (Index_ i = start, end = start + length; i < end; ++i) {
                    const auto neg_ptr = my_neg_f.data() + sanisizer::product_unsafe<std::size_t>(i, num_dim_);
                    if (my_options.leaf_approximation) {
                        my_parallel_buffer[i] = my_tree.compute_non_edge_forces_from_leaves(i, neg_ptr, my_leaf_workspace);
                    } else {
                        my_parallel_buffer[i] = my_tree.compute_non_edge_forces(i, my_options.theta, neg_ptr);
                    }
                }
            });
 
            my_non_edge_sum = std::accumulate(my_parallel_buffer.begin(), my_parallel_buffer.end(), static_cast<Float_>(0));
            return;
        }
 
        my_non_edge_sum = 0;
        for (Index_ i = 0; i < num_obs; ++i) {
            const auto neg_ptr = my_neg_f.data() + sanisizer::product_unsafe<std::size_t>(i, num_dim_);
            if (my_options.leaf_approximation) {
                my_non_edge_sum += my_tree.compute_non_edge_forces_from_leaves(i, neg_ptr, my_leaf_workspace);
            } else {
                my_non_edge_sum += my_tree.compute_non_edge_forces(i, my_options.theta, neg_ptr);
            }
        }
    }
 
public:
    Float_ cost(const Float_* const Y) {
        my_tree.set(Y);
        std::fill(my_neg_f.begin(), my_neg_f.end(), 0);
        compute_non_edge_forces();
 
        const Index_ num_obs = num_observations();
        Float_ total = 0;
        for (Index_ i = 0; i < num_obs; ++i) {
            const auto& cur_neighbors = my_neighbors[i];
            const auto self = Y + sanisizer::product_unsafe<std::size_t>(i, num_dim_);
 
            for (const auto& x : cur_neighbors) {
                const auto neighbor = Y + sanisizer::product_unsafe<std::size_t>(x.first, num_dim_);
                Float_ sqdist = 0;
                for (std::size_t d = 0; d < num_dim_; ++d) {
                    const Float_ delta = self[d] - neighbor[d];
                    sqdist += delta * delta;
                }
 
                const Float_ qprob = (static_cast<Float_>(1) / (static_cast<Float_>(1) + sqdist)) / my_non_edge_sum;
                constexpr Float_ lim = std::numeric_limits<Float_>::min();
                total += x.second * std::log(std::max(lim, x.second) / std::max(lim, qprob));
            }
        }
 
        return total;
    }
};
 
}
 
#endif